Local Bifurcation Analysis and Global Dynamics Estimation of a Novel 4-Dimensional Hyperchaotic System

Abstract

In this paper, we present a novel 4-dimensional (4D) smooth quadratic autonomous hyperchaotic system with complex dynamics. In order to investigate the dynamics evolution of the system, the Lyapunov exponent spectrum, bifurcation diagram and various phase portraits are provided. The local dynamics of this hyperchaotic system, such as the stability, pitchfork bifurcation, and Hopf bifurcation of equilibrium point, are analyzed by using the center manifold theorem and bifurcation theory. About the global dynamics, the ultimate bound sets of the system are found by combining the Lyapunov function method and appropriate optimization method. Numerical simulations are given to demonstrate the emergence of the two bifurcations and show the ultimate boundary regions.

Dynamic Analysis and Circuit Realization of a Novel No-Equilibrium 5D Memristive Hyperchaotic System with Hidden Extreme Multistability

“…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]. From the physical circuit realization point of view, the corresponding 5D memristive hyperchaotic circuit is achieved by utilizing a memristor to substitute a linear coupling resistor and adding DC sources to realize two constant terms.…”

Periodic solutions for a four-dimensional hyperchaotic system

“…It can generate double-wing chaotic and hyperchaotic attractors with only one equilibrium point [11]. In 2017, Zhou et al proposed a four-dimensional smooth quadratic autonomous hyperchaotic system with complex dynamics, and analyzed the stability of the hyperchaotic system, pitchfork bifurcation, Hopf bifurcation and other local dynamics problems by using the central manifold theorem and bifurcation theory [12]. In 2019, Rajagopal et al proposed an improved hyperchaotic van der Pol-Duffing snap oscillator.…”

“…In this paper, from the perspective of local dynamics, a four-dimensional smooth quadratic autonomous hyperchaotic system [12] is studied:…”

Local bifurcation analysis of brushless DC motor

“…The third problem is that the rigorous methods were hardly utilized in the studies of BLDCM dynamics. So far, the rigorous bifurcation methods such as center manifold theorem and normal form theorem have been applied mainly on numerical chaotic systems . In numerical chaotic systems, however, the parameters reflect no real physical quantity.…”

“…So far, the rigorous bifurcation methods such as center manifold theorem and normal form theorem 24 have been applied mainly on numerical chaotic systems. [25][26][27] In numerical chaotic systems, however, the parameters reflect no real physical quantity. In real physical systems, parameter choice options are limited as there exist parameters which have serious constraints.…”