Summary
International Symposium on Nonlinear Theory and its Applications
2005
Session Number:2-4-3
Session:
Number:2-4-3-3
Switching Dynamics in Four Coupled Line Array of Oscillators with Hard-Type Nonlinearity
Kuniyasu Shimizu, Tetsuro Endo,
pp.174-177
Publication Date:2005/10/18
Online ISSN:2188-5079
Summary:
This paper investigates various bifurcations and related dynamics such as transitional phenomenon in four coupled line array of oscillators with hard-type nonlinearity. This system has some periodic attractors for comparatively large ε value (= a parameter showing the degree of nonlinearity), and they disappear for a certain value of ε via saddle-node(S-N) bifurcation to become quasi-periodic attractors when ε is decreased. Sometimes, there exists a heteroclinic cycle at the bifurcation point. In such cases, the system presents the switching phenomenon right after the S-N bifurcation. We clarify the existence of some heteroclinic cycles by drawing unstable manifold of saddles in Poincare section, and demonstrate that the switching phenomenon is caused by the heteroclinic cycle by computer simulation. At last, we introduce wave propagation phenomenon briefly.