Dynamic analysis and multistability of a novel four-wing chaotic system with smooth piecewise quadratic nonlinearity

Abstract

In this contribution, a new four-wing chaotic system with a smooth piecewise quadratic nonlinearity is introduced. The novel system is inspired from the cubic one introduced by Sampath et al. (2015). Fundamental 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 when suitable set of parameters are chosen including a single two-wing and four-wing chaotic attractors. Further analysis of the novel system shows that four disconnected coexisting stable states can be observed with different initial values. Moreover, the smooth quadratic nonlinearity is easily implemented by using off-the-shelf electronic components (instead of analog multiplier ship in the case of a cubic nonlinearity). The synchronization and the feasibility of the proposed mathematical model are also presented by developing an adaptive synchronization scheme of two identical four-wing chaotic systems and using PSpice simulations based on an electronic analog of the model.