Unusual dynamics and hidden attractors of the Rabinovich–Fabrikant system

Abstract

This paper presents some unusual dynamics of the Rabinovich-Fabrikant system, such as "virtual" saddles, "tornado"-like stable cycles and hidden chaotic attractors. Due to the strong nonlinearity and high complexity, the results are obtained numerically with some insightful descriptions and discussions.

Hidden Attractors on One Path: Glukhovsky–Dolzhansky, Lorenz, and Rabinovich Systems

“…The classification of attractors as being hidden or self-excited was introduced by G. Leonov and N. Kuznetsov in connection with the discovery of the first hidden Chua attractor [16,17,[27][28][29] and has captured much attention of scientists from around the world (see, e.g. [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48]).…”

Hidden chaotic attractors in fractional-order systems

“…The system, initially designed as a physical system, describes the stochasticity arising from the modulation instability in a dissipative medium. However, as revealed numerically in [54] and [55], the system of integer order presents unusual and extremely rich dynamics, including multistability, an important ingredient for potential existence of hidden attractor. The equilibria are X * 0 and X * 1,2 ∓x * 1,2 , ±y * 1,2 , z * 1,2 , X * 3,4 ∓x * 3,4 , ±y * 3,4 , z * 3,4 ,…”

A new three-dimensional chaotic flow with one stable equilibrium: dynamical properties and complexity analysis

“…The rst one is hidden attractor. An attractor is called hidden if its basin of attraction does not intersect with a small neighborhood of any equilibrium point [15][16][17][18]. The second one is self-excited attractor.…”