Bifurcation and Chaos in a Novel 4D-Autonomous System Without Linear Terms: Theoretical Analysis and Electronic Circuit Realization

There are only a few works focused on the design of nonlinear oscillators without linear terms in a lower-order polynomial system. In this paper, a new 4D-autonomous chaotic system with only quadratic nonlinearities is proposed. The preliminary analysis of the introduced model shows that it displays 16 equilibrium points, two of which can undergo Hopf bifurcation. Its complete analysis, based on quantitative and qualitative nonlinear dynamics tools, is presented. We demonstrate that when changing the system parameters, very rich and interesting phenomena are obtained including, for instance, chaos, period-doubling bifurcation, periodic window, periodic oscillations, offset boosting property, and anti-monotonicity. More interestingly, in some ranges of system parameters, the value of the Lyapunov exponent remains unchanged and thus our model exhibits the exciting characteristic of a constant Lyapunov exponent. Furthermore, a pair of symmetric chaotic attractor–repellor is found on the proposed system when the time is reversed. To our best knowledge, this work represents the first report on a 4D-polynomial chaotic system without linear terms investigated up to date. An appropriate analog circuit is constructed to verify and demonstrate the theoretical study.

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