Abstract
In this contribution, a new elegant hyperjerk system with three equilibria and hyperbolic sine nonlinearity is investigated. In contrast to other models of hyperjerk systems where either hidden or self-excited attractors are obtained, the case reported in this work represents a unique one which displays the coexistence of self-excited chaotic attractors and stable fixed points. The dynamic properties of the new system are explored in terms of equilibrium point analyses, symmetry and dissipation, and existence of attractors as well. Common analysis tools (i.e., bifurcation diagram, Lyapunov exponents, and phase portraits) are used to highlight some important phenomena such as period-doubling bifurcation, chaos, periodic windows, and symmetric restoring crises. More interestingly, the system under consideration shows the coexistence of several types of stable states, including the coexistence of two, three, four, six, eight, and ten coexisting attractors. In addition, the system is shown to display antimonotonicity and offset boosting. Laboratory experimental measurements show a very good coherence with the theoretical predictions.
Highlights
Most authors have been interested in chaotic systems because of their sensitivity to the initial conditions and to the variation of system parameters
Several authors have studied the latter. These systems exhibit multistability phenomenon which are the coexistence of multiple attractors solely depending on the initial conditions. ese attractors are generally classified into two categories, namely, self-excited and hidden attractors [15,16,17,18,19,20]
Remember that self-excited attractors exist in systems with unstable equilibrium points [21,22,23]
Summary
Most authors have been interested in chaotic systems because of their sensitivity to the initial conditions and to the variation of system parameters. These systems exhibit multistability phenomenon which are the coexistence of multiple attractors solely depending on the initial conditions. Interested by the self-excited attractors, many authors applied different techniques to hyperjerk systems. Some of these authors introduced different types of nonlinearities. Leutcho et al [21] presented a new hyperjerk circuit with hyperbolic sine function and demonstrated that the novel proposed system is the unique one which is capable to exhibit the coexistence of nine periodic and chaotic attractors.
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