Successive continuation for locating connecting orbits

A successive continuation method for locating connecting orbits in parametrized systems of autonomous ODEs is considered. A local convergence analysis is presented and several illustrative numerical examples are given.

[1]  John Guckenheimer,et al.  On Computing Connecting Orbits: General Algorithm and Applications to the Sine-Gordon and Hodgkin-Huxley Equations (Special Section on Nonlinear Theory and Its Applications) , 1994 .

[2]  Yu. A. Kuznetsov,et al.  NUMERICAL DETECTION AND CONTINUATION OF CODIMENSION-TWO HOMOCLINIC BIFURCATIONS , 1994 .

[3]  L. Chua,et al.  A universal circuit for studying and generating chaos. I. Routes to chaos , 1993 .

[4]  Mark J. Friedman,et al.  Numerical computation of heteroclinic orbits , 1989 .

[5]  D. Barden,et al.  An introduction to differential manifolds , 2003 .

[6]  C. Wu,et al.  A Universal Circuit for Studying and Generating Chaos-Part I: Routes , 1993 .

[7]  Allan Jepsow,et al.  The computation of paths of homoclinic orbits , 1994 .

[8]  Henri Berestycki,et al.  Travelling fronts in cylinders , 1992 .

[9]  Mark J. Friedman,et al.  Numerical computation and continuation of invariant manifolds connecting fixed points , 1991 .

[10]  N. Anders Petersson,et al.  Computation and Stability of Fluxons in a Singularly Perturbed Sine-Gordon Model of the Josephson Junction , 1994, SIAM J. Appl. Math..

[11]  E. Dowell,et al.  Chaotic Vibrations: An Introduction for Applied Scientists and Engineers , 1988 .

[12]  Björn Sandstede,et al.  Convergence estimates for the numerical approximation of homoclinic solutions , 1997 .

[13]  L. Franquelo,et al.  Periodicity and chaos in an autonomous electronic system , 1984 .

[14]  Alan R. Champneys,et al.  Numerical detection and continuation of codimension-two homoclinic orbits , 1994 .

[15]  Wolf-Jürgen Beyn Global Bifurcations and their Numerical Computation , 1990 .

[16]  G. Ermentrout,et al.  Analysis of neural excitability and oscillations , 1989 .

[17]  Bo Deng CONSTRUCTING HOMOCLINIC ORBITS AND CHAOTIC ATTRACTORS , 1994 .

[18]  J. Dieudonne Foundations of Modern Analysis , 1969 .

[19]  H. B. Keller,et al.  Boundary Value Problems on Semi-Infinite Intervals and Their Numerical Solution , 1980 .

[20]  Alejandro J. Rodríguez-Luis,et al.  A Method for Homoclinic and Heteroclinic Continuation in Two and Three Dimensions , 1990 .

[21]  Björn Sandstede,et al.  A numerical toolbox for homoclinic bifurcation analysis , 1996 .

[22]  H. B. Keller,et al.  NUMERICAL ANALYSIS AND CONTROL OF BIFURCATION PROBLEMS (II): BIFURCATION IN INFINITE DIMENSIONS , 1991 .

[23]  Malomed,et al.  Vibration modes of a gap soliton in a nonlinear optical medium. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[24]  Nadine Aubry,et al.  The dynamics of coherent structures in the wall region of a turbulent boundary layer , 1988, Journal of Fluid Mechanics.

[25]  Alejandro J. Rodríguez-Luis,et al.  A case study for homoclinic chaos in an autonomous electronic circuit: a trip taken from Takens-Bogdanov to Hopf-Sbil'nikov , 1993 .

[26]  Mark J. Friedman,et al.  Numerical analysis and accurate computation of heteroclinic orbits in the case of center manifolds , 1993 .

[27]  Wolf-Jürgen Beyn,et al.  The Numerical Computation of Connecting Orbits in Dynamical Systems , 1990 .

[28]  Mark J. Friedman,et al.  On locating connecting orbits , 1994 .

[29]  H. B. Keller Global Homotopies and Newton Methods , 1978 .

[30]  Gene H. Golub,et al.  Matrix computations , 1983 .

[31]  Mark J. Friedman,et al.  Computational methods for global analysis of homoclinic and heteroclinic orbits: A case study , 1993 .

[32]  Stephen Schecter,et al.  Numerical computation of saddle-node homoclinic bifurcation points , 1993 .

[33]  E. Dowell,et al.  Chaotic Vibrations: An Introduction for Applied Scientists and Engineers , 1988 .

[34]  Peter Gray,et al.  Chemical Oscillations and Instabilities: Non-Linear Chemical Kinetics , 1990 .