Edit Profile (opens in new tab) Mischaikow, Konstantin Compute Distance To: Compute Author ID: mischaikow.konstantin Published as: Mischaikow, Konstantin; Mischaikow, K.; Mischaikov, Konstantin; Mischiakow, Konstantin more...less Documents Indexed: 127 Publications since 1987, including 1 Book 5 Contributions as Editor Co-Authors: 98 Co-Authors with 118 Joint Publications 1,773 Co-Co-Authors all top 5 Co-Authors 14 single-authored 16 Gedeon, Tomáš 16 Kokubu, Hiroshi 15 Mrozek, Marian 11 Kalies, William D. 11 Oka, Hiroe 10 Harker, Shaun 9 Hutson, Vivian 8 Gameiro, Marcio F. 7 Pilarczyk, Paweł 6 Day, Sarah L. 6 Hattori, Harumi 5 Kramár, Miroslav 5 Lessard, Jean-Philippe 5 Nanda, Vidit 5 Reineck, James F. 5 Wanner, Thomas 4 Arai, Zin 4 Cummins, Bree 4 McCord, Christopher K. 4 Vandervorst, Robertus C. A. M. 4 Vickers, Glenn T. 4 Yi, Yingfei 3 Lou, Yuan 3 Schatz, Michael F. 2 Boczko, Erik M. 2 Bush, Justin 2 Carbinatto, Maria C. 2 Flores, Gilberto 2 Franzosa, Robert D. 2 Goullet, Arnaud 2 Hiraoka, Yasuaki 2 Junge, Oliver 2 Kaczynski, Tomasz 2 Kepley, Shane 2 Kondic, Lou 2 Kurtuldu, Huseyin 2 Levanger, Rachel 2 Maier-Paape, Stanislaus 2 Mireles-James, Jason D. 2 Poláčik, Peter 2 van den Berg, Jan Bouwe 2 Weibel, Charles A. 2 Wolkowicz, Gail S. K. 2 Zgliczyński, Piotr 2 Zhang, Lun 1 Alsing, Paul M. 1 Bambusi, Dario 1 Batko, Bogdan 1 Blair, Howard A. 1 Corne, Matthew 1 Cowan, Wes 1 Cyranka, Jacek 1 Dockery, Jack D. 1 Duncan, William 1 Ferry, Steven C. 1 Fiedler, Bernold 1 Grinfeld, Michael 1 Huttinga, Zane 1 Izumi, Shunsuke 1 Jaquette, Jonathan 1 Jones, Gordon 1 Kasti, Dinesh 1 Kovalcinova, Lenka 1 Krishan, Kapilanjan 1 Kuksin, Sergeĭ B. 1 Kwapisz, Jaroslaw 1 López-Gómez, Julián 1 Luzzatto, Stefano 1 Madruga, Santiago 1 Martínez, Salomé 1 Miller, Ulrich 1 Miller, Warner Allen 1 Minzoni, Antonmaria Alessio 1 Miyaji, Tomoyuki 1 Mok, Kafung 1 Moll, Victor Hugo 1 Morita, Yoshihisa 1 Nishiura, Yasumasa 1 Obayashi, Ippei 1 Ogawa, Toshiyuki 1 Oka, Hireo 1 Patterson, Kate 1 Paul, Mark R. 1 Pelinovsky, Dmitry Efimovich 1 Pernarowski, Mark 1 Przybylski, Mateusz 1 Smith, Hal Leslie 1 Spendlove, Kelly 1 Suri, Balachandra 1 Szymczak, Andrzej 1 Takaishi, Takeshi 1 Tanaka, Kazunaga 1 Thieme, Horst R. 1 Tithof, Jeffrey 1 Traldi, Eliane 1 Watson, Greg I. 1 Weilandt, Frank 1 Xu, Mu all top 5 Serials 15 Journal of Differential Equations 11 SIAM Journal on Applied Dynamical Systems 8 Journal of Dynamics and Differential Equations 5 Journal of Mathematical Biology 5 SIAM Journal on Mathematical Analysis 5 Foundations of Computational Mathematics 4 Physica D 4 Japan Journal of Industrial and Applied Mathematics 3 Transactions of the American Mathematical Society 3 Journal of Computational Dynamics 3 Nonlinear Analysis. Theory, Methods & Applications 3 Journal of Applied and Computational Topology 2 Nonlinearity 2 Mathematics of Computation 2 Proceedings of the American Mathematical Society 2 The Annals of Applied Probability 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 Chaos 2 Homology, Homotopy and Applications 1 Archive for Rational Mechanics and Analysis 1 Journal of Fluid Mechanics 1 Rocky Mountain Journal of Mathematics 1 Bulletin of Mathematical Biology 1 Mathematics and Computers in Simulation 1 Michigan Mathematical Journal 1 SIAM Journal on Numerical Analysis 1 Topology and its Applications 1 Ergodic Theory and Dynamical Systems 1 Applied Numerical Mathematics 1 Discrete & Computational Geometry 1 Journal of the American Mathematical Society 1 Differential and Integral Equations 1 Dynamic Systems and Applications 1 Bulletin of the American Mathematical Society. New Series 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Topological Methods in Nonlinear Analysis 1 Physics of Fluids 1 Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica 1 Electronic Research Announcements of the American Mathematical Society 1 Discrete and Continuous Dynamical Systems 1 Resenhas do Instituto do Matemática e Estatística da Universidade de São Paulo 1 Revista Matemática Complutense 1 Discrete and Continuous Dynamical Systems. Series B 1 Acta Numerica 1 Applied Mathematical Sciences 1 Banach Center Publications 1 RIMS Kôkyûroku Bessatsu 1 Axioms 1 SIAM Journal on Applied Algebra and Geometry all top 5 Fields 74 Dynamical systems and ergodic theory (37-XX) 37 Partial differential equations (35-XX) 34 Ordinary differential equations (34-XX) 24 Biology and other natural sciences (92-XX) 19 Algebraic topology (55-XX) 15 Numerical analysis (65-XX) 10 Fluid mechanics (76-XX) 7 General topology (54-XX) 6 Order, lattices, ordered algebraic structures (06-XX) 6 Computer science (68-XX) 5 General and overarching topics; collections (00-XX) 3 Manifolds and cell complexes (57-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Probability theory and stochastic processes (60-XX) 2 Integral equations (45-XX) 2 Operator theory (47-XX) 2 Statistics (62-XX) 2 Mechanics of particles and systems (70-XX) 1 Mathematical logic and foundations (03-XX) 1 Combinatorics (05-XX) 1 Algebraic geometry (14-XX) 1 Difference and functional equations (39-XX) 1 Functional analysis (46-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Convex and discrete geometry (52-XX) 1 Differential geometry (53-XX) 1 Mechanics of deformable solids (74-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 117 Publications have been cited 2,466 times in 1,430 Documents Cited by ▼ Year ▼ The evolution of dispersal. Zbl 1052.92042Hutson, V.; Martinez, S.; Mischaikow, K.; Vickers, G. T. 202 2003 The evolution of slow dispersal rates: a reaction diffusion model. Zbl 0921.92021Dockery, Jack; Hutson, Vivian; Mischaikow, Konstantin; Pernarowski, Mark 200 1998 Computational homology. Zbl 1039.55001Kaczynski, Tomasz; Mischaikow, Konstantin; Mrozek, Marian 108 2004 Asymptotically autonomous semiflows: Chain recurrence and Lyapunov functions. Zbl 0829.34037Mischaikow, Konstantin; Smith, Hal; Thieme, Horst R. 102 1995 Chaos in the Lorenz equations: A computer-assisted proof. Zbl 0820.58042Mischaikow, Konstantin; Mrozek, Marian 98 1995 The evolution of dispersal rates in a heterogeneous time-periodic environment. Zbl 0996.92035Hutson, V.; Mischaikow, K.; Poláčik, P. 95 2001 Validated continuation for equilibria of PDEs. Zbl 1151.65074Day, Sarah; Lessard, Jean-Philippe; Mischaikow, Konstantin 75 2007 Convergence in competition models with small diffusion coefficients. Zbl 1074.35054Hutson, V.; Lou, Y.; Mischaikow, K. 60 2005 Homoclinic orbits in a first order superquadratic Hamiltonian system: Convergence of subharmonic orbits. Zbl 0787.34041Tanaka, Kazunaga; Mischaikow, Konstantin 60 1991 Morse theory for filtrations and efficient computation of persistent homology. Zbl 1278.57030Mischaikow, Konstantin; Nanda, Vidit 60 2013 Conley index. Zbl 1035.37010Mischaikow, Konstantin; Mrozek, Marian 53 2002 A database schema for the analysis of global dynamics of multiparameter systems. Zbl 1186.37021Arai, Zin; Kalies, William; Kokubu, Hiroshi; Mischaikow, Konstantin; Oka, Hiroe; Pilarczyk, Paweł 51 2009 Rigorous numerics for symmetric connecting orbits: even homoclinics of the Gray-Scott equation. Zbl 1231.34081van den Berg, Jan Bouwe; Mireles-James, Jason D.; Lessard, Jean-Philippe; Mischaikow, Konstantin 44 2011 Spatial heterogeneity of resources versus Lotka-Volterra dynamics. Zbl 1023.35047Hutson, V.; Lou, Y.; Mischaikow, K. 43 2002 Rigorous numerics for partial differential equations: The Kuramoto-Sivashinsky equation. Zbl 0984.65101Zgliczyński, Piotr; Mischaikow, Konstantin 40 2001 An algorithmic approach to chain recurrence. Zbl 1099.37010Kalies, W. D.; Mischaikow, K.; VanderVorst, R. C. A. M. 39 2005 Global smooth solution curves using rigorous branch following. Zbl 1206.37045van den Berg, Jan Bouwe; Lessard, Jean-Philippe; Mischaikow, Konstantin 39 2010 Competing species near a degenerate limit. Zbl 1043.35080Hutson, V.; Lou, Y.; Mischaikow, K.; Polácik, P. 39 2003 Isolating neighborhoods and chaos. Zbl 0840.58033Mischaikow, Konstantin; Mrozek, Marian 35 1995 Chaos in the Lorenz equations: A computer assisted proof. II: Details. Zbl 0913.58038Mischaikow, Konstantin; Mrozek, Marian 35 1998 Travelling waves for mutualist species. Zbl 0815.35044Mischaikow, Konstantin; Hutson, Vivian 34 1993 Rigorous numerics for global dynamics: a study of the Swift-Hohenberg equation. Zbl 1058.35050Day, Sarah; Hiraoka, Yasuaki; Mischaikow, Konstantin; Ogawa, Toshiyuki 33 2005 Limit behaviour for a competing species problem with diffusion. Zbl 0848.35057Hutson, V.; López-Gómez, J.; Mischaikow, K.; Vickers, G. 33 1995 Rigorous a posteriori computation of (un)stable manifolds and connecting orbits for analytic maps. Zbl 1330.37029Mireles James, J. D.; Mischaikow, Konstantin 32 2013 Combinatorial-topological framework for the analysis of global dynamics. Zbl 1319.37004Bush, Justin; Gameiro, Marcio; Harker, Shaun; Kokubu, Hiroshi; Mischaikow, Konstantin; Obayashi, Ippei; Pilarczyk, Paweł 30 2012 A topological measurement of protein compressibility. Zbl 1320.55004Gameiro, Marcio; Hiraoka, Yasuaki; Izumi, Shunsuke; Kramar, Miroslav; Mischaikow, Konstantin; Nanda, Vidit 28 2015 A rigorous numerical method for the global analysis of infinite-dimensional discrete dynamical systems. Zbl 1059.37068Day, S.; Junge, O.; Mischaikow, K. 27 2004 Non-local dispersal. Zbl 1212.35484Grinfeld, M.; Hines, G.; Hutson, V.; Mischaikow, K.; Vickers, G. T. 27 2005 Discrete Morse theoretic algorithms for computing homology of complexes and maps. Zbl 1387.55010Harker, Shaun; Mischaikow, Konstantin; Mrozek, Marian; Nanda, Vidit 27 2014 Chaos in the Lorenz equations: A computer assisted proof. III: Classical parameter values. Zbl 0979.37015Mischaikow, Konstantin; Mrozek, Marian; Szymczak, Andrzej 26 2001 A predator-prey system involving group defense: A connection matrix approach. Zbl 0724.34015Mischaikow, Konstantin; Wolkowicz, Gail 25 1990 Travelling waves in predator-prey systems. Zbl 0815.35045Mischaikow, Konstantin; Reineck, James F. 25 1993 On the global dynamics of attractors for scalar delay equations. Zbl 0861.58023McCord, Christopher; Mischaikow, Konstantin 24 1996 Global asymptotic dynamics of gradient-like bistable equations. Zbl 0841.35014Mischaikow, Konstantin 23 1995 Combinatorial representation of parameter space for switching networks. Zbl 1360.37180Cummins, Bree; Gedeon, Tomas; Harker, Shaun; Mischaikow, Konstantin; Mok, Kafung 22 2016 Validated continuation over large parameter ranges for equilibria of PDEs. Zbl 1166.65379Gameiro, Marcio; Lessard, Jean-Philippe; Mischaikow, Konstantin 21 2008 The connection matrix theory for semiflows on (not necessarily locally compact) metric spaces. Zbl 0676.54048Franzosa, Robert D.; Mischaikow, Konstantin 20 1988 Rigorous numerics for the Cahn-Hilliard equation on the unit square. Zbl 1160.37418Maier-Paape, Stanislaus; Miller, Ulrich; Mischaikow, Konstantin; Wanner, Thomas 20 2008 Horseshoes and the Conley index spectrum. Zbl 0971.37005Carbinatto, Maria C.; Kwapisz, Jaroslaw; Mischaikow, Konstantin 19 2000 Graph approach to the computation of the homology of continuous maps. Zbl 1104.55001Mischaikow, Konstantin; Mrozek, Marian; Pilarczyk, Pawel 17 2005 Structure of the global attractor of cyclic feedback systems. Zbl 0823.34057Gedeon, Tomáš; Mischaikow, Konstantin 17 1995 Analysis of Kolmogorov flow and Rayleigh-Bénard convection using persistent homology. Zbl 1415.76582Kramár, Miroslav; Levanger, Rachel; Tithof, Jeffrey; Suri, Balachandra; Xu, Mu; Paul, Mark; Schatz, Michael F.; Mischaikow, Konstantin 17 2016 Structure of the attractor of the Cahn-Hilliard equation on a square. Zbl 1148.35008Maier-Paape, Stanislaus; Mischaikow, Konstantin; Wanner, Thomas 17 2007 Lattice structures for attractors. I. Zbl 1346.37013Kalies, William D.; Mischaikow, Konstantin; Vandervorst, Robert C. A. M. 16 2014 Zeta functions, periodic trajectories, and the Conley index. Zbl 0833.34045McCord, Christopher; Mischaikow, Konstantin; Mrozek, Marian 16 1995 Topological techniques for efficient rigorous computation in dynamics. Zbl 1123.37328Mischaikow, Konstantin 15 2002 On Conley index theory: A brief introduction. Zbl 0946.37010Mischaikow, Konstantin 15 1999 A dynamical system approach to a phase transition problem. Zbl 0772.35029Hattori, Harumi; Mischaikow, Konstantin 14 1991 Conley index theory. Zbl 0847.58062Mischaikow, Konstantin 14 1995 Global dynamics for steep nonlinearities in two dimensions. Zbl 1376.34019Gedeon, Tomáš; Harker, Shaun; Kokubu, Hiroshi; Mischaikow, Konstantin; Oka, Hiroe 14 2017 Rigorous computations of homoclinic tangencies. Zbl 1210.37008Arai, Zin; Mischaikow, Konstantin 13 2006 Polygonal approximation of flows. Zbl 1118.37017Boczko, Erik; Kalies, William D.; Mischaikow, Konstantin 13 2007 Stability and uniqueness of slowly oscillating periodic solutions to Wright’s equation. Zbl 1382.34069Jaquette, Jonathan; Lessard, Jean-Philippe; Mischaikow, Konstantin 13 2017 Connected simple systems, transition matrices and heteroclinic bifurcations. Zbl 0763.34028McCord, Christopher; Mischaikow, Konstantin 12 1992 Homology and symmetry breaking in Rayleigh-Bénard convection: experiments and simulations. Zbl 1182.76403Krishan, Kapilanjan; Kurtuldu, Huseyin; Schatz, Michael F.; Gameiro, Marcio; Mischaikow, Konstantin; Madruga, Santiago 12 2007 Computing homology. Zbl 1028.55001Kaczynski, Tomasz; Mischaikow, Konstantin; Mrozek, Marian 12 2003 A study of rigorous ODE integrators for multi-scale set-oriented computations. Zbl 1382.65199Miyaji, Tomoyuki; Pilarczyk, Paweł; Gameiro, Marcio; Kokubu, Hiroshi; Mischaikow, Konstantin 11 2016 Algebraic transition matrices in the Conley index theory. Zbl 0896.58053Franzosa, Robert; Mischaikow, Konstantin 11 1998 Quantifying force networks in particulate systems. Zbl 1349.74083Kramár, Miroslav; Goullet, Arnaud; Kondic, Lou; Mischaikow, Konstantin 10 2014 Dynamics of bifurcations for variational problems with \(O(3)\) equivariance: A Conley index approach. Zbl 0756.49003Fiedler, Bernold; Mischaikow, Konstantin 10 1992 Lattice structures for attractors. II. Zbl 1373.37039Kalies, William D.; Mischaikow, Konstantin; Vandervorst, Robert C. A. M. 10 2016 Efficient computation of Lyapunov functions for Morse decompositions. Zbl 1366.37031Goullet, Arnaud; Harker, Shaun; Mischaikow, Konstantin; Kalies, William D.; Kasti, Dinesh 8 2015 Chaotic solutions in slowly varying perturbations of Hamiltonian systems with applications to shallow water sloshing. Zbl 1005.37028Gedeon, Tomáš; Kokubu, Hiroshi; Mischaikow, Konstantin; Oka, Hiroe 8 2002 Probabilistic validation of homology computations for nodal domains. Zbl 1131.60047Mischaikow, Konstantin; Wanner, Thomas 7 2007 Dynamics on the global attractor of a gradient flow arising from the Ginzburg-Landau equation. Zbl 0807.58029Mischaikow, Konstantin; Morita, Yoshihisa 7 1994 Quantitative hyperbolicity estimates in one-dimensional dynamics. Zbl 1154.37324Day, S.; Kokubu, H.; Luzzatto, S.; Mischaikow, K.; Oka, H.; Pilarczyk, P. 7 2008 Cubical approximation and computation of homology. Zbl 0938.55012Kalies, William D.; Mischaikow, Konstantin; Watson, Greg 7 1999 Transition systems. Zbl 0677.34046Mischaikow, Konstantin 6 1989 Topological horseshoes of traveling waves for a fast-slow predator-prey system. Zbl 1143.34032Gameiro, Marcio; Gedeon, Tomáš; Kalies, William; Kokubu, Hiroshi; Mischaikow, Konstantin; Oka, Hiroe 6 2007 On the existence of intermediate magnetohydrodynamic shock waves. Zbl 0695.76030Mischaikow, Konstantin; Hattori, Harumi 6 1990 Probabilistic and numerical validation of homology computations for nodal domains. Zbl 1141.60025Day, Sarah; Kalies, William D.; Mischaikow, Konstantin; Wanner, Thomas 6 2007 Conley-Morse databases for the angular dynamics of Newton’s method on the plane. Zbl 1338.37004Bush, Justin; Cowan, Wes; Harker, Shaun; Mischaikow, Konstantin 6 2016 Existence of generalized homoclinic orbits for one parameter families of flows. Zbl 0661.34038Mischaikow, Konstantin 6 1988 Discretization strategies for computing Conley indices and Morse decompositions of flows. Zbl 1373.37043Weilandt, Frank; Mrozek, Marian; Mischaikow, Konstantin 5 2016 Horseshoes and the Conley index spectrum. II: The theorem is sharp. Zbl 0954.37009Carbinatto, M. C.; Mischaikow, K. 5 1999 Measuring the departures from the Boussinesq approximation in Rayleigh-Bénard convection experiments. Zbl 1241.76186Kurtuldu, H.; Mischaikow, K.; Schatz, M. F. 5 2011 Model rejection and parameter reduction via time series. Zbl 1393.37092Cummins, Bree; Gedeon, Tomas; Harker, Shaun; Mischaikow, Konstantin 5 2018 Singular index pairs. Zbl 0943.34028Mischaikow, Konstantin; Mrozek, Marian; Reineck, James F. 5 1999 The Conley index for fast-slow systems. I: One-dimensional slow variable. Zbl 0945.34029Gedeon, Tomáš; Kokubu, Hiroshi; Mischaikow, Konstantin; Oka, Hiroe; Reineck, James F. 5 1999 Graph-based topological approximation of saddle-node bifurcation in maps. Zbl 1254.37014Arai, Zin; Gameiro, Marcio; Gedeon, Tomas; Kokubu, Hiroshi; Mischaikow, Konstantin; Oka, Hiroe 4 2012 Inducing a map on homology from a correspondence. Zbl 1337.55006Harker, Shaun; Kokubu, Hiroshi; Mischaikow, Konstantin; Pilarczyk, Paweł 4 2016 Dynamics of cyclic feedback systems. Zbl 0848.34031Gedeon, T.; Mischaikow, K. 4 1994 On the slow motions of phase boundaries in the Korteweg theory of capillarity. Zbl 0788.35117Hattori, Harumi; Mischaikow, Konstantin 4 1992 Existence of infinitely many connecting orbits in a singularly perturbed ordinary differential equation. Zbl 0898.34047Kokubu, Hiroshi; Mischaikow, Konstantin; Oka, Hiroe 4 1996 Reconstructing functions from random samples. Zbl 1330.55017Ferry, Steve; Mischaikow, Konstantin; Nanda, Vidit 3 2014 The structure of isolated invariant sets and the Conley index. Zbl 0802.34051Mischaikow, Konstantin 3 1993 Conley’s connection matrix. Zbl 0655.34036Mischaikow, Konstantin 3 1987 Equivalence of topological and singular transition matrices in the Conley index theory. Zbl 0853.58080McCord, Christopher K.; Mischaikow, Konstantin 3 1995 Topology-guided sampling of nonhomogeneous random processes. Zbl 1213.60072Mischaikow, Konstantin; Wanner, Thomas 3 2010 When activators repress and repressors activate: a qualitative analysis of the Shea-Ackers model. Zbl 1166.92021Gedeon, Tomáš; Mischaikow, Konstantin; Patterson, Kate; Traldi, Eliane 3 2008 Towards automated chaos verification. Zbl 1102.37027Day, Sarah; Junge, Oliver; Mischaikow, Konstantin 3 2005 Connecting orbit structure of monotone solutions in the shadow system. Zbl 0902.35058Kokubu, Hiroshi; Mischaikow, Konstantin; Nishiura, Yasumasa; Oka, Hireo; Takaishi, Takeshi 3 1997 Conley index theory. Zbl 0913.00021 3 1999 Conley index approach to sampled dynamics. Zbl 1442.37088Batko, Bogdan; Mischaikow, Konstantin; Mrozek, Marian; Przybylski, Mateusz 3 2020 The conley index for fast-slow systems. II: multidimensional slow variable. Zbl 1107.34051Gedeon, Tomáš; Kokubu, Hiroshi; Mischaikow, Konstantin; Oka, Hiroe 2 2006 Multiple travelling waves in evolutionary game dynamics. Zbl 1306.91020Hutson, V.; Mischaikow, K.; Vickers, G. T. 2 2000 Homoclinic orbits in Hamiltonian systems and heteroclinic orbits in gradient and gradient-like systems. Zbl 0692.34029Mischaikow, Konstantin 2 1989 Singular limits for travelling waves for a pair of equations. Zbl 0852.35066Hutson, Vivian; Mischaikow, Konstantin 2 1996 Special issue in celebration of Jack K. Hale’s 70th birthday. Part 2 of 4 parts. Zbl 0969.00109 2 2000 Global dynamics for switching systems and their extensions by linear differential equations. Zbl 1380.34035Huttinga, Zane; Cummins, Bree; Gedeon, Tomáš; Mischaikow, Konstantin 2 2018 Equilibria and their stability in networks with steep sigmoidal nonlinearities. Zbl 1483.37107Duncan, William; Gedeon, Tomas; Kokubu, Hiroshi; Mischaikow, Konstantin; Oka, Hiroe 2 2021 Computing linear extensions for polynomial posets subject to algebraic constraints. Zbl 07374246Kepley, Shane; Mischaikow, Konstantin; Zhang, Lun 2 2021 A computational framework for connection matrix theory. Zbl 1487.37018Harker, Shaun; Mischaikow, Konstantin; Spendlove, Kelly 1 2021 Conley index approach to sampled dynamics. Zbl 1442.37088Batko, Bogdan; Mischaikow, Konstantin; Mrozek, Marian; Przybylski, Mateusz 3 2020 Contractibility of a persistence map preimage. Zbl 1458.37083Cyranka, Jacek; Mischaikow, Konstantin; Weibel, Charles 1 2020 A comparison framework for interleaved persistence modules. Zbl 1443.55001Harker, Shaun; Kramár, Miroslav; Levanger, Rachel; Mischaikow, Konstantin 2 2019 Model rejection and parameter reduction via time series. Zbl 1393.37092Cummins, Bree; Gedeon, Tomas; Harker, Shaun; Mischaikow, Konstantin 5 2018 Global dynamics for switching systems and their extensions by linear differential equations. Zbl 1380.34035Huttinga, Zane; Cummins, Bree; Gedeon, Tomáš; Mischaikow, Konstantin 2 2018 Global dynamics for steep nonlinearities in two dimensions. Zbl 1376.34019Gedeon, Tomáš; Harker, Shaun; Kokubu, Hiroshi; Mischaikow, Konstantin; Oka, Hiroe 14 2017 Stability and uniqueness of slowly oscillating periodic solutions to Wright’s equation. Zbl 1382.34069Jaquette, Jonathan; Lessard, Jean-Philippe; Mischaikow, Konstantin 13 2017 Topological signals of singularities in Ricci flow. Zbl 1422.57062Alsing, Paul M.; Blair, Howard A.; Corne, Matthew; Jones, Gordon; Miller, Warner A.; Mischaikow, Konstantin; Nanda, Vidit 1 2017 Combinatorial representation of parameter space for switching networks. Zbl 1360.37180Cummins, Bree; Gedeon, Tomas; Harker, Shaun; Mischaikow, Konstantin; Mok, Kafung 22 2016 Analysis of Kolmogorov flow and Rayleigh-Bénard convection using persistent homology. Zbl 1415.76582Kramár, Miroslav; Levanger, Rachel; Tithof, Jeffrey; Suri, Balachandra; Xu, Mu; Paul, Mark; Schatz, Michael F.; Mischaikow, Konstantin 17 2016 A study of rigorous ODE integrators for multi-scale set-oriented computations. Zbl 1382.65199Miyaji, Tomoyuki; Pilarczyk, Paweł; Gameiro, Marcio; Kokubu, Hiroshi; Mischaikow, Konstantin 11 2016 Lattice structures for attractors. II. Zbl 1373.37039Kalies, William D.; Mischaikow, Konstantin; Vandervorst, Robert C. A. M. 10 2016 Conley-Morse databases for the angular dynamics of Newton’s method on the plane. Zbl 1338.37004Bush, Justin; Cowan, Wes; Harker, Shaun; Mischaikow, Konstantin 6 2016 Discretization strategies for computing Conley indices and Morse decompositions of flows. Zbl 1373.37043Weilandt, Frank; Mrozek, Marian; Mischaikow, Konstantin 5 2016 Inducing a map on homology from a correspondence. Zbl 1337.55006Harker, Shaun; Kokubu, Hiroshi; Mischaikow, Konstantin; Pilarczyk, Paweł 4 2016 A topological measurement of protein compressibility. Zbl 1320.55004Gameiro, Marcio; Hiraoka, Yasuaki; Izumi, Shunsuke; Kramar, Miroslav; Mischaikow, Konstantin; Nanda, Vidit 28 2015 Efficient computation of Lyapunov functions for Morse decompositions. Zbl 1366.37031Goullet, Arnaud; Harker, Shaun; Mischaikow, Konstantin; Kalies, William D.; Kasti, Dinesh 8 2015 Discrete Morse theoretic algorithms for computing homology of complexes and maps. Zbl 1387.55010Harker, Shaun; Mischaikow, Konstantin; Mrozek, Marian; Nanda, Vidit 27 2014 Lattice structures for attractors. I. Zbl 1346.37013Kalies, William D.; Mischaikow, Konstantin; Vandervorst, Robert C. A. M. 16 2014 Quantifying force networks in particulate systems. Zbl 1349.74083Kramár, Miroslav; Goullet, Arnaud; Kondic, Lou; Mischaikow, Konstantin 10 2014 Reconstructing functions from random samples. Zbl 1330.55017Ferry, Steve; Mischaikow, Konstantin; Nanda, Vidit 3 2014 Morse theory for filtrations and efficient computation of persistent homology. Zbl 1278.57030Mischaikow, Konstantin; Nanda, Vidit 60 2013 Rigorous a posteriori computation of (un)stable manifolds and connecting orbits for analytic maps. Zbl 1330.37029Mireles James, J. D.; Mischaikow, Konstantin 32 2013 Combinatorial-topological framework for the analysis of global dynamics. Zbl 1319.37004Bush, Justin; Gameiro, Marcio; Harker, Shaun; Kokubu, Hiroshi; Mischaikow, Konstantin; Obayashi, Ippei; Pilarczyk, Paweł 30 2012 Graph-based topological approximation of saddle-node bifurcation in maps. Zbl 1254.37014Arai, Zin; Gameiro, Marcio; Gedeon, Tomas; Kokubu, Hiroshi; Mischaikow, Konstantin; Oka, Hiroe 4 2012 Rigorous numerics for symmetric connecting orbits: even homoclinics of the Gray-Scott equation. Zbl 1231.34081van den Berg, Jan Bouwe; Mireles-James, Jason D.; Lessard, Jean-Philippe; Mischaikow, Konstantin 44 2011 Measuring the departures from the Boussinesq approximation in Rayleigh-Bénard convection experiments. Zbl 1241.76186Kurtuldu, H.; Mischaikow, K.; Schatz, M. F. 5 2011 Global smooth solution curves using rigorous branch following. Zbl 1206.37045van den Berg, Jan Bouwe; Lessard, Jean-Philippe; Mischaikow, Konstantin 39 2010 Topology-guided sampling of nonhomogeneous random processes. Zbl 1213.60072Mischaikow, Konstantin; Wanner, Thomas 3 2010 A database schema for the analysis of global dynamics of multiparameter systems. Zbl 1186.37021Arai, Zin; Kalies, William; Kokubu, Hiroshi; Mischaikow, Konstantin; Oka, Hiroe; Pilarczyk, Paweł 51 2009 A database schema for the analysis of global dynamics. Zbl 1183.37026Arai, Zin; Kalies, William; Kokubu, Hiroshi; Mischaikow, Konstantin; Oka, Hiroe; Pilarczyk, Pawel 1 2009 Validated continuation over large parameter ranges for equilibria of PDEs. Zbl 1166.65379Gameiro, Marcio; Lessard, Jean-Philippe; Mischaikow, Konstantin 21 2008 Rigorous numerics for the Cahn-Hilliard equation on the unit square. Zbl 1160.37418Maier-Paape, Stanislaus; Miller, Ulrich; Mischaikow, Konstantin; Wanner, Thomas 20 2008 Quantitative hyperbolicity estimates in one-dimensional dynamics. Zbl 1154.37324Day, S.; Kokubu, H.; Luzzatto, S.; Mischaikow, K.; Oka, H.; Pilarczyk, P. 7 2008 When activators repress and repressors activate: a qualitative analysis of the Shea-Ackers model. Zbl 1166.92021Gedeon, Tomáš; Mischaikow, Konstantin; Patterson, Kate; Traldi, Eliane 3 2008 Validated continuation for equilibria of PDEs. Zbl 1151.65074Day, Sarah; Lessard, Jean-Philippe; Mischaikow, Konstantin 75 2007 Structure of the attractor of the Cahn-Hilliard equation on a square. Zbl 1148.35008Maier-Paape, Stanislaus; Mischaikow, Konstantin; Wanner, Thomas 17 2007 Polygonal approximation of flows. Zbl 1118.37017Boczko, Erik; Kalies, William D.; Mischaikow, Konstantin 13 2007 Homology and symmetry breaking in Rayleigh-Bénard convection: experiments and simulations. Zbl 1182.76403Krishan, Kapilanjan; Kurtuldu, Huseyin; Schatz, Michael F.; Gameiro, Marcio; Mischaikow, Konstantin; Madruga, Santiago 12 2007 Probabilistic validation of homology computations for nodal domains. Zbl 1131.60047Mischaikow, Konstantin; Wanner, Thomas 7 2007 Topological horseshoes of traveling waves for a fast-slow predator-prey system. Zbl 1143.34032Gameiro, Marcio; Gedeon, Tomáš; Kalies, William; Kokubu, Hiroshi; Mischaikow, Konstantin; Oka, Hiroe 6 2007 Probabilistic and numerical validation of homology computations for nodal domains. Zbl 1141.60025Day, Sarah; Kalies, William D.; Mischaikow, Konstantin; Wanner, Thomas 6 2007 Rigorous computations of homoclinic tangencies. Zbl 1210.37008Arai, Zin; Mischaikow, Konstantin 13 2006 The conley index for fast-slow systems. II: multidimensional slow variable. Zbl 1107.34051Gedeon, Tomáš; Kokubu, Hiroshi; Mischaikow, Konstantin; Oka, Hiroe 2 2006 Convergence in competition models with small diffusion coefficients. Zbl 1074.35054Hutson, V.; Lou, Y.; Mischaikow, K. 60 2005 An algorithmic approach to chain recurrence. Zbl 1099.37010Kalies, W. D.; Mischaikow, K.; VanderVorst, R. C. A. M. 39 2005 Rigorous numerics for global dynamics: a study of the Swift-Hohenberg equation. Zbl 1058.35050Day, Sarah; Hiraoka, Yasuaki; Mischaikow, Konstantin; Ogawa, Toshiyuki 33 2005 Non-local dispersal. Zbl 1212.35484Grinfeld, M.; Hines, G.; Hutson, V.; Mischaikow, K.; Vickers, G. T. 27 2005 Graph approach to the computation of the homology of continuous maps. Zbl 1104.55001Mischaikow, Konstantin; Mrozek, Marian; Pilarczyk, Pawel 17 2005 Towards automated chaos verification. Zbl 1102.37027Day, Sarah; Junge, Oliver; Mischaikow, Konstantin 3 2005 Computational homology. Zbl 1039.55001Kaczynski, Tomasz; Mischaikow, Konstantin; Mrozek, Marian 108 2004 A rigorous numerical method for the global analysis of infinite-dimensional discrete dynamical systems. Zbl 1059.37068Day, S.; Junge, O.; Mischaikow, K. 27 2004 Selection of slow diffusion in a reaction diffusion model: limiting cases. Zbl 1073.35104Flores, Gilberto; Mischaikow, Konstantin 1 2004 The evolution of dispersal. Zbl 1052.92042Hutson, V.; Martinez, S.; Mischaikow, K.; Vickers, G. T. 202 2003 Competing species near a degenerate limit. Zbl 1043.35080Hutson, V.; Lou, Y.; Mischaikow, K.; Polácik, P. 39 2003 Computing homology. Zbl 1028.55001Kaczynski, Tomasz; Mischaikow, Konstantin; Mrozek, Marian 12 2003 Conley index. Zbl 1035.37010Mischaikow, Konstantin; Mrozek, Marian 53 2002 Spatial heterogeneity of resources versus Lotka-Volterra dynamics. Zbl 1023.35047Hutson, V.; Lou, Y.; Mischaikow, K. 43 2002 Topological techniques for efficient rigorous computation in dynamics. Zbl 1123.37328Mischaikow, Konstantin 15 2002 Chaotic solutions in slowly varying perturbations of Hamiltonian systems with applications to shallow water sloshing. Zbl 1005.37028Gedeon, Tomáš; Kokubu, Hiroshi; Mischaikow, Konstantin; Oka, Hiroe 8 2002 The evolution of dispersal rates in a heterogeneous time-periodic environment. Zbl 0996.92035Hutson, V.; Mischaikow, K.; Poláčik, P. 95 2001 Rigorous numerics for partial differential equations: The Kuramoto-Sivashinsky equation. Zbl 0984.65101Zgliczyński, Piotr; Mischaikow, Konstantin 40 2001 Chaos in the Lorenz equations: A computer assisted proof. III: Classical parameter values. Zbl 0979.37015Mischaikow, Konstantin; Mrozek, Marian; Szymczak, Andrzej 26 2001 Special issue in celebration of Jack K. Hale’s 70th birthday. Part 3 of 4 parts. Zbl 0982.00063 1 2001 Horseshoes and the Conley index spectrum. Zbl 0971.37005Carbinatto, Maria C.; Kwapisz, Jaroslaw; Mischaikow, Konstantin 19 2000 Multiple travelling waves in evolutionary game dynamics. Zbl 1306.91020Hutson, V.; Mischaikow, K.; Vickers, G. T. 2 2000 Special issue in celebration of Jack K. Hale’s 70th birthday. Part 2 of 4 parts. Zbl 0969.00109 2 2000 On Conley index theory: A brief introduction. Zbl 0946.37010Mischaikow, Konstantin 15 1999 Cubical approximation and computation of homology. Zbl 0938.55012Kalies, William D.; Mischaikow, Konstantin; Watson, Greg 7 1999 Horseshoes and the Conley index spectrum. II: The theorem is sharp. Zbl 0954.37009Carbinatto, M. C.; Mischaikow, K. 5 1999 Singular index pairs. Zbl 0943.34028Mischaikow, Konstantin; Mrozek, Marian; Reineck, James F. 5 1999 The Conley index for fast-slow systems. I: One-dimensional slow variable. Zbl 0945.34029Gedeon, Tomáš; Kokubu, Hiroshi; Mischaikow, Konstantin; Oka, Hiroe; Reineck, James F. 5 1999 Conley index theory. Zbl 0913.00021 3 1999 Directional transition matrix. Zbl 0956.37007Kokubu, Hiroshi; Mischaikow, Konstantin; Oka, Hiroe 1 1999 Post-fertilization traveling waves on eggs. Zbl 0944.35042Flores, Gilberto; Minzoni, Antonmaria; Mischiakow, Konstantin; Moll, Victor 1 1999 The evolution of slow dispersal rates: a reaction diffusion model. Zbl 0921.92021Dockery, Jack; Hutson, Vivian; Mischaikow, Konstantin; Pernarowski, Mark 200 1998 Chaos in the Lorenz equations: A computer assisted proof. II: Details. Zbl 0913.58038Mischaikow, Konstantin; Mrozek, Marian 35 1998 Algebraic transition matrices in the Conley index theory. Zbl 0896.58053Franzosa, Robert; Mischaikow, Konstantin 11 1998 An approach to practical persistence. Zbl 0927.92030Hutson, V.; Mischaikow, K. 2 1998 Connecting orbit structure of monotone solutions in the shadow system. Zbl 0902.35058Kokubu, Hiroshi; Mischaikow, Konstantin; Nishiura, Yasumasa; Oka, Hireo; Takaishi, Takeshi 3 1997 On the global dynamics of attractors for scalar delay equations. Zbl 0861.58023McCord, Christopher; Mischaikow, Konstantin 24 1996 Existence of infinitely many connecting orbits in a singularly perturbed ordinary differential equation. Zbl 0898.34047Kokubu, Hiroshi; Mischaikow, Konstantin; Oka, Hiroe 4 1996 Singular limits for travelling waves for a pair of equations. Zbl 0852.35066Hutson, Vivian; Mischaikow, Konstantin 2 1996 Asymptotically autonomous semiflows: Chain recurrence and Lyapunov functions. Zbl 0829.34037Mischaikow, Konstantin; Smith, Hal; Thieme, Horst R. 102 1995 Chaos in the Lorenz equations: A computer-assisted proof. Zbl 0820.58042Mischaikow, Konstantin; Mrozek, Marian 98 1995 Isolating neighborhoods and chaos. Zbl 0840.58033Mischaikow, Konstantin; Mrozek, Marian 35 1995 Limit behaviour for a competing species problem with diffusion. Zbl 0848.35057Hutson, V.; López-Gómez, J.; Mischaikow, K.; Vickers, G. 33 1995 Global asymptotic dynamics of gradient-like bistable equations. Zbl 0841.35014Mischaikow, Konstantin 23 1995 Structure of the global attractor of cyclic feedback systems. Zbl 0823.34057Gedeon, Tomáš; Mischaikow, Konstantin 17 1995 Zeta functions, periodic trajectories, and the Conley index. Zbl 0833.34045McCord, Christopher; Mischaikow, Konstantin; Mrozek, Marian 16 1995 Conley index theory. Zbl 0847.58062Mischaikow, Konstantin 14 1995 Equivalence of topological and singular transition matrices in the Conley index theory. Zbl 0853.58080McCord, Christopher K.; Mischaikow, Konstantin 3 1995 Dynamics on the global attractor of a gradient flow arising from the Ginzburg-Landau equation. Zbl 0807.58029Mischaikow, Konstantin; Morita, Yoshihisa 7 1994 Dynamics of cyclic feedback systems. Zbl 0848.34031Gedeon, T.; Mischaikow, K. 4 1994 A product theorem for connection matrices and the structure of connecting orbits. Zbl 0818.34024Mischaikow, Konstantin; Reineck, James F. 1 1994 Travelling waves for mutualist species. Zbl 0815.35044Mischaikow, Konstantin; Hutson, Vivian 34 1993 Travelling waves in predator-prey systems. Zbl 0815.35045Mischaikow, Konstantin; Reineck, James F. 25 1993 ...and 17 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,707 Authors 58 Mischaikow, Konstantin 45 Lessard, Jean-Philippe 45 Lou, Yuan 41 Li, Wan-Tong 34 Mireles-James, Jason D. 34 Mrozek, Marian 24 Gedeon, Tomáš 24 Wanner, Thomas 23 Shen, Wenxian 22 Sun, Jianwen 22 van den Berg, Jan Bouwe 22 Zgliczyński, Piotr 18 Lam, King-Yeung 18 Zhao, Xiao-Qiang 17 Gameiro, Marcio F. 17 Shi, Junping 17 Yang, Feiying 16 Cosner, Chris 15 Pilarczyk, Paweł 15 Wang, Mingxin 13 Cantrell, Robert Stephen 13 Coville, Jerome 13 Kalies, William D. 13 Ruan, Shigui 13 Wang, Yuanshi 12 Du, Yihong 12 Hiraoka, Yasuaki 11 Hafstein, Sigurður Freyr 11 Kaczynski, Tomasz 11 Kokubu, Hiroshi 11 Peng, Rui 11 Wang, Zhi Cheng 10 Giesl, Peter 10 Girardin, Léo 10 Harker, Shaun 10 Martínez, Salomé 10 Nanda, Vidit 10 Rossi, Julio Daniel 10 Vandervorst, Robertus C. A. M. 10 Wei, Guowei 10 Zou, Xingfu 9 Breden, Maxime 9 Cummins, Bree 9 He, Xiaoqing 9 Zanolin, Fabio 8 Ahn, Inkyung 8 Castelli, Roberto 8 Day, Sarah L. 8 Ding, Yanheng 8 Liu, Shuang 8 Ni, Wei-Ming 8 Wu, YiXiang 7 Braverman, Elena 7 Choi, Wonhyung 7 DeAngelis, Donald L. 7 Ghrist, Robert W. 7 Kim, Yong Jung 7 Lin, Guo 7 Nadin, Grégoire 7 Nolasco de Carvalho, Alexandre 7 Romero, Ana 7 Srzednicki, Roman 7 Tang, De 7 Wilczak, Daniel 7 Wójcik, Klaudiusz 7 Wu, Chufen 7 Zhou, Peng 6 Allili, Madjid 6 Arioli, Gianni 6 Batko, Bogdan 6 Berestycki, Henri 6 Bubenik, Peter 6 Capinski, Maciej J. 6 Cyranka, Jacek 6 Dłotko, Paweł 6 Fiedler, Bernold 6 Galias, Zbigniew 6 Hamel, François 6 Kamrujjaman, Md. 6 Kepley, Shane 6 Kramár, Miroslav 6 Landi, Claudia 6 Langa, Jose’ Antonio 6 Lutscher, Frithjof 6 Ni, Wenjie 6 Sander, Evelyn 6 Wang, Qi 6 Wang, Yuxia 6 Wiseman, Jim 6 Wu, Jianhua 6 Yang, Xiaosong 6 Zhang, Fubao 6 Zhang, Jimin 5 Bai, Xueli 5 Chen, Shanshan 5 Franzosa, Robert D. 5 Gidea, Marian 5 González-Díaz, Rocío 5 Guo, Shangjiang 5 Hattori, Harumi ...and 1,607 more Authors all top 5 Cited in 243 Serials 165 Journal of Differential Equations 60 Discrete and Continuous Dynamical Systems. 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Series S 3 Foundations of Data Science 2 Communications on Pure and Applied Mathematics 2 Indian Journal of Pure & Applied Mathematics 2 Journal of Computational Physics 2 Journal of the Franklin Institute 2 Journal of Statistical Physics 2 Periodica Mathematica Hungarica 2 The Mathematical Intelligencer 2 Advances in Mathematics ...and 143 more Serials all top 5 Cited in 50 Fields 601 Partial differential equations (35-XX) 550 Biology and other natural sciences (92-XX) 487 Dynamical systems and ergodic theory (37-XX) 287 Ordinary differential equations (34-XX) 164 Numerical analysis (65-XX) 146 Algebraic topology (55-XX) 80 Computer science (68-XX) 76 Integral equations (45-XX) 69 Operator theory (47-XX) 45 Manifolds and cell complexes (57-XX) 40 Probability theory and stochastic processes (60-XX) 39 Global analysis, analysis on manifolds (58-XX) 38 Statistics (62-XX) 37 Systems theory; control (93-XX) 33 General topology (54-XX) 32 Mechanics of particles and systems (70-XX) 30 Combinatorics (05-XX) 24 Fluid mechanics (76-XX) 22 Statistical mechanics, structure of matter (82-XX) 21 Mechanics of deformable solids (74-XX) 20 Difference and functional equations (39-XX) 20 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 19 Category theory; homological algebra (18-XX) 13 Calculus of variations and optimal control; optimization (49-XX) 12 Order, lattices, ordered algebraic structures (06-XX) 12 Convex and discrete geometry (52-XX) 11 Information and communication theory, circuits (94-XX) 10 Differential geometry (53-XX) 10 Operations research, mathematical programming (90-XX) 7 Functional analysis (46-XX) 7 Classical thermodynamics, heat transfer (80-XX) 7 Quantum theory (81-XX) 5 Mathematical logic and foundations (03-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 5 Approximations and expansions (41-XX) 5 Relativity and gravitational theory (83-XX) 4 Algebraic geometry (14-XX) 4 Real functions (26-XX) 4 Optics, electromagnetic theory (78-XX) 3 Commutative algebra (13-XX) 3 Associative rings and algebras (16-XX) 3 Group theory and generalizations (20-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Geophysics (86-XX) 2 General and overarching topics; collections (00-XX) 2 Number theory (11-XX) 2 Integral transforms, operational calculus (44-XX) 1 History and biography (01-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Astronomy and astrophysics (85-XX) Citations by Year