Edit Profile (opens in new tab) Rubin, Jonathan E. Co-Author Distance Author ID: rubin.jonathan-e Published as: Rubin, Jonathan E.; Rubin, Jonathan; Rubin, J. E.; Rubin, J.; Rubin, Jonathan. E. more...less Homepage: http://www.math.pitt.edu/~rubin/ External Links: MGP · ORCID · Wikidata · Google Scholar · dblp Documents Indexed: 84 Publications since 1990, including 5 Additional arXiv Preprints 2 Contributions as Editor Co-Authors: 90 Co-Authors with 76 Joint Publications 1,589 Co-Co-Authors all top 5 Co-Authors 6 single-authored 9 Swigon, David 7 Terman, David Hillel 6 Clermont, Gilles 5 Ermentrout, Bard G. 5 Letson, Benjamin 5 Vodovotz, Yoram 4 Day, Judy D. 4 Duan, Xiaoyu 4 Ermentrout, George Bard 4 Wang, Yangyang 4 Wechselberger, Martin 3 Josić, Krešimir 3 Signerska-Rynkowska, Justyna 3 Stanhope, Shelby R. 3 Su, Jianzhong 3 Touboul, Jonathan David 2 Bose, Amitabha 2 Chow, Carson C. 2 Curtu, Rodica 2 Daun, Silvia 2 Dunmyre, Justin R. 2 John, Sushmita Rose 2 Jones, Christopher K. R. T. 2 Krauskopf, Bernd 2 Osan, Remus 2 Osinga, Hinke Maria 2 Park, Choongseok 2 Phillips, Ryan S. 2 Ramirez-Zuniga, Ivan 2 Reynolds, Angela 2 Smith, Jeffrey C. 2 Vidal, Alexandre 2 Wang, Jiaoyan 2 Young, Glenn 1 Abdulla, Muhammad U. 1 Afrazi, Amin 1 An, Gary 1 Arciero, Julia C. 1 Bacak, Bartholomew J. 1 Best, Janet A. 1 Bianco, Simone 1 Borisyuk, Alla 1 Burstein, David 1 Butera, Robert J. jun. 1 Codianni, Marcello G. 1 Constantine, Gregory M. 1 Costello, Willie 1 Csete, Marie 1 Del Negro, Christopher A. 1 Demir, Mahmut 1 Drover, Jonathan D. 1 Duanmu, M. 1 Dunovan, K. 1 Gittis, Aryn H. 1 Hackam, David 1 Jalics, Jozsi Z. 1 Jimenez, Nicolas D. 1 Kapitula, Todd M. 1 Kevrekidis, Panayotis G. 1 Kirk, Vivien 1 Kubota, Shigeru 1 Manica, Evandro 1 Matías, Manuel A. 1 Maxey, Martin R. 1 Medvedev, Georgi S. 1 Mihalaş, Ştefan 1 Molkov, Yaroslav I. 1 Nan, Pingyu 1 Niebur, Ernst 1 Parker, John E. 1 Parks, Helen F. 1 Perez Gonzalez, Humberto 1 Ran, André C. M. 1 Redl, Heinz 1 Roberts, Kerry-Lyn 1 Rodman, Leiba X. 1 Romo, Ranulfo 1 Roy, Anirban 1 Rybak, Ilya A. 1 Salman, Hanna 1 Shevtsova, Natalia A. 1 Siggers, Richard 1 Snyder, Abigail C. 1 Thomas, Peter J. 1 Troy, William C. 1 Vainchtein, Anna 1 Verstynen, Timothy 1 Vich, Catalina 1 Vo, Theodore 1 Voit, Eberhard Otto 1 Whalen, Timothy C. 1 Whitaker, Nathaniel 1 Winternitz, Pavel 1 Yu, Zhuojun 1 Zenker, Sven all top 5 Serials 15 SIAM Journal on Applied Dynamical Systems 8 Journal of Computational Neuroscience 6 SIAM Journal on Applied Mathematics 6 Journal of Theoretical Biology 4 Physica D 4 Discrete and Continuous Dynamical Systems. Series B 4 The Journal of Mathematical Neuroscience 3 Biological Cybernetics 3 Chaos 2 Inverse Problems 2 Journal of Mathematical Biology 2 Mathematical Biosciences 2 Nonlinearity 2 Bulletin of Mathematical Biology 2 Neural Computation 2 SIAM/ASA Journal on Uncertainty Quantification 1 Journal of Mathematical Physics 1 Linear Algebra and its Applications 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Journal of Dynamics and Differential Equations 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Journal of Nonlinear Science 1 Discrete and Continuous Dynamical Systems 1 Network: Computation in Neural Systems 1 Communications in Nonlinear Science and Numerical Simulation 1 Algebraic & Geometric Topology 1 Mathematical Biosciences and Engineering all top 5 Fields 62 Biology and other natural sciences (92-XX) 39 Ordinary differential equations (34-XX) 23 Dynamical systems and ergodic theory (37-XX) 6 Partial differential equations (35-XX) 6 Systems theory; control (93-XX) 5 Integral equations (45-XX) 5 Numerical analysis (65-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 3 Statistics (62-XX) 3 Optics, electromagnetic theory (78-XX) 2 Combinatorics (05-XX) 2 Algebraic topology (55-XX) 1 General and overarching topics; collections (00-XX) 1 Nonassociative rings and algebras (17-XX) 1 Category theory; homological algebra (18-XX) 1 Probability theory and stochastic processes (60-XX) 1 Computer science (68-XX) 1 Mechanics of particles and systems (70-XX) 1 Fluid mechanics (76-XX) 1 Statistical mechanics, structure of matter (82-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 70 Publications have been cited 741 times in 478 Documents Cited by ▼ Year ▼ Multi-timescale systems and fast-slow analysis. Zbl 1377.92035 Bertram, Richard; Rubin, Jonathan E. 67 2017 Giant squid-hidden canard: the 3D geometry of the Hodgkin-Huxley model. Zbl 1125.92015 Rubin, Jonathan; Wechselberger, Martin 53 2007 A reduced mathematical model of the acute inflammatory response. I: Derivation of model and analysis of anti-inflammation. Zbl 1441.92013 Reynolds, Angela; Rubin, Jonathan; Clermont, Gilles; Day, Judy; Vodovotz, Yoram; Bard Ermentrout, G. 46 2006 The selection of mixed-mode oscillations in a Hodgkin-Huxley model with multiple timescales. Zbl 1306.34060 Rubin, Jonathan; Wechselberger, Martin 38 2008 Geometric singular perturbation analysis of neuronal dynamics. Zbl 1015.34048 Rubin, Jonathan E.; Terman, David 32 2002 Analysis of a canard mechanism by which excitatory synaptic coupling can synchronize neurons at low firing frequencies. Zbl 1121.34059 Drover, Jonathan; Rubin, Jonathan; Su, Jianzhong; Ermentrout, Bard 26 2004 The dynamic range of bursting in a model respiratory pacemaker network. Zbl 1106.34023 Best, Janet; Borisyuk, Alla; Rubin, Jonathan; Terman, David; Wechselberger, Martin 25 2005 Effects of noise on elliptic bursters. Zbl 1083.37533 Su, Jianzhong; Rubin, Jonathan; Terman, David 24 2004 A reduced mathematical model of the acute inflammatory response. II: Capturing scenarios of repeated endotoxin administration. Zbl 1441.92011 Day, Judy; Rubin, Jonathan; Vodovotz, Yoram; Chow, Carson C.; Reynolds, Angela; Clermont, Gilles 24 2006 Averaging, folded singularities, and torus canards: explaining transitions between bursting and spiking in a coupled neuron model. Zbl 1360.37183 Roberts, Kerry-Lyn; Rubin, Jonathan E.; Wechselberger, Martin 20 2015 Stimulus-driven traveling solutions in continuum neuronal models with a general smooth firing rate function. Zbl 1209.92009 Ermentrout, G. Bard; Jalics, Jozsi Z.; Rubin, Jonathan E. 20 2010 Understanding and distinguishing three-time-scale oscillations: case study in a coupled Morris-Lecar system. Zbl 1329.34094 Nan, Pingyu; Wang, Yangyang; Kirk, Vivien; Rubin, Jonathan E. 19 2015 Interaction of canard and singular Hopf mechanisms in a neural model. Zbl 1241.34058 Curtu, R.; Rubin, J. 18 2011 Existence and stability of standing hole solutions to complex Ginzburg-Landau equations. Zbl 1012.35043 Kapitula, Todd; Rubin, Jonathan 18 2000 Synchronized activity and loss of synchrony among heterogeneous conditional oscillators. Zbl 1015.34027 Rubin, Jonathan; Terman, David 17 2002 Sustained spatial patterns of activity in neuronal populations without recurrent excitation. Zbl 1075.45011 Rubin, Jonathan E.; Troy, William C. 17 2004 Analysis of clustered firing patterns in synaptically coupled networks of oscillators. Zbl 1002.92004 Rubin, Jonathan; Terman, David 17 2000 Settling and asymptotic motion of aerosol particles in a cellular flow field. Zbl 0841.76089 Rubin, J.; Jones, C. K. R. T.; Maxey, M. 15 1995 Mechanistic simulations of inflammation: current state and future prospects. Zbl 1158.92318 Vodovotz, Yoram; Constantine, Gregory; Rubin, Jonathan; Csete, Marie; Voit, Eberhard O.; An, Gary 15 2009 An ensemble of models of the acute inflammatory response to bacterial lipopolysaccharide in rats: results from parameter space reduction. Zbl 1398.92053 Daun, Silvia; Rubin, Jonathan; Vodovotz, Yoram; Roy, Anirban; Parker, Robert; Clermont, Gilles 11 2008 A new frame for an old (phase) portrait: finding rivers and other flow features in the plane. Zbl 1405.34032 Letson, Benjamin; Rubin, Jonathan E. 11 2018 Analysis of interacting local oscillation mechanisms in three-timescale systems. Zbl 1369.34078 Letson, Benjamin; Rubin, Jonathan E.; Vo, Theodore 11 2017 Existence of standing pulse solutions to an inhomogeneous reaction-diffusion system. Zbl 0896.34041 Jones, Christopher K. R. T.; Rubin, Jonathan E. 10 1998 Identifiability of linear and linear-in-parameters dynamical systems from a single trajectory. Zbl 1303.93066 Stanhope, S.; Rubin, J. E.; Swigon, D. 10 2014 Multiple timescale mixed bursting dynamics in a respiratory neuron model. Zbl 1382.92099 Wang, Yangyang; Rubin, Jonathan E. 10 2016 Regular traveling waves in a one-dimensional network of Theta neurons. Zbl 1012.34034 Osan, Remus; Rubin, Jonathan; Ermentrout, Bard 9 2002 LOR for analysis of periodic dynamics: a one-stop shop approach. Zbl 1461.34065 Letson, Benjamin; Rubin, Jonathan E. 9 2020 Cooperation of intrinsic bursting and calcium oscillations underlying activity patterns of model pre-Bötzinger complex neurons. Zbl 1276.92019 Park, Choongseok; Rubin, Jonathan E. 9 2013 Locally contractive dynamics in generalized integrate-and-fire neurons. Zbl 1284.37030 Jimenez, Nicolas D.; Mihalas, Stefan; Brown, Richard; Niebur, Ernst; Rubin, Jonathan 9 2013 Interactions of persistent sodium and calcium-activated nonspecific cationic currents yield dynamically distinct bursting regimes in a model of respiratory neurons. Zbl 1446.92042 Dunmyre, Justin R.; Del Negro, Christopher A.; Rubin, Jonathan E. 9 2011 Wild oscillations in a nonlinear neuron model with resets. II: Mixed-mode oscillations. Zbl 1375.34075 Rubin, Jonathan E.; Signerska-Rynkowska, Justyna; Touboul, Jonathan D.; Vidal, Alexandre 9 2017 Wild oscillations in a nonlinear neuron model with resets. I: Bursting, spike-adding and chaos. Zbl 1371.37032 Rubin, Jonathan E.; Signerska-Rynkowska, Justyna; Touboul, Jonathan D.; Vidal, Alexandre 8 2017 Combinatorial \(N_\infty\) operads. Zbl 1482.55011 Rubin, Jonathan 8 2021 Stability, bifurcations and edge oscillations in standing pulse solutions to an inhomogeneous reaction-diffusion system. Zbl 1089.35511 Rubin, J. E. 7 1999 Point symmetries of conditionally integrable nonlinear evolution equations. Zbl 0722.58026 Rubin, J.; Winternitz, P. 7 1990 Using nonlinear model predictive control to find optimal therapeutic strategies to modulate inflammation. Zbl 1259.92036 Day, Judy; Rubin, Jonathan; Clermont, Gilles 7 2010 Complex bursting dynamics in an embryonic respiratory neuron model. Zbl 1437.92031 Wang, Yangyang; Rubin, Jonathan E. 6 2020 Robustness of solutions of the inverse problem for linear dynamical systems with uncertain data. Zbl 1391.93051 Stanhope, S.; Rubin, J. E.; Swigon, D. 6 2017 Explicit maps to predict activation order in multiphase rhythms of a coupled cell network. Zbl 1291.92046 Rubin, Jonathan E.; Terman, David 5 2012 The geometry of neuronal recruitment. Zbl 1097.92011 Rubin, Jonathan; Bose, Amitabha 5 2006 Oscillatory bursting mechnisms in respiratory pacemaker neurons and networks. Zbl 1404.92046 Butera, Robert; Rubin, Jonathan; Terman, David; Smith, Jeffrey 4 2005 Mathematical modeling of energy consumption in the acute inflammatory response. Zbl 1406.92114 Ramirez-Zuniga, Ivan; Rubin, Jonathan E.; Swigon, David; Clermont, Gilles 4 2019 Direct complements of invariant Lagrangian subspaces and minimal factorizations of skew-symmetric rational matrix functions. Zbl 0780.15009 Ran, André C. M.; Rodman, Leiba; Rubin, Jonathan E. 4 1993 Optimal intrinsic dynamics for bursting in a three-cell network. Zbl 1195.34068 Dunmyre, Justin R.; Rubin, Jonathan E. 4 2010 The firing of an excitable neuron in the presence of stochastic trains of strong synaptic inputs. Zbl 1115.92012 Rubin, Jonathan; Josić, Krešimir 4 2007 Identification of affine dynamical systems from a single trajectory. Zbl 1451.34021 Duan, X.; Rubin, J. E.; Swigon, D. 4 2020 Multiple-spike waves in a one-dimensional integrate-and-fire neural network. Zbl 1063.92015 Oşan, Remus; Curtu, Rodica; Rubin, Jonathan; Ermentrout, Bard 3 2004 On the importance of the Jacobian determinant in parameter inference for random parameter and random measurement error models. Zbl 1433.62091 Swigon, David; Stanhope, Shelby R.; Zenker, Sven; Rubin, Jonathan E. 3 2019 Timescales and mechanisms of sigh-like bursting and spiking in models of rhythmic respiratory neurons. Zbl 1395.92048 Wang, Yangyang; Rubin, Jonathan E. 3 2017 Tailoring inputs to achieve maximal neuronal firing. Zbl 1259.92011 Wang, Jiaoyan; Costello, Willie; Rubin, Jonathan E. 3 2011 First return maps for the dynamics of synaptically coupled conditional bursters. Zbl 1266.37052 Manica, Evandro; Medvedev, Georgi S.; Rubin, Jonathan E. 3 2010 Type III responses to transient inputs in hybrid nonlinear neuron models. Zbl 1476.37107 Rubin, Jonathan E.; Signerska-Rynkowska, Justyna; Touboul, Jonathan D. 3 2021 A boundary value approach to optimization with an application to salmonella competition. Zbl 1335.92085 Young, Glenn; Ermentrout, Bard; Rubin, Jonathan E. 3 2015 Interacting oscillations in neural control of breathing: modeling and qualitative analysis. Zbl 1446.92072 Rubin, Jonathan E.; Bacak, Bartholomew J.; Molkov, Yaroslav I.; Shevtsova, Natalia A.; Smith, Jeffrey C.; Rybak, Ilya A. 2 2011 Local orthogonal rectification: deriving natural coordinates to study flows relative to manifolds. Zbl 1450.34014 Letson, Benjamin; Rubin, Jonathan E. 2 2020 A nonlocal eigenvalue problem for the stability of a traveling wave in a neuronal medium. Zbl 1052.92018 Rubin, Jonathan E. 2 2004 Coherent behavior in neuronal networks. Some papers based on the presentations at the workshop, Mallorca, Spain, October 17–20, 2007. Zbl 1321.92033 2 2009 Conditions for multi-functionality in a rhythm generating network inspired by turtle scratching. Zbl 1351.92011 Snyder, Abigail C.; Rubin, Jonathan E. 2 2015 Traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators. Zbl 1364.34043 Duanmu, M.; Whitaker, N.; Kevrekidis, P. G.; Vainchtein, A.; Rubin, J. E. 2 2016 Slow negative feedback enhances robustness of square-wave bursting. Zbl 1518.92031 John, Sushmita Rose; Krauskopf, Bernd; Osinga, Hinke M.; Rubin, Jonathan E. 2 2023 Dynamics of ramping bursts in a respiratory neuron model. Zbl 1494.92032 Abdulla, Muhammad U.; Phillips, Ryan S.; Rubin, Jonathan E. 2 2022 Corticostriatal synaptic weight evolution in a two-alternative forced choice task: a computational study. Zbl 1453.92025 Vich, C.; Dunovan, K.; Verstynen, Timothy; Rubin, J. 1 2020 Interactions of solitary pulses of E. coli in a one-dimensional nutrient gradient. Zbl 1451.92209 Young, Glenn; Demir, Mahmut; Salman, Hanna; Ermentrout, G. Bard; Rubin, Jonathan E. 1 2019 Deriving information about architecture from activity patterns in coupled cell systems. Zbl 1090.34041 Josic, Kresimir; Rubin, Jonathan 1 2005 Competition between transients in the rate of approach to a fixed point. Zbl 1185.37037 Day, Judy; Rubin, Jonathan E.; Chow, Carson C. 1 2009 The roles of ascending sensory signals and top-down central control in the entrainment of a locomotor CPG. Zbl 1460.92035 Codianni, Marcello G.; Daun, Silvia; Rubin, Jonathan E. 1 2020 The dynamics of a forced coupled network of active elements. Zbl 1214.37058 Parks, Helen F.; Ermentrout, Bard; Rubin, Jonathan E. 1 2011 A novel mechanism for ramping bursts based on slow negative feedback in model respiratory neurons. Zbl 07901178 John, Sushmita R.; Phillips, Ryan S.; Rubin, Jonathan E. 1 2024 A data-driven model of the role of energy in sepsis. Zbl 1480.92049 Ramirez-Zuniga, Ivan; Rubin, Jonathan. E.; Swigon, David; Redl, Heinz; Clermont, Gilles 1 2022 Qualitative inverse problems: mapping data to the features of trajectories and parameter values of an ODE model. Zbl 07691091 Duan, X.; Rubin, J. E.; Swigon, D. 1 2023 A novel mechanism for ramping bursts based on slow negative feedback in model respiratory neurons. Zbl 07901178 John, Sushmita R.; Phillips, Ryan S.; Rubin, Jonathan E. 1 2024 Slow negative feedback enhances robustness of square-wave bursting. Zbl 1518.92031 John, Sushmita Rose; Krauskopf, Bernd; Osinga, Hinke M.; Rubin, Jonathan E. 2 2023 Qualitative inverse problems: mapping data to the features of trajectories and parameter values of an ODE model. Zbl 07691091 Duan, X.; Rubin, J. E.; Swigon, D. 1 2023 Dynamics of ramping bursts in a respiratory neuron model. Zbl 1494.92032 Abdulla, Muhammad U.; Phillips, Ryan S.; Rubin, Jonathan E. 2 2022 A data-driven model of the role of energy in sepsis. Zbl 1480.92049 Ramirez-Zuniga, Ivan; Rubin, Jonathan. E.; Swigon, David; Redl, Heinz; Clermont, Gilles 1 2022 Combinatorial \(N_\infty\) operads. Zbl 1482.55011 Rubin, Jonathan 8 2021 Type III responses to transient inputs in hybrid nonlinear neuron models. Zbl 1476.37107 Rubin, Jonathan E.; Signerska-Rynkowska, Justyna; Touboul, Jonathan D. 3 2021 LOR for analysis of periodic dynamics: a one-stop shop approach. Zbl 1461.34065 Letson, Benjamin; Rubin, Jonathan E. 9 2020 Complex bursting dynamics in an embryonic respiratory neuron model. Zbl 1437.92031 Wang, Yangyang; Rubin, Jonathan E. 6 2020 Identification of affine dynamical systems from a single trajectory. Zbl 1451.34021 Duan, X.; Rubin, J. E.; Swigon, D. 4 2020 Local orthogonal rectification: deriving natural coordinates to study flows relative to manifolds. Zbl 1450.34014 Letson, Benjamin; Rubin, Jonathan E. 2 2020 Corticostriatal synaptic weight evolution in a two-alternative forced choice task: a computational study. Zbl 1453.92025 Vich, C.; Dunovan, K.; Verstynen, Timothy; Rubin, J. 1 2020 The roles of ascending sensory signals and top-down central control in the entrainment of a locomotor CPG. Zbl 1460.92035 Codianni, Marcello G.; Daun, Silvia; Rubin, Jonathan E. 1 2020 Mathematical modeling of energy consumption in the acute inflammatory response. Zbl 1406.92114 Ramirez-Zuniga, Ivan; Rubin, Jonathan E.; Swigon, David; Clermont, Gilles 4 2019 On the importance of the Jacobian determinant in parameter inference for random parameter and random measurement error models. Zbl 1433.62091 Swigon, David; Stanhope, Shelby R.; Zenker, Sven; Rubin, Jonathan E. 3 2019 Interactions of solitary pulses of E. coli in a one-dimensional nutrient gradient. Zbl 1451.92209 Young, Glenn; Demir, Mahmut; Salman, Hanna; Ermentrout, G. Bard; Rubin, Jonathan E. 1 2019 A new frame for an old (phase) portrait: finding rivers and other flow features in the plane. Zbl 1405.34032 Letson, Benjamin; Rubin, Jonathan E. 11 2018 Multi-timescale systems and fast-slow analysis. Zbl 1377.92035 Bertram, Richard; Rubin, Jonathan E. 67 2017 Analysis of interacting local oscillation mechanisms in three-timescale systems. Zbl 1369.34078 Letson, Benjamin; Rubin, Jonathan E.; Vo, Theodore 11 2017 Wild oscillations in a nonlinear neuron model with resets. II: Mixed-mode oscillations. Zbl 1375.34075 Rubin, Jonathan E.; Signerska-Rynkowska, Justyna; Touboul, Jonathan D.; Vidal, Alexandre 9 2017 Wild oscillations in a nonlinear neuron model with resets. I: Bursting, spike-adding and chaos. Zbl 1371.37032 Rubin, Jonathan E.; Signerska-Rynkowska, Justyna; Touboul, Jonathan D.; Vidal, Alexandre 8 2017 Robustness of solutions of the inverse problem for linear dynamical systems with uncertain data. Zbl 1391.93051 Stanhope, S.; Rubin, J. E.; Swigon, D. 6 2017 Timescales and mechanisms of sigh-like bursting and spiking in models of rhythmic respiratory neurons. Zbl 1395.92048 Wang, Yangyang; Rubin, Jonathan E. 3 2017 Multiple timescale mixed bursting dynamics in a respiratory neuron model. Zbl 1382.92099 Wang, Yangyang; Rubin, Jonathan E. 10 2016 Traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators. Zbl 1364.34043 Duanmu, M.; Whitaker, N.; Kevrekidis, P. G.; Vainchtein, A.; Rubin, J. E. 2 2016 Averaging, folded singularities, and torus canards: explaining transitions between bursting and spiking in a coupled neuron model. Zbl 1360.37183 Roberts, Kerry-Lyn; Rubin, Jonathan E.; Wechselberger, Martin 20 2015 Understanding and distinguishing three-time-scale oscillations: case study in a coupled Morris-Lecar system. Zbl 1329.34094 Nan, Pingyu; Wang, Yangyang; Kirk, Vivien; Rubin, Jonathan E. 19 2015 A boundary value approach to optimization with an application to salmonella competition. Zbl 1335.92085 Young, Glenn; Ermentrout, Bard; Rubin, Jonathan E. 3 2015 Conditions for multi-functionality in a rhythm generating network inspired by turtle scratching. Zbl 1351.92011 Snyder, Abigail C.; Rubin, Jonathan E. 2 2015 Identifiability of linear and linear-in-parameters dynamical systems from a single trajectory. Zbl 1303.93066 Stanhope, S.; Rubin, J. E.; Swigon, D. 10 2014 Cooperation of intrinsic bursting and calcium oscillations underlying activity patterns of model pre-Bötzinger complex neurons. Zbl 1276.92019 Park, Choongseok; Rubin, Jonathan E. 9 2013 Locally contractive dynamics in generalized integrate-and-fire neurons. Zbl 1284.37030 Jimenez, Nicolas D.; Mihalas, Stefan; Brown, Richard; Niebur, Ernst; Rubin, Jonathan 9 2013 Explicit maps to predict activation order in multiphase rhythms of a coupled cell network. Zbl 1291.92046 Rubin, Jonathan E.; Terman, David 5 2012 Interaction of canard and singular Hopf mechanisms in a neural model. Zbl 1241.34058 Curtu, R.; Rubin, J. 18 2011 Interactions of persistent sodium and calcium-activated nonspecific cationic currents yield dynamically distinct bursting regimes in a model of respiratory neurons. Zbl 1446.92042 Dunmyre, Justin R.; Del Negro, Christopher A.; Rubin, Jonathan E. 9 2011 Tailoring inputs to achieve maximal neuronal firing. Zbl 1259.92011 Wang, Jiaoyan; Costello, Willie; Rubin, Jonathan E. 3 2011 Interacting oscillations in neural control of breathing: modeling and qualitative analysis. Zbl 1446.92072 Rubin, Jonathan E.; Bacak, Bartholomew J.; Molkov, Yaroslav I.; Shevtsova, Natalia A.; Smith, Jeffrey C.; Rybak, Ilya A. 2 2011 The dynamics of a forced coupled network of active elements. Zbl 1214.37058 Parks, Helen F.; Ermentrout, Bard; Rubin, Jonathan E. 1 2011 Stimulus-driven traveling solutions in continuum neuronal models with a general smooth firing rate function. Zbl 1209.92009 Ermentrout, G. Bard; Jalics, Jozsi Z.; Rubin, Jonathan E. 20 2010 Using nonlinear model predictive control to find optimal therapeutic strategies to modulate inflammation. Zbl 1259.92036 Day, Judy; Rubin, Jonathan; Clermont, Gilles 7 2010 Optimal intrinsic dynamics for bursting in a three-cell network. Zbl 1195.34068 Dunmyre, Justin R.; Rubin, Jonathan E. 4 2010 First return maps for the dynamics of synaptically coupled conditional bursters. Zbl 1266.37052 Manica, Evandro; Medvedev, Georgi S.; Rubin, Jonathan E. 3 2010 Mechanistic simulations of inflammation: current state and future prospects. Zbl 1158.92318 Vodovotz, Yoram; Constantine, Gregory; Rubin, Jonathan; Csete, Marie; Voit, Eberhard O.; An, Gary 15 2009 Coherent behavior in neuronal networks. Some papers based on the presentations at the workshop, Mallorca, Spain, October 17–20, 2007. Zbl 1321.92033 2 2009 Competition between transients in the rate of approach to a fixed point. Zbl 1185.37037 Day, Judy; Rubin, Jonathan E.; Chow, Carson C. 1 2009 The selection of mixed-mode oscillations in a Hodgkin-Huxley model with multiple timescales. Zbl 1306.34060 Rubin, Jonathan; Wechselberger, Martin 38 2008 An ensemble of models of the acute inflammatory response to bacterial lipopolysaccharide in rats: results from parameter space reduction. Zbl 1398.92053 Daun, Silvia; Rubin, Jonathan; Vodovotz, Yoram; Roy, Anirban; Parker, Robert; Clermont, Gilles 11 2008 Giant squid-hidden canard: the 3D geometry of the Hodgkin-Huxley model. Zbl 1125.92015 Rubin, Jonathan; Wechselberger, Martin 53 2007 The firing of an excitable neuron in the presence of stochastic trains of strong synaptic inputs. Zbl 1115.92012 Rubin, Jonathan; Josić, Krešimir 4 2007 A reduced mathematical model of the acute inflammatory response. I: Derivation of model and analysis of anti-inflammation. Zbl 1441.92013 Reynolds, Angela; Rubin, Jonathan; Clermont, Gilles; Day, Judy; Vodovotz, Yoram; Bard Ermentrout, G. 46 2006 A reduced mathematical model of the acute inflammatory response. II: Capturing scenarios of repeated endotoxin administration. Zbl 1441.92011 Day, Judy; Rubin, Jonathan; Vodovotz, Yoram; Chow, Carson C.; Reynolds, Angela; Clermont, Gilles 24 2006 The geometry of neuronal recruitment. Zbl 1097.92011 Rubin, Jonathan; Bose, Amitabha 5 2006 The dynamic range of bursting in a model respiratory pacemaker network. Zbl 1106.34023 Best, Janet; Borisyuk, Alla; Rubin, Jonathan; Terman, David; Wechselberger, Martin 25 2005 Oscillatory bursting mechnisms in respiratory pacemaker neurons and networks. Zbl 1404.92046 Butera, Robert; Rubin, Jonathan; Terman, David; Smith, Jeffrey 4 2005 Deriving information about architecture from activity patterns in coupled cell systems. Zbl 1090.34041 Josic, Kresimir; Rubin, Jonathan 1 2005 Analysis of a canard mechanism by which excitatory synaptic coupling can synchronize neurons at low firing frequencies. Zbl 1121.34059 Drover, Jonathan; Rubin, Jonathan; Su, Jianzhong; Ermentrout, Bard 26 2004 Effects of noise on elliptic bursters. Zbl 1083.37533 Su, Jianzhong; Rubin, Jonathan; Terman, David 24 2004 Sustained spatial patterns of activity in neuronal populations without recurrent excitation. Zbl 1075.45011 Rubin, Jonathan E.; Troy, William C. 17 2004 Multiple-spike waves in a one-dimensional integrate-and-fire neural network. Zbl 1063.92015 Oşan, Remus; Curtu, Rodica; Rubin, Jonathan; Ermentrout, Bard 3 2004 A nonlocal eigenvalue problem for the stability of a traveling wave in a neuronal medium. Zbl 1052.92018 Rubin, Jonathan E. 2 2004 Geometric singular perturbation analysis of neuronal dynamics. Zbl 1015.34048 Rubin, Jonathan E.; Terman, David 32 2002 Synchronized activity and loss of synchrony among heterogeneous conditional oscillators. Zbl 1015.34027 Rubin, Jonathan; Terman, David 17 2002 Regular traveling waves in a one-dimensional network of Theta neurons. Zbl 1012.34034 Osan, Remus; Rubin, Jonathan; Ermentrout, Bard 9 2002 Existence and stability of standing hole solutions to complex Ginzburg-Landau equations. Zbl 1012.35043 Kapitula, Todd; Rubin, Jonathan 18 2000 Analysis of clustered firing patterns in synaptically coupled networks of oscillators. Zbl 1002.92004 Rubin, Jonathan; Terman, David 17 2000 Stability, bifurcations and edge oscillations in standing pulse solutions to an inhomogeneous reaction-diffusion system. Zbl 1089.35511 Rubin, J. E. 7 1999 Existence of standing pulse solutions to an inhomogeneous reaction-diffusion system. Zbl 0896.34041 Jones, Christopher K. R. T.; Rubin, Jonathan E. 10 1998 Settling and asymptotic motion of aerosol particles in a cellular flow field. Zbl 0841.76089 Rubin, J.; Jones, C. K. R. T.; Maxey, M. 15 1995 Direct complements of invariant Lagrangian subspaces and minimal factorizations of skew-symmetric rational matrix functions. Zbl 0780.15009 Ran, André C. M.; Rodman, Leiba; Rubin, Jonathan E. 4 1993 Point symmetries of conditionally integrable nonlinear evolution equations. Zbl 0722.58026 Rubin, J.; Winternitz, P. 7 1990 all cited Publications top 5 cited Publications all top 5 Cited by 828 Authors 41 Rubin, Jonathan E. 17 Wechselberger, Martin 15 Desroches, Mathieu 15 Vo, Theodore 13 Krupa, Martin 10 Kühn, Christian 9 Ermentrout, George Bard 9 Sun, Xiaobin 9 Xie, Yingchao 8 Bertram, Richard 8 Kaper, Tasso J. 8 Rotstein, Horacio G. 8 Signerska-Rynkowska, Justyna 8 Swigon, David 8 Wilson, Dan D. 7 Kirk, Vivien 7 Lafortune, Stéphane 7 Shilnikov, Andrey L. 7 Terman, David Hillel 7 Vodovotz, Yoram 6 Bi, Qinsheng 6 Clermont, Gilles 6 Day, Judy D. 6 Duan, Lixia 6 Laing, Carlo R. 6 Osinga, Hinke Maria 6 Popović, Nikola 5 Androulakis, Ioannis P. 5 Bose, Amitabha 5 da Silva, Severino Horácio 5 Ermentrout, Bard G. 5 Haller, George 5 Kilpatrick, Zachary P. 5 Krauskopf, Bernd 5 Liu, Shenquan 5 Liu, Wei 5 Olufsen, Mette Sofie 5 Ottesen, Johnny Tom 5 Sneyd, James 5 Tabak, Joël 5 Touboul, Jonathan David 5 Vidal, Alexandre 5 Wang, Yangyang 4 Belykh, Igor V. 4 Bressloff, Paul C. 4 Campbell, Sue Ann 4 Coombes, Stephen 4 De Maesschalck, Peter 4 Einevoll, Gaute T. 4 Ersöz, Elif Köksal 4 Ghazaryan, Anna R. 4 Kevrekidis, Ioannis George 4 Letson, Benjamin 4 Li, Shihu 4 Medvedev, Georgi S. 4 Park, Choongseok 4 Pei, Bin 4 Rodrigues, Serafim 4 Song, Jian 4 Thieullen, Michèle 4 Thomas, Peter J. 4 Uldall Kristiansen, K. 4 Voit, Eberhard Otto 4 Wyller, John A. 4 Xu, Yong 3 Ahn, Sungwoo 3 Avitabile, Daniele 3 Awal, Naziru M. 3 Bartłomiejczyk, Piotr 3 Bel, Andrea L. 3 Canavier, Carmen C. 3 Chen, Guanrong 3 Djouadi, Seddik M. 3 Duan, Jinqiao 3 Duan, Xiaoyu 3 Dunster, Joanne L. 3 Eilertsen, Justin S. 3 Epstein, Irving R. 3 Fernández-García, Soledad 3 Granados, Albert 3 Hong, Wei 3 Jardón-Kojakhmetov, Hildeberto 3 Kaklamanos, Panagiotis 3 Kopell, Nancy J. 3 Llovera Trujillo, Frank 3 Manukian, Vahagn 3 Marasco, Addolorata 3 Migliore, Michele 3 Park, Youngmin 3 Pereira, Antônio Luiz 3 Rankin, James 3 Röckner, Michael 3 Sapsis, Themistoklis P. 3 Schnell, Santiago 3 Sensi, Mattia 3 Su, Jianzhong 3 Wang, Jiaoyan 3 Young, Glenn 3 Zhang, Xiaofang 3 Zhao, Na ...and 728 more Authors all top 5 Cited in 92 Serials 48 Physica D 39 SIAM Journal on Applied Dynamical Systems 36 Chaos 33 Journal of Theoretical Biology 25 Journal of Computational Neuroscience 23 Mathematical Biosciences 20 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 17 The Journal of Mathematical Neuroscience 16 Communications in Nonlinear Science and Numerical Simulation 15 Journal of Mathematical Biology 14 Journal of Differential Equations 13 Biological Cybernetics 13 Bulletin of Mathematical Biology 11 Journal of Nonlinear Science 10 Discrete and Continuous Dynamical Systems. Series B 9 SIAM Journal on Applied Mathematics 6 Chaos, Solitons and Fractals 6 Journal of Dynamics and Differential Equations 5 Neural Computation 4 Linear Algebra and its Applications 4 Physics of Fluids 4 Nonlinear Dynamics 4 Nonlinear Analysis. Real World Applications 4 Mathematical Modelling of Natural Phenomena 4 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 3 Inverse Problems 3 Mathematical Methods in the Applied Sciences 3 SIAM Journal on Mathematical Analysis 3 SIAM Review 3 Differential Equations and Dynamical Systems 3 Mathematical Biosciences and Engineering 3 SIAM/ASA Journal on Uncertainty Quantification 3 Electronic Research Archive 2 Communications in Mathematical Physics 2 Journal of Computational Physics 2 Applied Mathematics and Computation 2 Applied Mathematics and Optimization 2 Transactions of the American Mathematical Society 2 Neural Networks 2 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 2 Discrete and Continuous Dynamical Systems. Series S 1 International Journal of Control 1 Journal of Fluid Mechanics 1 Journal of Mathematical Analysis and Applications 1 Journal of Statistical Physics 1 Nonlinearity 1 Physics Letters. A 1 Physics Reports 1 Reviews of Modern Physics 1 International Journal of Mathematics and Mathematical Sciences 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Ricerche di Matematica 1 Studies in Applied Mathematics 1 Theoretical Computer Science 1 Zeitschrift für Analysis und ihre Anwendungen 1 Stochastic Analysis and Applications 1 Acta Mathematicae Applicatae Sinica. English Series 1 European Journal of Applied Mathematics 1 Japan Journal of Industrial and Applied Mathematics 1 Applied Mathematical Modelling 1 Automation and Remote Control 1 International Journal of Computer Mathematics 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Stochastic Processes and their Applications 1 Topological Methods in Nonlinear Analysis 1 NoDEA. Nonlinear Differential Equations and Applications 1 Complexity 1 Bernoulli 1 Mathematical Problems in Engineering 1 Mathematical Physics, Analysis and Geometry 1 Regular and Chaotic Dynamics 1 International Journal of Applied Mathematics and Computer Science 1 Journal of Biological Systems 1 Qualitative Theory of Dynamical Systems 1 International Journal of Nonlinear Sciences and Numerical Simulation 1 Dynamical Systems 1 Stochastics and Dynamics 1 Multiscale Modeling & Simulation 1 Computational Biology and Chemistry 1 Journal of Statistical Mechanics: Theory and Experiment 1 Computational & Mathematical Methods in Medicine 1 São Paulo Journal of Mathematical Sciences 1 Advances in Mathematical Physics 1 Journal of Computational Dynamics 1 ISRN Biomathematics 1 Discontinuity, Nonlinearity, and Complexity 1 Nelineĭnaya Dinamika 1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Applied Mathematics and Nonlinear Sciences 1 SN Partial Differential Equations and Applications 1 Mathematics in Applied Sciences and Engineering 1 Frontiers of Mathematics all top 5 Cited in 32 Fields 308 Biology and other natural sciences (92-XX) 206 Ordinary differential equations (34-XX) 127 Dynamical systems and ergodic theory (37-XX) 76 Partial differential equations (35-XX) 38 Probability theory and stochastic processes (60-XX) 28 Mechanics of particles and systems (70-XX) 21 Integral equations (45-XX) 20 Numerical analysis (65-XX) 20 Systems theory; control (93-XX) 19 Fluid mechanics (76-XX) 8 Statistical mechanics, structure of matter (82-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 5 Operator theory (47-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 5 Statistics (62-XX) 5 Mechanics of deformable solids (74-XX) 5 Geophysics (86-XX) 4 Computer science (68-XX) 4 Optics, electromagnetic theory (78-XX) 4 Operations research, mathematical programming (90-XX) 3 Difference and functional equations (39-XX) 3 Functional analysis (46-XX) 3 Classical thermodynamics, heat transfer (80-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Information and communication theory, circuits (94-XX) 2 Combinatorics (05-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Quantum theory (81-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Differential geometry (53-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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