Antimonotonicity, chaos, quasi-periodicity and coexistence of hidden attractors in a new simple 4-D chaotic system with hyperbolic cosine nonlinearity

Abstract Recently, the study of systems with hidden attractors has become one of the most followed topics owing to their fundamental and technological importance. This contribution is focused on a new simple 4-D chaotic system (whose nonlinearity is a hyperbolic function) inspired by the quadratic system introduced by [Jay and Roy Nonlinear Dyn (2017) 89:1845–1862]. Basic properties of the new system are discussed and its complex behaviors are characterized using dynamic systems analysis tools. This system exhibits a rich repertoire of dynamic behaviors including chaos, chaos 2-torus, and quasi-periodic. Other interesting phenomena such as multistability, antimonotonicity, and torus-doubling bifurcations are also reported. Moreover, the hyperbolic cosine nonlinearity is easily implemented by using a pair of semiconductor diodes (no analog multiplier is involved). We confirm the feasibility of the proposed theoretical model using PSpice simulations and a physical realization based on an electronic analog implementation of the model.