Basic structures of the Shilnikov homoclinic bifurcation scenario.
We find numerically small scale basic structures of homoclinic bifurcation curves in the parameter space of the Chua circuit. The distribution of these basic structures in the parameter space and their geometrical properties constitute a complete homoclinic bifurcation scenario of this system. Furthermore, these structures and the scenario are theoretically demonstrated to be generic to a large class of dynamical systems that presents, as the Chua circuit, Shilnikov homoclinic orbits. We classify the complexity of primary and subsidiary homoclinic orbits by their order given by the number of their returning loops. Our results confirm previous predictions of structures of homoclinic bifurcation curves and extend this study to high order primary orbits. Furthermore, we identify accumulations of bifurcation curves of subsidiary homoclinic orbits into bifurcation curves of both primary and subsidiary orbits.
Medrano-T
Rene O
RO
Instituto de Física, Universidade de São Paulo, C. P. 66318, CEP 05315-970 São Paulo, SP, Brazil. medrano@if.usp.br
Baptista
Murilo S
MS
Caldas
Iberê L
IL
D000465:Algorithms; D001683:Biological Clocks / Q000502:physiology*; D003198:Computer Simulation; D004735:Energy Transfer; D008954:Models, Biological; D017711:Nonlinear Dynamics