Summary
International Symposium on Nonlinear Theory and Its Applications
2015
Session Number:A2L-D
Session:
Number:A2L-D-1
Chenciner Bubbles and Hysteresis
Shuya Hidaka, Naohiko Inaba, Kyohei Kamiyama, Munehisa Sekikawa, Tetsuro Endo,
pp.53-56
Publication Date:2015/12/1
Online ISSN:2188-5079
Summary:
This study investigates quasi-periodic bifurcations and Arnol'd resonance webs generated in a coupled delayed logistic map. Because a single delayed logistic map generates an invariant closed curve corresponding to a two-dimensional torus in vector fields via a Neimark-Sacker bifurcation, the coupled delayed logistic map can exhibit an invariant torus corresponding to a three-dimensional torus in vector fields. The Lyapunov analysis is conducted, and it is clarified that Chenciner bubbles are generated by saddle-node bifurcations and Neimark-Sacker bifurcations. Inevitable hysteresis is accompanied with Chenciner bubbles.