Dynamical analysis and electronic circuit realization of an equilibrium free 3D chaotic system with a large number of coexisting attractors

Abstract In recent years, a growing interest has been devoted to the design and analysis of chaotic systems without equilibrium point. In the present contribution, we further investigate the dynamics of an equilibrium free 3D chaotic system with quadratic nonlinearities recently introduced by Yan et al. [Optik 127 (2016) 1363–1367]. Standard nonlinear diagnostic tools such as bifurcation diagrams, graphs of largest Lyapunov exponent, phase portraits, frequency spectra and Poincare sections are plotted to characterize the dynamics of the model in terms of its parameters. It is found that the system experiences a large number of coexisting attractors for some suitable sets of its parameters, depending solely on the choice of initial conditions. Up to twelve coexisting stable attractors are revealed. An electronic analogue of the system is designed and implemented in Pspice. A very good agreement is observed between Spice based simulation results and the theoretical analysis. To the best of the authors’ knowledge, this interesting and singular behavior (i.e. the coexistence of a large number of stable attractors, including periodic, quasi-periodic and chaotic attractors) has not yet been reported both in a third order system and thus deserves dissemination.