Continuation techniques and interactive software for bifurcation analysis of ODEs and iterated maps: physics

[1]  Yieh-Hei Wan,et al.  Computation of the Stability Condition for the Hopf Bifurcation of Diffeomorphisms on $\mathbb{R}^2 $ , 1978 .

[2]  B. Hassard,et al.  Theory and applications of Hopf bifurcation , 1981 .

[3]  Vladimir Igorevich Arnold,et al.  Geometrical Methods in the Theory of Ordinary Differential Equations , 1983 .

[4]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[5]  Allan D. Jepson,et al.  Singular Points and their Computation , 1984 .

[6]  W. Rheinboldt Numerical analysis of parametrized nonlinear equations , 1986 .

[7]  R. Seydel From Equilibrium to Chaos: Practical Bifurcation and Stability Analysis , 1988 .

[8]  I. Schreiber,et al.  Interactive System for Studies in Nonlinear Dynamics , 1990 .

[9]  Dirk Roose,et al.  Aspects of Continuation Software , 1990 .

[10]  A. I. Khibnik,et al.  LINLBF: A Program for Continuation and Bifurcation Analysis of Equilibria Up to Codimension Three , 1990 .

[11]  Bodo Werner,et al.  COMPUTATION OF HOPF BRANCHES BIFURCATING FROM TAKENS-BOGDANOV POINTS FOR PROBLEMS WITH SYMMETRIES , 1991 .

[12]  Andreas Hohmann,et al.  Symbolic exploitation of symmetry in numerical pathfollowing , 1991, IMPACT Comput. Sci. Eng..

[13]  Numerical analysis of the flip bifurcation of maps , 1991 .

[14]  R. Seydel TUTORIAL ON CONTINUATION , 1991 .

[15]  Y. Kuznetsov,et al.  BIFURCATIONS AND CHAOS IN A PERIODIC PREDATOR-PREY MODEL , 1992 .

[16]  Roman Borisyuk,et al.  Analysis of Oscillatory Regimes of a Coupled Neural Oscillator System with Application to Visual Cortex Modeling , 1992 .

[17]  Dirk Roose,et al.  Numerical Bifurcation Analysis of a Model of Coupled Neural Oscillators , 1992 .

[18]  Ernst Hairer,et al.  Solving Ordinary Differential Equations I: Nonstiff Problems , 2009 .