multistability

Complex Dynamics and Chaos in the Rabinovich – Fabrikant Model

Authors: Kuznetsov A. P., Kuznetsov S. P., Turukina L. V.

Background and Objectives: In the work we consider a finitedimensional three-mode model of the nonlinear parabolic equation. It was proposed in 1979 by M. I. Rabinovich and A. L. Fabrikant. It describes the stochasticity arising from the modulation instability in a non-equilibrium dissipative medium with a spectrally narrow amplification increment. The Rabinovich – Fabrikant system presents some extremely rich dynamics die to the third-order nonlinearities presented in the equations. The considered system is universal.

Influence of the Co-Phase Harmonis Excitation on the Dynamics of the Two Coupled Period Doubling Systems

Authors: Popova E. S., Seleznev E. P.

The system of two coupled maps under in-phase harmonic forcing is investigated numerically. By calculating of the lyapunov exponent spectrum the structure of control parameters space is investigated, the existence regions of the various multistable states are presented, the structure of the basins of attraction is studed.