A simple Jerk-like system without equilibrium: Asymmetric coexisting hidden attractors, bursting oscillation and double full Feigenbaum remerging trees. (March 2019)

• Record Type: Journal Article
• Authors: Zhang, Sen; Zeng, Yicheng
• Is Part Of: Chaos, solitons and fractals. Volume 120(2019)
• Page Start: 25
• Page End: 40
• Publication Date: 2019-03
• Subjects: No-equilibrium Jerk-like chaotic system -- Asymmetric coexisting hidden attractor -- Bursting oscillation -- Double Feigenbaum remerging tree -- Hardware electronic circuit; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2018.12.036
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: A novel no-equilibrium Jerk-like chaotic system is constructed and explored. The system generates various asymmetric coexisting hidden attractors. Transient chaos, periodic bursting oscillation and transient periodic bursting oscillation behaviors are obtained. The unique phenomenon of one to two full Feigenbaum remerging trees is also observed. The hardware experimental results are performed to prove the numerical simulations. Abstract: The topic associated with hidden attractor and multistability has been received considerable attention recently. In this paper, a novel no-equilibrium Jerk-like chaotic system is constructed and explored. Particularly, owing to the absence of the equilibria, such a new system can be categorized as a system with hidden attractors. More interestingly, this system holds three conspicuous characteristics. The first one is that various asymmetric coexisting hidden attractors and complicated transient chaos behaviors are obtained. The second one is the new finding of the periodic bursting oscillation and unusual phenomenon of transient periodic bursting oscillation in the system. The third one is the observation of the amazing and rare phenomenon of one to two full Feigenbaum remerging trees, namely, antimonotonicity. To the best knowledge of us, the last two special features are first discovered and have never been reported, especially in such no-equilibrium chaotic system that exhibits hidden attractors. With the help of phase portraits, time series, bifurcation diagram, Lyapunov exponents, chaotic dynamical diagram, basin of attraction and so forth, the rich hidden dynamical properties of this system are systematically analyzed and investigated. Additionally, a hardware electronic circuit on a breadboard is carried out. A very good similarity between the hardware experimental results and the theoretical analysis testifies the feasibility and practicality of this original system.