Abstract
In this paper, a novel no-equilibrium 5D memristive hyperchaotic system is proposed, which is achieved by introducing an ideal flux-controlled memristor model and two constant terms into an improved 4D self-excited hyperchaotic system. The system parameters-dependent and memristor initial conditions-dependent dynamical characteristics of the proposed memristive hyperchaotic system are investigated in terms of phase portrait, Lyapunov exponent spectrum, bifurcation diagram, Poincaré map, and time series. Then, the hidden dynamic attractors such as periodic, quasiperiodic, chaotic, and hyperchaotic attractors are found under the variation of its system parameters. Meanwhile, the most striking phenomena of hidden extreme multistability, transient hyperchaotic behavior, and offset boosting control are revealed for appropriate sets of the memristor and other initial conditions. Finally, a hardware electronic circuit is designed, and the experimental results are well consistent with the numerical simulations, which demonstrate the feasibility of this novel 5D memristive hyperchaotic system.
Highlights
As an important branch of nonlinear science, chaos has undergone great evolution and development since the first three dimensional (3D) system showing butterfly-shaped chaotic attractor was reported by Lorenz in 1963 [1,2,3]
It is worth noting that the nonzero constant terms g and h are newly introduced, which can make the proposed 5D memristive hyperchaotic system have no equilibrium points. erefore, the nonzero constant terms g and h are especially valuable for the emergence of hidden extreme multistability in the presented system
With the help of equilibrium points, phase portrait, Lyapunov exponents (LEs) spectrum, bifurcation diagram, Poincaremap, and time series, the striking and complex nonlinear dynamical behaviors of the novel 5D memristive hyperchaotic system are broadly investigated by numerical simulations, including hidden hyperchaotic attractor, hidden extreme multistability, transient hyperchaotic behavior, and offset boosting control
Summary
As an important branch of nonlinear science, chaos has undergone great evolution and development since the first three dimensional (3D) system showing butterfly-shaped chaotic attractor was reported by Lorenz in 1963 [1,2,3]. Ese memristor-based chaotic/hyperchaotic systems could exhibit numerous nonlinear dynamical behaviors, such as hidden or self-excited attractors, and coexisting multiple [28] or coexisting infinitely many attractors [29, 30]. Motivated by the abovementioned considerations, a novel no-equilibrium 5D memristive hyperchaotic system is proposed in this paper, which is achieved through introducing an ideal flux-controlled memristor model and two constant terms into an improved 4D self-excited hyperchaotic system by [53]. Based on the 4D hyperchaotic system (2), the aforementioned ideal flux-controlled memristor model is introduced to the first equation, and the flux φ that passes through the memristor became a new state variable denoted as U. It is worth noting that the nonzero constant terms g and h are newly introduced, which can make the proposed 5D memristive hyperchaotic system have no equilibrium points. erefore, the nonzero constant terms g and h are especially valuable for the emergence of hidden extreme multistability in the presented system
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