Edit Profile (opens in new tab) Rand, Richard H. Compute Distance To: Compute Author ID: rand.richard-h Published as: Rand, Richard H.; Rand, Richard; Rand, R. H.; Rand, R. more...less Documents Indexed: 134 Publications since 1967, including 3 Books 1 Further Contribution Biographic References: 1 Publication Co-Authors: 86 Co-Authors with 116 Joint Publications 986 Co-Co-Authors all top 5 Co-Authors 13 single-authored 9 Wesson, Elizabeth N. 7 Pender, Jamol 6 Sah, Si Mohamed 5 Coppola, Vincent T. 5 Storti, Duane W. 5 Vakakis, Alexander F. 5 Verdugo, Anael 5 Zounes, Randolph S. 4 Keith, William L. 4 Ng, Leslie 4 Zehnder, Alan T. 3 Belhaq, Mohamed 3 Bridge, Jacqueline 3 Heckman, Christoffer R. 3 Month, Leslie Anne 3 Morrison, Tina M. 3 Recktenwald, Geoffrey 3 Ruelas, Rocio E. 3 Sheheitli, Hiba 3 Suchorsky, Meghan Kathleen 3 Tseng, Shoei-Fu 2 Abouhazim, Nazha 2 Bhaskar, Aditya 2 Chakraborty, Tapesh 2 Cooke, J. R. 2 Guckenheimer, John M. 2 Haberman, Richard 2 Hastings, Rachel 2 Holmes, Philip J. 2 Howland, Howard 2 Kinsey, R. J. 2 Kovacic, Ivana 2 Len, Jonathan L. 2 Mendelowitz, Lee 2 Mingori, D. Lewis 2 Moon, Francis C. 2 Niklas, K. J. 2 Novitzky, Sophia 2 Pandey, Manoj Kumar 2 Quinn, D. Dane 2 Ramani, Deepak V. 2 Rand, David G. 2 Schlomiuk, Dana I. 2 Shayak, B. 2 Upadhyaya, Shrinivasa K. 2 Wirkus, Stephen A. 1 Adaricheva, Kira Vladislavovna 1 Alfriend, Kyle T. 1 Armbruster, Dieter 1 Barcilon, Albert 1 Bernstein, Alexander 1 Block, Henry David 1 Camacho, Erika T. 1 Cao, Shiping 1 Caswell, Hal 1 Chati, M. 1 Cohen, Avis H. 1 Coniglio, Anthony 1 de Wolff, Babette A. J. 1 Dercole, Fabio 1 DiMaggio, Frank L. 1 Doldo, Philip 1 Ellenson, J. L. 1 Fiedler, Bernold 1 Gilmour, Robert F. jun. 1 Gladman, Brett 1 Golnaraghi, M. Farid 1 Gross, Louis J. 1 Guennoun, Kamar 1 Holmes, Catherine A. 1 Johnson, I. R. 1 Johnson, Timothy Lee 1 Kotas, Jakob 1 Lakrad, Faouzi 1 Lewis, Donald C. 1 Li, Guangxuan 1 Lubkin, Sharon R. 1 Miura, Robert M. 1 Nation, James B. 1 Newman, A. L. 1 Newman, William I. 1 Nicholson, Phil 1 Nieto, Alejandro López 1 Niu, Xueyan 1 O’Neil, Michael 1 Rompala, Kevin 1 Roughgarden, Joan 1 Rozhkov, Igor 1 Ruina, Andy L. 1 Schneider, Isabelle 1 Sen, Asok K. 1 Shaw, Steven W. 1 Strichartz, Robert S. 1 Stubna, Michael D. 1 Thornley, John H. M. 1 Wong, Jeffrey T. 1 Woods, Steven D. 1 Yazhbin, Max 1 Yuster, Thomas all top 5 Serials 22 International Journal of Non-Linear Mechanics 21 Nonlinear Dynamics 17 Communications in Nonlinear Science and Numerical Simulation 7 Journal of Mathematical Biology 6 Journal of Applied Mechanics 6 Journal of Applied Nonlinear Dynamics 4 Mechanics Research Communications 3 Acta Mechanica 3 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 3 Journal of Vibration and Control 2 Journal of the Acoustical Society of America 2 SIAM Journal on Applied Mathematics 2 Communications on Pure and Applied Analysis 2 SIAM Journal on Applied Dynamical Systems 1 AIAA Journal 1 Discrete Applied Mathematics 1 International Journal of Solids and Structures 1 Journal of Sound and Vibration 1 Nonlinearity 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Chaos, Solitons and Fractals 1 Journal of Guidance, Control and Dynamics 1 Applied Mathematics and Computation 1 Journal of Differential Equations 1 Mathematics of Operations Research 1 Dynamics and Stability of Systems 1 Queueing Systems 1 Expositiones Mathematicae 1 Celestial Mechanics and Dynamical Astronomy 1 Journal of Difference Equations and Applications 1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 1 Chaos 1 Applied Mathematical Sciences 1 Lectures on Mathematics in the Life Sciences 1 The College Mathematics Journal 1 Dynamic Games and Applications all top 5 Fields 68 Ordinary differential equations (34-XX) 54 Mechanics of particles and systems (70-XX) 21 Dynamical systems and ergodic theory (37-XX) 16 Biology and other natural sciences (92-XX) 8 Computer science (68-XX) 7 Mechanics of deformable solids (74-XX) 7 Operations research, mathematical programming (90-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Partial differential equations (35-XX) 4 Numerical analysis (65-XX) 3 Fluid mechanics (76-XX) 2 Special functions (33-XX) 2 Probability theory and stochastic processes (60-XX) 2 Systems theory; control (93-XX) 1 Mathematical logic and foundations (03-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Measure and integration (28-XX) 1 Difference and functional equations (39-XX) 1 Integral equations (45-XX) 1 Statistics (62-XX) 1 Optics, electromagnetic theory (78-XX) 1 Statistical mechanics, structure of matter (82-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 113 Publications have been cited 996 times in 685 Documents Cited by ▼ Year ▼ Perturbation methods, bifurcation theory and computer algebra. Zbl 0651.34001Rand, Richard H.; Armbruster, Dieter 60 1987 The nature of the coupling between segmental oscillators of the lamprey spinal generator for locomotion: a mathematical model. Zbl 0476.92003Cohen, Avis H.; Holmes, Philip J.; Rand, Richard H. 55 1982 Bifurcation of periodic motions in two weakly coupled van der Pol oscillators. Zbl 0447.70028Rand, R. H.; Holmes, P. J. 47 1980 The dynamics of two coupled van der Pol oscillators with delay coupling. Zbl 1021.70010Wirkus, Stephen; Rand, Richard 42 2002 Computer algebra in applied mathematics: an introduction to MACSYMA. Zbl 0583.68012Rand, R. H. 37 1984 The transition to chaos in a simple mechanical system. Zbl 0666.70030Shaw, Steven W.; Rand, Richard H. 32 1989 Averaging using elliptic functions: Approximation of limit cycles. Zbl 0699.34032Coppola, V. T.; Rand, R. H. 29 1990 Dynamics of three coupled van der Pol oscillators with application to circadian rhythms. Zbl 1120.34025Rompala, Kevin; Rand, Richard; Howland, Howard 26 2007 The transition from phase locking to drift in a system of two weakly coupled Van Der Pol oscillators. Zbl 0667.70028Chakraborty, Tapesh; Rand, Richard H. 25 1988 Integrability of plane quadratic vector fields. Zbl 0693.34030Schlomiuk, Dana; Guckenheimer, John; Rand, Richard 25 1990 Transition curves for the quasi-periodic Mathieu equation. Zbl 0916.34031Zounes, Randolph S.; Rand, Richard H. 24 1998 Queues with choice via delay differential equations. Zbl 1366.90082Pender, Jamol; Rand, Richard H.; Wesson, Elizabeth 23 2017 2:2:1 resonance in the quasiperiodic Mathieu equation. Zbl 1062.70596Rand, Richard; Guennoun, Kamar; Belhaq, Mohamed 21 2003 Hopf bifurcation in a DDE model of gene expression. Zbl 1134.34325Verdugo, Anael; Rand, Richard 20 2008 Dynamics of two van der Pol oscillators coupled via a bath. Zbl 1052.70013Camacho, Erika; Rand, Richard; Howland, Howard 19 2004 Hopf bifurcation formula for first order differential-delay equations. Zbl 1123.34334Rand, Richard; Verdugo, Anael 19 2007 Dynamics of two strongly coupled van der Pol oscillators. Zbl 0498.70037Storti, D. W.; Rand, R. H. 19 1982 Bifurcations in a Mathieu equation with cubic nonlinearities. Zbl 1029.70009Ng, Leslie; Rand, Richard 19 2002 An analysis of queues with delayed information and time-varying arrival rates. Zbl 1392.90055Pender, Jamol; Rand, Richard H.; Wesson, Elizabeth 17 2018 Global behavior of a nonlinear quasiperiodic Mathieu equation. Zbl 1003.34041Zounes, Randolph S.; Rand, Richard H. 16 2002 Modal analysis of a cracked beam. Zbl 1235.74056Chati, M.; Rand, R.; Mukherjee, S. 15 1997 Bifurcations and chaos in a forced zero-stiffness impact oscillator. Zbl 0714.73049Li, G. X.; Rand, R. H.; Moon, F. C. 15 1990 Ordered direct implicational basis of a finite closure system. Zbl 1288.06007Adaricheva, K.; Nation, J. B.; Rand, R. 14 2013 Dynamics of spinup through resonance. Zbl 0825.70085Rand, R. H.; Kinsey, R. J.; Mingori, D. L. 12 1992 Analytical approximation for period-doubling following a Hopf bifurcation. Zbl 0684.58030Rand, Richard H. 12 1989 Perturbation analysis of entrainment in a micromechanical limit cycle oscillator. Zbl 1124.34026Pandey, Manoj; Rand, Richard; Zehnder, Alan 12 2007 \(2:1\) Resonance in the delayed nonlinear Mathieu equation. Zbl 1193.70031Morrison, Tina M.; Rand, Richard H. 12 2007 Normal modes and global dynamics of a two-degree-of-freedom non-linear system. I: Low energies. Zbl 0765.70014Vakakis, A. F.; Rand, R. H. 11 1992 Hopf bifurcations in delayed rock-paper-scissors replicator dynamics. Zbl 1348.91051Wesson, Elizabeth; Rand, Richard 11 2016 A direct method for non-linear normal modes. Zbl 0296.70021Rand, Richard H. 11 1974 Frequency locking in a forced Mathieu–Van der Pol–Duffing system. Zbl 1279.34042Pandey, Manoj; Rand, Richard H.; Zehnder, Alan T. 11 2008 Degenerate homoclinic cycles in perturbations of quadratic Hamiltonian systems. Zbl 0677.58038Guckenheimer, John; Rand, Richard; Schlomiuk, Dana 10 1989 Subharmonic resonance in the nonlinear Mathieu equation. Zbl 1116.34322Zounes, Randolph S.; Rand, Richard H. 10 2002 \(2:1:1\) resonance in the quasi-periodic Mathieu equation. Zbl 1132.34041Rand, Richard; Morrison, Tina 10 2005 A stochastic analysis of queues with customer choice and delayed information. Zbl 1466.60190Pender, Jamol; Rand, Richard; Wesson, Elizabeth 9 2020 Center manifold analysis of a DDE model of gene expression. Zbl 1221.37197Verdugo, Anael; Rand, Richard 9 2008 Dynamics of three coupled limit cycle oscillators with application to artificial intelligence. Zbl 1221.34099Mendelowitz, Lee; Verdugo, Anael; Rand, Richard 9 2009 Nonlinear dynamics in queueing theory: determining the size of oscillations in queues with delay. Zbl 1417.34202Novitzky, Sophia; Pender, Jamol; Rand, Richard H.; Wesson, Elizabeth 8 2019 Hopf bifurcations in two-strategy delayed replicator dynamics. Zbl 1334.34180Wesson, Elizabeth; Rand, Richard; Rand, David 8 2016 Non-linear dynamics of a system of coupled oscillators with essential stiffness non-linearities. Zbl 1348.34073Vakakis, Alexander F.; Rand, Richard H. 8 2004 A pair of van der Pol oscillators coupled by fractional derivatives. Zbl 1258.34074Suchorsky, M. K.; Rand, R. H. 8 2012 Topics in nonlinear dynamics with computer algebra. Zbl 0853.70001Rand, Richard H. 8 1994 Bifurcations in a Mathieu equation with cubic nonlinearities. II. Zbl 1043.34040Ng, Leslie; Rand, Richard 8 2002 Limiting the oscillations in queues with delayed information through a novel type of delay announcement. Zbl 1455.34086Novitzky, Sophia; Pender, Jamol; Rand, Richard H.; Wesson, Elizabeth 7 2020 Dynamics of two strongly coupled relaxation oscillators. Zbl 0589.34043Storti, D. W.; Rand, R. H. 7 1986 A simplified model of coupled relaxation oscillators. Zbl 0614.73024Storti, Duane; Rand, Richard H. 7 1987 Vibrations of fluid-filled spherical and spheroidal shells. Zbl 0161.44304Rand, R.; DiMaggio, F. 7 1967 Stability of the triangular points in the elliptic restricted problem of three bodies. Zbl 0179.53203Alfriend, K. T.; Rand, R. H. 7 1969 Dynamics of four coupled phase-only oscillators. Zbl 1122.70015Rand, Richard; Wong, Jeffrey 7 2008 Using delay to quench undesirable vibrations. Zbl 1218.34085Suchorsky, M. K.; Sah, S. M.; Rand, R. H. 7 2010 Normal modes and global dynamics of a two-degree-of-freedom non-linear system. II: High energies. Zbl 0765.70015Vakakis, A. F.; Rand, R. H. 6 1992 Straight-line backbone curve. Zbl 1304.34071Kovacic, Ivana; Rand, Richard 6 2013 A higher order approximation for non-linear normal modes in two degree of freedom systems. Zbl 0223.34019Rand, Richard H. 6 1971 Analysis of a nonlinear partial difference equation, and its application to cardiac dynamics. Zbl 1012.39004Stubna, Michael D.; Rand, Richard H.; Gilmour, Robert F. jun. 6 2002 Evolutionary dynamics of a system with periodic coefficients. Zbl 1217.91018Rand, Richard H.; Yazhbin, Max; Rand, David G. 5 2011 On the existence and bifurcation of minimal normal modes. Zbl 0421.70029Johnson, T. L.; Rand, R. H. 5 1979 Dynamics of microbubble oscillators with delay coupling. Zbl 1268.34073Heckman, C. R.; Rand, R. H. 5 2013 Dynamics of a ring of three coupled relaxation oscillators. Zbl 1221.34094Bridge, J.; Mendelowitz, L.; Rand, R.; Sah, S.; Verdugo, A. 5 2009 Bifurcation of nonlinear normal modes in a class of two degree of freedom systems. Zbl 0793.70014Rand, R. H.; Pak, C. H.; Vakakis, A. F. 5 1992 A numerical investigation of the dynamics of a system of two time-delay coupled relaxation oscillators. Zbl 1056.34082Sen, Asok K.; Rand, Richard H. 5 2003 Nonlinear effects on coexistence phenomenon in parametric excitation. Zbl 1026.70024Ng, Leslie; Rand, Richard 5 2003 Dynamics of a system exhibiting the global bifurcation of a limit cycle at infinity. Zbl 0647.34033Keith, W. L.; Rand, R. H. 5 1985 Differential-delay equations. Zbl 1253.34065Rand, Richard 4 2011 Determinacy of degenerate equilibria with linear part \(x'=y\), \(y'=0\) using MACSYMA. Zbl 0624.65068Rand, R. H.; Keith, W. L. 4 1987 Perturbation solution for secondary bifurcation in the quadratically-damped Mathieu equation. Zbl 1348.34059Ramani, Deepak V.; Keith, William L.; Rand, Richard H. 4 2004 An application of the Poincaré map to the stability of nonlinear normal modes. Zbl 0449.70021Month, L. A.; Rand, R. H. 4 1980 Resonant capture in a system of two coupled homoclinic oscillators. Zbl 0949.34506Rand, R. H.; Quinn, D. D. 4 1995 A quasiperiodic Mathieu equation. Zbl 0918.34033Rand, Richard; Zounes, Randolph; Hastings, Rachel 4 1995 Parametric resonance of Hopf bifurcation. Zbl 1096.70011Rand, Richard; Barcilon, Albert; Morrison, Tina 4 2005 Perturbation methods and computer algebra in mechanics. Zbl 0828.73080Rand, R. H. 3 1994 Resonant capture and separatrix crossing in dual-spin spacecraft. Zbl 0941.70021Haberman, Richard; Rand, Richard; Yuster, Thomas 3 1999 How to pump a swing. Zbl 0995.70502Wirkus, Stephen; Rand, Richard; Ruina, Andy 3 1998 1:1 and 2:1 phase entrainment in a system of two coupled limit cycle oscillators. Zbl 0547.92001Keith, W. L.; Rand, R. H. 3 1984 Computer algebra implementation of Lie transforms for Hamiltonian systems: Application to the nonlinear stability of \(L_ 4\). Zbl 0696.70015Coppola, V. T.; Rand, R. H. 3 1989 Coexistence phenomenon in autoparametric excitation of two degree of freedom systems. Zbl 1349.70044Recktenwald, Geoffrey; Rand, Richard 3 2005 Torsional vibrations of elastic prolate spheroids. Zbl 0164.26804Rand, R. H. 3 1968 Self-thinning and community persistence in a simple size-structured dynamical model of plant growth. Zbl 1086.92036Dercole, F.; Niklas, K.; Rand, R. 3 2005 Oscillatory reaction-diffusion equations on rings. Zbl 0802.92002Lubkin, Sharon; Rand, Richard 3 1994 The geometrical stability of non-linear normal modes in two degree of freedom systems. Zbl 0264.70022Rand, Richard H. 3 1973 Breaking the symmetry in queues with delayed information. Zbl 1470.90023Doldo, Philip; Pender, Jamol; Rand, Richard 2 2021 Alternate models of replicator dynamics. Zbl 1300.92065Wesson, Elizabeth N.; Rand, Richard H. 2 2013 Asymptotic analysis of the Hopf-Hopf bifurcation in a time-delay system. Zbl 1304.34124Heckman, Christoffer R.; Rand, Richard H. 2 2012 Nonlinear control of dual-spin spacecraft during despin through precession phase lock. Zbl 0855.93057Kinsey, R. J.; Mingori, D. L.; Rand, R. H. 2 1996 Dynamics of a nonlinear parametrically-excited PDE: 2-term truncation. Zbl 0868.35007Rand, Richard H. 2 1996 Delay terms in the slow flow. Zbl 1356.70031Sah, Si Mohamed; Rand, Richard H. 2 2016 Coexistence of infinitely many large, stable, rapidly oscillating periodic solutions in time-delayed Duffing oscillators. Zbl 1443.34070Fiedler, Bernold; Nieto, Alejandro López; Rand, Richard H.; Sah, Si Mohamed; Schneider, Isabelle; de Wolff, Babette 2 2020 Hopf bifurcation in a stomatal oscillator. Zbl 0467.92005Rand, R. H.; Upadhyaya, S. K.; Cooke, J. R.; Storti, D. W. 2 1981 Coupled oscillators as a model for nonlinear parametric excitation. Zbl 0489.70018Holmes, Catherine A.; Rand, Richard H. 2 1981 Bifurcation of 4:1 subharmonics in the nonlinear Mathieu equation. Zbl 0501.70028Month, Leslie Anne; Rand, Richard H. 2 1982 Slow passage through multiple parametric resonance tongues. Zbl 1273.70039Bridge, Jacqueline; Rand, Richard; Sah, Si Mohamed 2 2009 Three oscillator model of the heartbeat generator. Zbl 1221.34102Suchorsky, Meghan; Rand, Richard 2 2009 About a class of nonlinear oscillators with amplitude-independent frequency. Zbl 1281.34050Kovacic, Ivana; Rand, Richard 2 2013 The damped nonlinear quasiperiodic Mathieu equation near 2:2:1 resonance. Zbl 1141.70011Abouhazim, Nazha; Rand, Richard H.; Belhaq, Mohamed 2 2006 MACSYMA program to implement averging using elliptic functions. Zbl 0741.65055Coppola, Vincent T.; Rand, Richard H. 1 1991 Disappearance of resonance tongues. Zbl 1320.70017Ruelas, Rocio E.; Rand, Richard H. 1 2015 Nonlinear normal modes in a system with nonholonomic constraints. Zbl 1004.70009Rand, R. H.; Ramani, D. V. 1 2001 Dynamics of three coupled limit cycle oscillators with vastly different frequencies. Zbl 1280.34044Sheheitli, Hiba; Rand, Richard H. 1 2011 Dynamics of a model of two delay-coupled relaxation oscillators. Zbl 1222.37019Ruelas, R. E.; Rand, R. H. 1 2010 Fluid mechanics of green plants. Zbl 0564.76128Rand, Richard H. 1 1983 Center manifold reduction of the Hopf-Hopf bifurcation in a time delay system. Zbl 1330.34111Heckman, Christoffer; Kotas, Jakob; Rand, Richard 1 2013 Breaking the symmetry in queues with delayed information. Zbl 1470.90023Doldo, Philip; Pender, Jamol; Rand, Richard 2 2021 A stochastic analysis of queues with customer choice and delayed information. Zbl 1466.60190Pender, Jamol; Rand, Richard; Wesson, Elizabeth 9 2020 Limiting the oscillations in queues with delayed information through a novel type of delay announcement. Zbl 1455.34086Novitzky, Sophia; Pender, Jamol; Rand, Richard H.; Wesson, Elizabeth 7 2020 Coexistence of infinitely many large, stable, rapidly oscillating periodic solutions in time-delayed Duffing oscillators. Zbl 1443.34070Fiedler, Bernold; Nieto, Alejandro López; Rand, Richard H.; Sah, Si Mohamed; Schneider, Isabelle; de Wolff, Babette 2 2020 Nonlinear dynamics in queueing theory: determining the size of oscillations in queues with delay. Zbl 1417.34202Novitzky, Sophia; Pender, Jamol; Rand, Richard H.; Wesson, Elizabeth 8 2019 An analysis of queues with delayed information and time-varying arrival rates. Zbl 1392.90055Pender, Jamol; Rand, Richard H.; Wesson, Elizabeth 17 2018 Queues with choice via delay differential equations. Zbl 1366.90082Pender, Jamol; Rand, Richard H.; Wesson, Elizabeth 23 2017 Hopf bifurcations in delayed rock-paper-scissors replicator dynamics. Zbl 1348.91051Wesson, Elizabeth; Rand, Richard 11 2016 Hopf bifurcations in two-strategy delayed replicator dynamics. Zbl 1334.34180Wesson, Elizabeth; Rand, Richard; Rand, David 8 2016 Delay terms in the slow flow. Zbl 1356.70031Sah, Si Mohamed; Rand, Richard H. 2 2016 Disappearance of resonance tongues. Zbl 1320.70017Ruelas, Rocio E.; Rand, Richard H. 1 2015 Ordered direct implicational basis of a finite closure system. Zbl 1288.06007Adaricheva, K.; Nation, J. B.; Rand, R. 14 2013 Straight-line backbone curve. Zbl 1304.34071Kovacic, Ivana; Rand, Richard 6 2013 Dynamics of microbubble oscillators with delay coupling. Zbl 1268.34073Heckman, C. R.; Rand, R. H. 5 2013 Alternate models of replicator dynamics. Zbl 1300.92065Wesson, Elizabeth N.; Rand, Richard H. 2 2013 About a class of nonlinear oscillators with amplitude-independent frequency. Zbl 1281.34050Kovacic, Ivana; Rand, Richard 2 2013 Center manifold reduction of the Hopf-Hopf bifurcation in a time delay system. Zbl 1330.34111Heckman, Christoffer; Kotas, Jakob; Rand, Richard 1 2013 A pair of van der Pol oscillators coupled by fractional derivatives. Zbl 1258.34074Suchorsky, M. K.; Rand, R. H. 8 2012 Asymptotic analysis of the Hopf-Hopf bifurcation in a time-delay system. Zbl 1304.34124Heckman, Christoffer R.; Rand, Richard H. 2 2012 Dynamics of a mass-spring-pendulum system with vastly different frequencies. Zbl 1267.34065Sheheitli, Hiba; Rand, Richard H. 1 2012 Evolutionary dynamics of a system with periodic coefficients. Zbl 1217.91018Rand, Richard H.; Yazhbin, Max; Rand, David G. 5 2011 Differential-delay equations. Zbl 1253.34065Rand, Richard 4 2011 Dynamics of three coupled limit cycle oscillators with vastly different frequencies. Zbl 1280.34044Sheheitli, Hiba; Rand, Richard H. 1 2011 Using delay to quench undesirable vibrations. Zbl 1218.34085Suchorsky, M. K.; Sah, S. M.; Rand, R. H. 7 2010 Dynamics of a model of two delay-coupled relaxation oscillators. Zbl 1222.37019Ruelas, R. E.; Rand, R. H. 1 2010 Dynamics of three coupled limit cycle oscillators with application to artificial intelligence. Zbl 1221.34099Mendelowitz, Lee; Verdugo, Anael; Rand, Richard 9 2009 Dynamics of a ring of three coupled relaxation oscillators. Zbl 1221.34094Bridge, J.; Mendelowitz, L.; Rand, R.; Sah, S.; Verdugo, A. 5 2009 Slow passage through multiple parametric resonance tongues. Zbl 1273.70039Bridge, Jacqueline; Rand, Richard; Sah, Si Mohamed 2 2009 Three oscillator model of the heartbeat generator. Zbl 1221.34102Suchorsky, Meghan; Rand, Richard 2 2009 Origin of arrhythmias in a heart model. Zbl 1221.37193Sheheitli, Hiba; Rand, Richard 1 2009 Hopf bifurcation in a DDE model of gene expression. Zbl 1134.34325Verdugo, Anael; Rand, Richard 20 2008 Frequency locking in a forced Mathieu–Van der Pol–Duffing system. Zbl 1279.34042Pandey, Manoj; Rand, Richard H.; Zehnder, Alan T. 11 2008 Center manifold analysis of a DDE model of gene expression. Zbl 1221.37197Verdugo, Anael; Rand, Richard 9 2008 Dynamics of four coupled phase-only oscillators. Zbl 1122.70015Rand, Richard; Wong, Jeffrey 7 2008 Dynamics of three coupled van der Pol oscillators with application to circadian rhythms. Zbl 1120.34025Rompala, Kevin; Rand, Richard; Howland, Howard 26 2007 Hopf bifurcation formula for first order differential-delay equations. Zbl 1123.34334Rand, Richard; Verdugo, Anael 19 2007 Perturbation analysis of entrainment in a micromechanical limit cycle oscillator. Zbl 1124.34026Pandey, Manoj; Rand, Richard; Zehnder, Alan 12 2007 \(2:1\) Resonance in the delayed nonlinear Mathieu equation. Zbl 1193.70031Morrison, Tina M.; Rand, Richard H. 12 2007 Stability of strongly nonlinear normal modes. Zbl 1165.34378Recktenwald, Geoffrey; Rand, Richard 1 2007 Trigonometric simplification of a class of conservative nonlinear oscillators. Zbl 1187.70037Recktenwald, Geoffrey; Rand, Richard 1 2007 The damped nonlinear quasiperiodic Mathieu equation near 2:2:1 resonance. Zbl 1141.70011Abouhazim, Nazha; Rand, Richard H.; Belhaq, Mohamed 2 2006 \(2:1:1\) resonance in the quasi-periodic Mathieu equation. Zbl 1132.34041Rand, Richard; Morrison, Tina 10 2005 Parametric resonance of Hopf bifurcation. Zbl 1096.70011Rand, Richard; Barcilon, Albert; Morrison, Tina 4 2005 Coexistence phenomenon in autoparametric excitation of two degree of freedom systems. Zbl 1349.70044Recktenwald, Geoffrey; Rand, Richard 3 2005 Self-thinning and community persistence in a simple size-structured dynamical model of plant growth. Zbl 1086.92036Dercole, F.; Niklas, K.; Rand, R. 3 2005 Dynamics of two van der Pol oscillators coupled via a bath. Zbl 1052.70013Camacho, Erika; Rand, Richard; Howland, Howard 19 2004 Non-linear dynamics of a system of coupled oscillators with essential stiffness non-linearities. Zbl 1348.34073Vakakis, Alexander F.; Rand, Richard H. 8 2004 Perturbation solution for secondary bifurcation in the quadratically-damped Mathieu equation. Zbl 1348.34059Ramani, Deepak V.; Keith, William L.; Rand, Richard H. 4 2004 2:2:1 resonance in the quasiperiodic Mathieu equation. Zbl 1062.70596Rand, Richard; Guennoun, Kamar; Belhaq, Mohamed 21 2003 A numerical investigation of the dynamics of a system of two time-delay coupled relaxation oscillators. Zbl 1056.34082Sen, Asok K.; Rand, Richard H. 5 2003 Nonlinear effects on coexistence phenomenon in parametric excitation. Zbl 1026.70024Ng, Leslie; Rand, Richard 5 2003 The dynamics of two coupled van der Pol oscillators with delay coupling. Zbl 1021.70010Wirkus, Stephen; Rand, Richard 42 2002 Bifurcations in a Mathieu equation with cubic nonlinearities. Zbl 1029.70009Ng, Leslie; Rand, Richard 19 2002 Global behavior of a nonlinear quasiperiodic Mathieu equation. Zbl 1003.34041Zounes, Randolph S.; Rand, Richard H. 16 2002 Subharmonic resonance in the nonlinear Mathieu equation. Zbl 1116.34322Zounes, Randolph S.; Rand, Richard H. 10 2002 Bifurcations in a Mathieu equation with cubic nonlinearities. II. Zbl 1043.34040Ng, Leslie; Rand, Richard 8 2002 Analysis of a nonlinear partial difference equation, and its application to cardiac dynamics. Zbl 1012.39004Stubna, Michael D.; Rand, Richard H.; Gilmour, Robert F. jun. 6 2002 Nonlinear normal modes in a system with nonholonomic constraints. Zbl 1004.70009Rand, R. H.; Ramani, D. V. 1 2001 Non-linear modal interactions in the oscillations of a liquid drop in a gravitational field. Zbl 1345.76035Rozhkov, I.; Vakakis, A. F.; Rand, R. H. 1 2001 Sequences of orbits and the boundaries of the basin of attraction for two double heteroclinic orbits. Zbl 1068.70529Haberman, Richard; Rand, Richard 1 2000 Resonant capture and separatrix crossing in dual-spin spacecraft. Zbl 0941.70021Haberman, Richard; Rand, Richard; Yuster, Thomas 3 1999 Transition curves for the quasi-periodic Mathieu equation. Zbl 0916.34031Zounes, Randolph S.; Rand, Richard H. 24 1998 How to pump a swing. Zbl 0995.70502Wirkus, Stephen; Rand, Richard; Ruina, Andy 3 1998 Modal analysis of a cracked beam. Zbl 1235.74056Chati, M.; Rand, R.; Mukherjee, S. 15 1997 Nonlinear control of dual-spin spacecraft during despin through precession phase lock. Zbl 0855.93057Kinsey, R. J.; Mingori, D. L.; Rand, R. H. 2 1996 Dynamics of a nonlinear parametrically-excited PDE: 2-term truncation. Zbl 0868.35007Rand, Richard H. 2 1996 Resonant capture in a system of two coupled homoclinic oscillators. Zbl 0949.34506Rand, R. H.; Quinn, D. D. 4 1995 A quasiperiodic Mathieu equation. Zbl 0918.34033Rand, Richard; Zounes, Randolph; Hastings, Rachel 4 1995 Topics in nonlinear dynamics with computer algebra. Zbl 0853.70001Rand, Richard H. 8 1994 Perturbation methods and computer algebra in mechanics. Zbl 0828.73080Rand, R. H. 3 1994 Oscillatory reaction-diffusion equations on rings. Zbl 0802.92002Lubkin, Sharon; Rand, Richard 3 1994 Dynamics of spinup through resonance. Zbl 0825.70085Rand, R. H.; Kinsey, R. J.; Mingori, D. L. 12 1992 Normal modes and global dynamics of a two-degree-of-freedom non-linear system. I: Low energies. Zbl 0765.70014Vakakis, A. F.; Rand, R. H. 11 1992 Normal modes and global dynamics of a two-degree-of-freedom non-linear system. II: High energies. Zbl 0765.70015Vakakis, A. F.; Rand, R. H. 6 1992 Bifurcation of nonlinear normal modes in a class of two degree of freedom systems. Zbl 0793.70014Rand, R. H.; Pak, C. H.; Vakakis, A. F. 5 1992 MACSYMA program to implement averging using elliptic functions. Zbl 0741.65055Coppola, Vincent T.; Rand, Richard H. 1 1991 Averaging using elliptic functions: Approximation of limit cycles. Zbl 0699.34032Coppola, V. T.; Rand, R. H. 29 1990 Integrability of plane quadratic vector fields. Zbl 0693.34030Schlomiuk, Dana; Guckenheimer, John; Rand, Richard 25 1990 Bifurcations and chaos in a forced zero-stiffness impact oscillator. Zbl 0714.73049Li, G. X.; Rand, R. H.; Moon, F. C. 15 1990 The transition to chaos in a simple mechanical system. Zbl 0666.70030Shaw, Steven W.; Rand, Richard H. 32 1989 Analytical approximation for period-doubling following a Hopf bifurcation. Zbl 0684.58030Rand, Richard H. 12 1989 Degenerate homoclinic cycles in perturbations of quadratic Hamiltonian systems. Zbl 0677.58038Guckenheimer, John; Rand, Richard; Schlomiuk, Dana 10 1989 Computer algebra implementation of Lie transforms for Hamiltonian systems: Application to the nonlinear stability of \(L_ 4\). Zbl 0696.70015Coppola, V. T.; Rand, R. H. 3 1989 Resonance in a high-speed flexible-arm robot. Zbl 0681.70028Golnaraghi, M. F.; Moon, F. C.; Rand, R. H. 1 1989 Symbolic computation and perturbation methods using elliptic functions. Zbl 0689.33002Coppola, Vincent T.; Rand, Richard H. 1 1989 The transition from phase locking to drift in a system of two weakly coupled Van Der Pol oscillators. Zbl 0667.70028Chakraborty, Tapesh; Rand, Richard H. 25 1988 Perturbation methods, bifurcation theory and computer algebra. Zbl 0651.34001Rand, Richard H.; Armbruster, Dieter 60 1987 A simplified model of coupled relaxation oscillators. Zbl 0614.73024Storti, Duane; Rand, Richard H. 7 1987 Determinacy of degenerate equilibria with linear part \(x'=y\), \(y'=0\) using MACSYMA. Zbl 0624.65068Rand, R. H.; Keith, W. L. 4 1987 Dynamics of two strongly coupled relaxation oscillators. Zbl 0589.34043Storti, D. W.; Rand, R. H. 7 1986 Dynamics of a system exhibiting the global bifurcation of a limit cycle at infinity. Zbl 0647.34033Keith, W. L.; Rand, R. H. 5 1985 Computer algebra in applied mathematics: an introduction to MACSYMA. Zbl 0583.68012Rand, R. H. 37 1984 1:1 and 2:1 phase entrainment in a system of two coupled limit cycle oscillators. Zbl 0547.92001Keith, W. L.; Rand, R. H. 3 1984 Fluid mechanics of green plants. Zbl 0564.76128Rand, Richard H. 1 1983 The nature of the coupling between segmental oscillators of the lamprey spinal generator for locomotion: a mathematical model. Zbl 0476.92003Cohen, Avis H.; Holmes, Philip J.; Rand, Richard H. 55 1982 Dynamics of two strongly coupled van der Pol oscillators. Zbl 0498.70037Storti, D. W.; Rand, R. H. 19 1982 Bifurcation of 4:1 subharmonics in the nonlinear Mathieu equation. Zbl 0501.70028Month, Leslie Anne; Rand, Richard H. 2 1982 Dynamics of coupled stomatal oscillators. Zbl 0493.92006Rand, R. H.; Storti, D. W.; Upadhyaya, S. K.; Cooke, J. R. 1 1982 Hopf bifurcation in a stomatal oscillator. Zbl 0467.92005Rand, R. H.; Upadhyaya, S. K.; Cooke, J. R.; Storti, D. W. 2 1981 Coupled oscillators as a model for nonlinear parametric excitation. Zbl 0489.70018Holmes, Catherine A.; Rand, Richard H. 2 1981 ...and 13 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,125 Authors 45 Rand, Richard H. 17 Belhaq, Mohamed 16 Luo, Albert C. J. 13 Pender, Jamol 10 Llibre, Jaume 8 Xu, Jian 7 Gendelman, Oleg V. 7 Tkhaĭ, Valentin Nikolaevich 7 Vakakis, Alexander F. 7 Verdugo, Anael 7 Zhang, Tonghua 6 Bi, Qinsheng 6 Du, Zhengdong 6 Rashidi, Mohammad Mehdi 6 Yu, Pei 5 Chen, Yushu 5 Ermentrout, George Bard 5 Lakrad, Faouzi 5 Quinn, D. Dane 5 Song, Yongli 5 Strogatz, Steven Henry 5 Wesson, Elizabeth N. 5 Xu, Wei 4 Abouhazim, Nazha 4 Chatterjee, Anindya 4 Chung, Kwok-Wai 4 Dinarvand, Saeed 4 Elías-Zúñiga, Alex 4 Fahsi, Abdelhak 4 Holmes, Philip J. 4 Hu, Wenjun 4 Kiemel, Tim 4 Kuznetsov, Aleksandr Petrovich 4 Leung, Andrew Yee-Tak 4 Liu, Yirong 4 Porter, Mason Alexander 4 Rezazadeh, Ghader 4 Sah, Si Mohamed 4 Schlomiuk, Dana I. 4 Valls Anglés, Cláudia 4 Wang, Zaihua 4 Wirkus, Stephen A. 4 Younesian, Davood 4 Zhang, Gang 4 Zhang, Weinian 3 Balthazar, José Manoel 3 Barabanov, Ivan N. 3 Bergman, Lawrence A. 3 Bhattacharjee, Jayanta K. 3 Bridge, Jacqueline 3 Caldas, Iberê L. 3 Camacho, Erika T. 3 Chabi Orou, Jean B. 3 Collins, James J. 3 Coombes, Stephen 3 Corless, Robert Malcolm 3 Dankowicz, Harry J. 3 Doldo, Philip 3 Golnaraghi, M. Farid 3 Hacinliyan, Avadis Simon 3 Hamdi, Mustapha 3 Hoffman, Kathleen A. 3 Ishibashi, Kazuki 3 Kelso, J. A. Scott 3 Kopell, Nancy J. 3 Kovacic, Ivana 3 Li, Jibin 3 Li, Yurong 3 Lu, Qishao 3 Luongo, Angelo 3 Moiola, Jorge Luis 3 Rand, David G. 3 Sheheitli, Hiba 3 Siddiqui, Abdul Majeed 3 Stewart, Ian Nicholas 3 Sun, Zhongkui 3 Tian, Haiyan 3 Tschauner, Johann 3 Turukina, Ludmila V. 3 Vestroni, Fabrizio 3 Wahi, Pankaj 3 Zang, Hong 2 Avramov, Konstantin V. 2 Aybar, Orhan Ozgur 2 Azizi, Saber 2 Bajaj, Anil K. 2 Biswas, Subhadip 2 Bodnar, Marek 2 Bountis, Tassos C. 2 Bressloff, Paul C. 2 Cammarano, Andrea 2 Cartmell, Matthew P. 2 Chen, Xiaojie 2 Cohen, Avis H. 2 Coppola, Vincent T. 2 Cveticanin, Livija 2 Dadi, Zohreh 2 Dai, Shiqiang 2 Daun, Silvia 2 Daw, Andrew ...and 1,025 more Authors all top 5 Cited in 173 Serials 93 Nonlinear Dynamics 50 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 45 Communications in Nonlinear Science and Numerical Simulation 34 Physica D 30 Chaos, Solitons and Fractals 20 Chaos 17 Applied Mathematics and Computation 12 Biological Cybernetics 12 Journal of Mathematical Biology 11 Applied Mathematics and Mechanics. (English Edition) 10 Physica A 10 Meccanica 9 Journal of Vibration and Control 9 Nonlinear Analysis. Real World Applications 8 Applied Mathematical Modelling 8 Mathematical Problems in Engineering 8 Journal of Theoretical Biology 8 Journal of Applied Nonlinear Dynamics 7 Celestial Mechanics 6 Journal of Mathematical Analysis and Applications 6 Physics of Fluids 6 SIAM Journal on Applied Dynamical Systems 5 Acta Mechanica 5 Bulletin of Mathematical Biology 5 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 5 Journal of Symbolic Computation 5 Automation and Remote Control 5 Journal of Nonlinear Science 4 Computers & Mathematics with Applications 4 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 4 Automatica 4 Journal of Computational and Applied Mathematics 4 Dynamics and Stability of Systems 4 Queueing Systems 4 Qualitative Theory of Dynamical Systems 3 Journal of Applied Mathematics and Mechanics 3 Journal of Computational Physics 3 Journal of Mathematical Physics 3 Journal of Statistical Physics 3 Mathematical Biosciences 3 Journal of Differential Equations 3 Computational Mechanics 3 Archive of Applied Mechanics 3 Journal of Computer and Systems Sciences International 3 Complexity 3 Discrete and Continuous Dynamical Systems 3 Nonlinear Analysis. Theory, Methods & Applications 3 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 3 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 2 Computer Methods in Applied Mechanics and Engineering 2 Computer Physics Communications 2 International Journal of Control 2 International Journal of Engineering Science 2 Journal of Fluid Mechanics 2 Journal of the Franklin Institute 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Advances in Mathematics 2 Mathematics of Operations Research 2 Insurance Mathematics & Economics 2 Applied Numerical Mathematics 2 Numerical Methods for Partial Differential Equations 2 Computational Mathematics and Mathematical Physics 2 Acta Mechanica Sinica. (English Edition) 2 Continuum Mechanics and Thermodynamics 2 Computational and Applied Mathematics 2 NoDEA. Nonlinear Differential Equations and Applications 2 Journal of Computational Neuroscience 2 European Journal of Control 2 Abstract and Applied Analysis 2 Acta Mathematica Sinica. English Series 2 International Journal of Nonlinear Sciences and Numerical Simulation 2 Discrete and Continuous Dynamical Systems. Series B 2 Advances in Difference Equations 2 Acta Mechanica Sinica 2 International Journal of Biomathematics 2 Advances in Mathematical Physics 2 Science China. Technological Sciences 2 Dynamic Games and Applications 2 The Journal of Mathematical Neuroscience 2 Stochastic Systems 2 Discontinuity, Nonlinearity, and Complexity 1 Advances in Applied Probability 1 American Mathematical Monthly 1 Artificial Intelligence 1 Archive for Rational Mechanics and Analysis 1 Bulletin of the Australian Mathematical Society 1 Computers and Fluids 1 Communications in Mathematical Physics 1 European Journal of Physics 1 Fluid Dynamics 1 Ingenieur-Archiv 1 Physics Letters. A 1 Physics Reports 1 Rocky Mountain Journal of Mathematics 1 Mathematics of Computation 1 The Mathematical Intelligencer 1 Prikladnaya Matematika i Mekhanika 1 International Journal of Circuit Theory and Applications 1 International Journal for Numerical Methods in Engineering 1 Mathematics and Computers in Simulation ...and 73 more Serials all top 5 Cited in 38 Fields 327 Ordinary differential equations (34-XX) 183 Mechanics of particles and systems (70-XX) 149 Dynamical systems and ergodic theory (37-XX) 105 Biology and other natural sciences (92-XX) 70 Systems theory; control (93-XX) 54 Mechanics of deformable solids (74-XX) 43 Numerical analysis (65-XX) 36 Computer science (68-XX) 32 Fluid mechanics (76-XX) 29 Partial differential equations (35-XX) 21 Statistical mechanics, structure of matter (82-XX) 19 Probability theory and stochastic processes (60-XX) 19 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 17 Operations research, mathematical programming (90-XX) 7 Optics, electromagnetic theory (78-XX) 7 Classical thermodynamics, heat transfer (80-XX) 6 Quantum theory (81-XX) 5 Difference and functional equations (39-XX) 5 Information and communication theory, circuits (94-XX) 3 Combinatorics (05-XX) 3 Real functions (26-XX) 3 Operator theory (47-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Statistics (62-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Integral equations (45-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Algebraic geometry (14-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Topological groups, Lie groups (22-XX) 1 Potential theory (31-XX) 1 Special functions (33-XX) 1 Sequences, series, summability (40-XX) 1 Approximations and expansions (41-XX) 1 Global analysis, analysis on manifolds (58-XX) Citations by Year