Control and adaptive modified function projective synchronization of different hyperchaotic dynamical systems

M. M. El-Dessoky; Nehad Almohammadi; Ebraheem Alzahrani; M. M. El-Dessoky; Nehad Almohammadi; Ebraheem Alzahrani

doi:10.3934/math.20231201

AIMS Mathematics

2023, Volume 8, Issue 10: 23621-23634. doi: 10.3934/math.20231201

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Control and adaptive modified function projective synchronization of different hyperchaotic dynamical systems

1.
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
3.
Jamoum University College, Umm Al-Qura University, Makkah, Saudi Arabia

Received: 24 February 2023 Revised: 04 July 2023 Accepted: 07 July 2023 Published: 31 July 2023
MSC : 37N35, 34D06, 34H10

In this work, we consider an adaptive control method, which is simpler and generalized to obtain some conditions on the parameters for hyperchaotic models determined by using a Lyapunov direct method. Further, an adaptive controller for synchronization is designed by using Lyapunov functions by which the deriving system and the response system can realize adaptive modified function projective synchronization up to scaling matrix. Numerical simulation of each system is discussed in detail with graphical results. The graphical results are presented in detail in order to validate the theoretical results. These results in this article generalize and improve the corresponding results of the recent works.
- adaptive control,
- modified function projective synchronization,
- error dynamical system,
- Liu hyperchaotic,
- Chen hyperchaotic
Citation: M. M. El-Dessoky, Nehad Almohammadi, Ebraheem Alzahrani. Control and adaptive modified function projective synchronization of different hyperchaotic dynamical systems[J]. AIMS Mathematics, 2023, 8(10): 23621-23634. doi: 10.3934/math.20231201

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Abstract

In this work, we consider an adaptive control method, which is simpler and generalized to obtain some conditions on the parameters for hyperchaotic models determined by using a Lyapunov direct method. Further, an adaptive controller for synchronization is designed by using Lyapunov functions by which the deriving system and the response system can realize adaptive modified function projective synchronization up to scaling matrix. Numerical simulation of each system is discussed in detail with graphical results. The graphical results are presented in detail in order to validate the theoretical results. These results in this article generalize and improve the corresponding results of the recent works.

References

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