Coexistence of hidden attractors, 2-torus and 3-torus in a new simple 4-D chaotic system with hyperbolic cosine nonlinearity

Recently, the study of dynamic systems with hidden attractors has become one of the most followed research avenues owing to its theoretical and practical relevance. A new 4D system with hyperbolic cosine nonlinearity [instead of quadratic nonlinearity as in Jay and Roy (Int J Dyn Control, 2017)  https://doi.org/10.1007/s40435-017-0332-8] which can exhibit complex and varied dynamics including hidden attractors and multiple attractors is proposed. The proposed system is studied using numerical simulations and nonlinear analysis methods in order to characterize its dynamics with respect to its parameters. A particular feature of the new system is the simplicity of the corresponding electronic analogue (no analog multiplier chip is employed). Although the system has no equilibrium points, it can display rich behaviors such as chaos, 2-torus, and 3-torus behavior. Moreover, the phenomenon of multistability showing the coexistence of hidden attractors, 2-torus and 3-torus is also observed. In addition, the feasibility of the system is demonstrated through PSpice simulations based on an appropriate electronic analog of the model.

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