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A Chaotic Quadratic Bistable Hyperjerk System with Hidden Attractors and a Wide Range of Sample Entropy: Impulsive Stabilization

M. D. Vijayakumar

Centre for Materials Research, Chennai Institute of Technology, India

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Alireza Bahramian

Department of Biomedical Engineering, Amirkabir University of Technology, 424 Hafez Ave., Tehran 15875-4413, Iran

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Hayder Natiq

Information Technology Collage, Imam Ja’afar Al-Sadiq University, 10001 Baghdad, Iraq

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Karthikeyan Rajagopal

https://orcid.org/0000-0003-2993-7182

Centre for Nonlinear Systems, Chennai Institute of Technology, India

E-mail Address: karthikeyan.rajagopal@citchennai.net

Corresponding author.

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, and

Iqtadar Hussain

Department of Mathematics, Statistics and Physics, Qatar University, Doha 2713, Qatar

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https://doi.org/10.1142/S0218127421502539Cited by:5 (Source: Crossref)

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.

Keywords:

References

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