Multistability and hidden chaotic attractors in a new simple 4-D chaotic system with chaotic 2-torus behaviour

Abstract

The finding of hidden attractors in a chaotic/hyperchaotic system is more important, interesting and difficult than a self-excited attractor. This paper reports a new simple 4-D chaotic system with no equilibrium point and having hidden attractors with the coexistence of attractors (i.e. multistability). The proposed system has a total of eight terms including only one nonlinear term and hence, it is simple. It has only one bifurcation parameter. The system has complex dynamical behaviour. It exhibits 3-torus, 2-torus, chaotic and chaotic 2-torus behaviours. The coexistence of hidden attractors in the proposed system is analysed with phase portrait, Finite time Lyapunov spectrum, bifurcation diagram, Poincare map, instantaneous phase plot and 0–1 test. The system has chaotic behaviour with \(({+,0,-,-})\) sign of distinct Lyapunov exponents although the Jacobian matrix has rank less than four. Electronic circuit realisation is shown to validate the chaotic behaviour of the proposed system.