Periodic and strange attractors of the Rabinovich Fabrikant dynamical system

The pictures show periodic and strange attractors of the Rabinovich Fabrikant dynamical system [1] obtained with a special numerical method for the ODE [2].

This particular system has proved to be a great challenge for classical numerical methods and presents multiple chaotic attractors [3].

 

Periodic motion of Rabinovich Fabrikant system.

 

Chaotic attractor of Rabinovich Fabrikant system.

 

References
[1] Marius-F. Danca, and Guanrong Chen, Bifurcation and Chaos in a Complex Model of Dissipative Medium, IJBC, 14 (10), 2004, 3409-3447.
[2] Marius-F. Danca, A multistep algorithm for ODEs, Dynamics of Continuous, Discrete Impulsive and Systems, Series B: Applications and Algorithms, 2005, accepted.
[3] Xiaodong Luo, Marius-F. Danca, Michael Small and Guanrong Chen, On a dynamical System with Multiple Chaotic Attractors, IJBC, 2006, accepted.