Hopf bifurcation in three-dimensional based on chaos entanglement function. (December 2019)

• Record Type: Journal Article
• Authors: Yao, Kutorzi Edwin; Shi, Yufeng
• Is Part Of: Chaos, solitons & fractals. Volume 4(2019)
• Publication Date: 2019-12
• Subjects: Bifurcation -- Chaos entanglement -- Chaotic attractor -- Lyapunov exponent -- Time series; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Solitons; Fractals; Chaotic behavior in systems; Periodicals; Electronic journals; 003.7
• DOI: 10.1016/j.csfx.2020.100027
• Languages: English
• ISSNs: 2590-0544

Abstract

Highlights: A nonlinear system can have a more complicated steady-state behavior that is not equilibrium, periodic oscillation or oscillation. At any specific time a dynamical system has a state given by a set of real numbers that can be represented by a point in a suitable state margin. One has proposed a novel approach to generate contrived chaos by entangling two or mathematical product stable linear subsystems. The assumption has in mind that we can split up completely subsystems into two groups Hurwitz stable group and unstable group. Abstract: Chaotic entanglement is a new method used to deliver chaotic physical process, as suggested in this work. Primary rationale is to entangle more than two mathematical product stationery linear schemes by means of entanglement functions to make a chaotic system that develops in a chaotic manner.Existence of Hopf bifurcation is looked into by selecting the set aside bifurcation parameter. More accurately, we consider the stableness and bifurcations of sense of equilibrium in the modern chaotic system. In addition, there is involvement of chaos in mathematical systems that have one positive Lyapunov exponent. Furthermore, there are four requirements that are needed to achieve chaos entanglement. In that way through dissimilar linear schemes and dissimilar entanglement functions, a collection of fresh chaotic attractors has been created and abundant coordination compound dynamics are exhibited. The breakthrough suggests that it is not difficult any longer to construct new obviously planned chaotic systems/networks for applied science practical application such as chaos-based secure communication.