It is well known that the dynamics of very simple physical systems can be quite complex if a sufﬁcient amount of nonlin- earity is present. In this contribution, a novel jerk system with smooth composite tanh-cubic nonlinearity is proposed and investigated. Interestingly, the new nonlinearity takes advantage of the classical smooth cubic polynomial in the sense that it induces more complex and interesting dynamics (e.g. ﬁve equilibria instead of three in the case of a (traditional) cubic nonlinearity, multi-scroll, and multistability). The fundamental properties of the model are discussed including equilibria and stability, phase portraits, Poincaré sections, bifurcation diagrams and Lyapunov exponent’s plots. Period doubling bifurcation, antimonotonicity, chaos, hysteresis, and coexisting bifurcations are reported. In particular, a rare phenomenon is found in which two different pairs of coexisting limit cycles born from the Hopf bifurcation follow each a different sequence of period- doubling bifurcations, then merge to form a three-scroll chaotic attractor as a parameter is smoothly changed. As another major result of this work, several windows in the parameter space are depicted in which the novel jerk system develops the striking behaviour of multiple coexisting attractors (i.e. coexistence of three, four, six, or eight disjoint periodic and chaotic
International Journal of Dynamics and Control – Springer Journals
Published: May 28, 2018
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