论文信息 - The effect of discretization on homoclinic orbits

The effect of discretization on homoclinic orbits

The numerical analysis of the longtime behavior of a dynamical system $$(1)\,\mathop {\text{z}}\limits^., = \,{\text{f(z,}}\,\lambda ),{\text{z}}\, \in \,{\text{IR}}^{\text{m}},\,\lambda \, \in \,{\text{IR}}\,{\text{(a parameter)}}$$ usually follows two complementary approaches.

Wolf-Jürgen Beyn | W. Beyn

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

[2] Periodic solutions of finite difference equations , 1977 .

[3] F. Brezzi,et al. “Real” and “Ghost” Bifurcation Dynamics in Difference Schemes for ODEs , 1984 .

[4] J. Craggs. Applied Mathematical Sciences , 1973 .

[5] H. Mittelmann,et al. Numerical methods for bifurcation problems : proceedings of the conference at the University of Dortmund, August 22-26, 1983 , 1984 .

[6] Wolf-Jürgen Beyn,et al. On invariant closed curves for one-step methods , 1987 .

[7] Kenneth J. Palmer,et al. Exponential dichotomies and transversal homoclinic points , 1984 .

[8] H. T. Doan. Invariant curves for numerical methods , 1985 .

[9] J. Keener,et al. Infinite Period Bifurcation and Global Bifurcation Branches , 1981 .

[10] Peter A. Markowich. A Theory for the Approximation of Solutions of Boundary Value Problems on Infinite Intervals , 1982 .

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