Coexistence of Multiple Points, Limit Cycles, and Strange Attractors in a Simple Autonomous Hyperjerk Circuit with Hyperbolic Sine Function

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

Coexistence of Multiple Points, Limit Cycles, and Strange Attractors in a Simple Autonomous Hyperjerk Circuit with Hyperbolic Sine Function

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.</jats:p

Hidden dynamics of an optically injected laser diode subject to threshold electromagnetic induction: coexistence of multiple stable states

In this contribution, we perform a detailed study of the effect of electromagnetic induction on the dynamical behavior of laser diode modeled by novel single-mode four-dimensional rate equations. Memristor is used to describe electromagnetic induction effect. As result, the obtained model is equilibrium free thus displays hidden dynamics. Consequently, Shilnikov method is not suitable to explain the chaos mechanism in the introduced laser model. Furthermore, there is no heteroclinic nor homoclinic orbit. Based on numerical simulations, we found that the laser model displays hidden dynamics including period doubling bifurcation, multistability (with three different stable states) and crisis phenomena when the electromagnetic strength is varied. The circuit emulator of laser model investigated in this paper has been designed in the Pspice environment to further support numerical results

Extremely rich dynamics from hyperchaotic Hopfield neural network: Hysteretic dynamics, parallel bifurcation branches, coexistence of multiple stable states and its analog circuit implementation

In this work, we investigate the dynamics of a model of 4-neurons based hyperchaotic Hopfield neural network (HHNN) with a unique unstable node as a fixed point. The basic properties of the model including symmetry, dissipation, and condition of the existence of an attractor are explored. Our numerical simulations highlight several complex phenomena such as periodic orbits, quasi-periodic orbits, and chaotic and hyperchaotic orbits. More interestingly, it has been revealed several sets of synaptic weights matrix for which the HHNN studied display multiple coexisting attractors including two, three and four symmetric and disconnected attractors. Both hysteretic dynamics and parallel bifurcation branches justify the presence of these various coexisting attractors. Basins of attraction with the riddle structure of some of the coexisting attractors have been computed showing different regions in which each solution can be captured. Finally, PSpice simulations are used to further support the results of our previous analyses