Multi-scroll hidden attractors in improved Sprott A system

Abstract

In this paper, two simple 3D chaotic systems are constructed by introducing nonlinear functions into Sprott A system, which all have no equilibrium, and multi-scroll hidden attractors can be obtained. In the case of simple sine function without restricting its nonlinear dynamical range, the number of multi-scroll attractors has nothing to do with the system equilibria, which is only determined by the transient simulation time. In the other case, the introduced nonlinear function is composed of nonlinear part and linear part; thus, the nonlinearity of improved Sprott A system is limited in certain range, as a result, the number of multi-scroll hidden attractors can be selected arbitrarily within finite transient simulation time. Furthermore, the dynamical properties of two systems are studied through phase plane, time series, Poincare map and frequency spectra. Finally, an electronic circuit of improved Sprott A system is implemented in Pspice, and the results of electronic circuit are consistent with that of the numerical simulation.