Multistability and the transformation of tori in driven Ikeda map with weak dissipation

A.P.Kuznetsov, E.Yu. Latuhina, A.V. Savin

Saratov State University , Russia

It is rather well known that a lot of attractors coexist in dynamical systems with weak dissipation. It seems to be interesting to consider the system with weak dissipation driven by signal which frequency is incommensurable with the eigenfrequency of the system. It is obvious that periodic attractors transform to quasiperiodical attractors, or tori, due to that influence. But one can expect some nontrivial effects, e.g. nonlocal bifurcations, in the case of a large number of coexisting attractors, for example, due to the increase of the attractor size. We consider the Ikeda map which is one of the classic models of nonlinear dynamics, driven by external signal and investigate the coexisting tori and their evolution in the case of weak dissipation.