Paper Info
Title
A Chaotic Quadratic Bistable Hyperjerk System with Hidden Attractors and a Wide Range of Sample Entropy: Impulsive Stabilization
Abstract
Hidden attractors generated by the interactions of dynamical variables may have no equilibrium point in their basin of attraction. They have grabbed the attention of mathematicians who investigate strange attractors. Besides, quadratic hyperjerk systems are under the magnifying glass of these mathematicians because of their elegant structures. In this paper, a quadratic hyperjerk system is introduced that can generate chaotic attractors. The dynamical behaviors of the oscillator are investigated by plotting their Lyapunov exponents and bifurcation diagrams. The multistability of the hyperjerk system is investigated using the basin of attraction. It is revealed that the system is bistable when one of its attractors is hidden. Besides, the complexity of the systems' attractors is investigated using sample entropy as the complexity feature. It is revealed how changing the parameters can affect the complexity of the systems' time series. In addition, one of the hyperjerk system equilibrium points is stabilized using impulsive control. All real initial conditions become the equilibrium points of the basin of attraction using the stabilizing method.
Year
DOI
Venue
2021
10.1142/S0218127421502539
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Keywords
DocType
Volume
Chaos, multistability, bifurcation, complexity, Lyapunov exponent
Journal
31
Issue
ISSN
Citations 
16
0218-1274
0
PageRank 
References 
Authors
0.34
0
5
Name
Order
Citations
PageRank
M. D. Vijayakumar101.35
Alireza Bahramian200.34
Hayder Natiq302.70
Karthikeyan Rajagopal405.07
Iqtadar Hussain536.46