Dynamic analysis of a novel jerk system with composite tanh-cubic nonlinearity: chaos, multi-scroll, and multiple coexisting attractors

Dynamic analysis of a novel jerk system with composite tanh-cubic nonlinearity: chaos,... 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 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Dynamics and Control Springer Journals

Dynamic analysis of a novel jerk system with composite tanh-cubic nonlinearity: chaos, multi-scroll, and multiple coexisting attractors

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Engineering; Vibration, Dynamical Systems, Control; Control; Complexity
ISSN
2195-268X
eISSN
2195-2698
D.O.I.
10.1007/s40435-018-0444-9
Publisher site
See Article on Publisher Site

Abstract

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

Journal

International Journal of Dynamics and ControlSpringer Journals

Published: May 28, 2018

References

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