Paper Info
Title
Hidden and Self-Excited Collective Dynamics of a New Multistable Hyper-Jerk System with Unique Equilibrium
Abstract
Nonlinear dynamical systems with hidden attractors belong to a recent and hot area of research. Such systems can exist in different forms, such as without equilibrium or with a stable equilibrium point. This paper focuses on the dynamics of a new 4D chaotic hyper-jerk system with a unique equilibrium point. It is shown that the new hyper-jerk system effectively exhibits different hidden behaviors, which are hidden point attractor, hidden periodic attractor, and hidden chaotic state. Collective behaviors of the system are studied in terms of the equilibrium point, bifurcation diagrams, phase portraits, frequency spectra, and two-parameter Lyapunov exponents. Some remarkable and exciting properties are found in the new snap system, such as period-doubling transition, asymmetric bubbles, and coexisting bifurcations. Also, we demonstrate that it is possible to generate different varieties of two, three, four, or five coexisting hidden and self-excited attractors in the introduced model. In addition, the amplitude and offset of the hidden chaotic attractors are perfectly controlled for possible application in engineering. Furthermore, a circuit design has been implemented to support the physical feasibility of the proposed model.
Year
DOI
Venue
2022
10.1142/S0218127422500638
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Keywords
DocType
Volume
Hyper-jerk system, stable equilibrium, hidden attractor, multistability, control
Journal
32
Issue
ISSN
Citations 
05
0218-1274
0
PageRank 
References 
Authors
0.34
0
6
Name
Order
Citations
PageRank
M. D. Vijayakumar101.35
Hayder Natiq202.70
Gervais Dolvis Leutcho300.34
Karthikeyan Rajagopal405.07
Sajad Jafari518433.07
Iqtadar Hussain636.46