Reversal of period-doubling and extreme multistability in a novel 4D chaotic system with hyperbolic cosine nonlinearity

Recently, the study of nonlinear systems with an infinite number of coexisting attractors has become one of the most followed topics owing to their fundamental and technological importance. This contribution is focused on a new 4D autonomous system (whose nonlinearity is a hyperbolic function) inspired by the quadratic system introduced by Jay and Roy (Optik, http://dx.doi.org/https://doi.org/10.1016/j.ijleo.2017.07.042, 2017). Basic properties of the new system are discussed and its complex behaviors are characterized using classical nonlinear diagnostic tools. This system exhibits a rich repertoire of dynamic behaviors including chaos, chaos 2-torus, and quasi-periodicity. Interesting and striking phenomena such as antimonotonicity and extreme multistability are reported. Moreover, the hyperbolic cosine nonlinearity is easily implemented by using only two semiconductor diodes (no analog multiplier is involved) connected in parallel. We confirm the feasibility of the proposed theoretical model using PSpice simulations based on an analog computer of the model. © 2018, Springer-Verlag GmbH Germany, part of Springer Nature.