Stability analysis of chaotic generalized Lotka-Volterra system via active compound difference anti-synchronization method

Harindri Chaudhary; Mohammad Sajid; Santosh Kaushik; Ali Allahem; Harindri Chaudhary; Mohammad Sajid; Santosh Kaushik; Ali Allahem

doi:10.3934/mbe.2023413

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 5: 9410-9422. doi: 10.3934/mbe.2023413

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Stability analysis of chaotic generalized Lotka-Volterra system via active compound difference anti-synchronization method

1.
Department of Mathematics, Deshbandhu College, University of Delhi, New Delhi 110019, India
2.
Department of Mechanical Engineering, College of Engineering, Qassim University, Buraydah 51452, Saudi Arabia
3.
Department of Mathematics, Bhagini Nivedita College, University of Delhi, New Delhi 110043, India
4.
Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia

Academic Editor: Xiaodi Li

Received: 23 November 2022 Revised: 18 February 2023 Accepted: 13 March 2023 Published: 17 March 2023

This work deals with a systematic approach for the investigation of compound difference anti-synchronization (CDAS) scheme among chaotic generalized Lotka-Volterra biological systems (GLVBSs). First, an active control strategy (ACS) of nonlinear type is described which is specifically based on Lyapunov's stability analysis (LSA) and master-slave framework. In addition, the biological control law having nonlinear expression is constructed for attaining asymptotic stability pattern for the error dynamics of the discussed GLVBSs. Also, simulation results through MATLAB environment are executed for illustrating the efficacy and correctness of considered CDAS approach. Remarkably, our attained analytical outcomes have been in outstanding conformity with the numerical outcomes. The investigated CDAS strategy has numerous significant applications to the fields of encryption and secure communication.
- chaotic system,
- generalized Lotka-Volterra system,
- anti-synchronization,
- active control strategy,
- compound difference synchronization,
- Lyapunov stability analysis,
- simulation,
- Lyapunov functions
Citation: Harindri Chaudhary, Mohammad Sajid, Santosh Kaushik, Ali Allahem. Stability analysis of chaotic generalized Lotka-Volterra system via active compound difference anti-synchronization method[J]. Mathematical Biosciences and Engineering, 2023, 20(5): 9410-9422. doi: 10.3934/mbe.2023413

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Abstract

This work deals with a systematic approach for the investigation of compound difference anti-synchronization (CDAS) scheme among chaotic generalized Lotka-Volterra biological systems (GLVBSs). First, an active control strategy (ACS) of nonlinear type is described which is specifically based on Lyapunov's stability analysis (LSA) and master-slave framework. In addition, the biological control law having nonlinear expression is constructed for attaining asymptotic stability pattern for the error dynamics of the discussed GLVBSs. Also, simulation results through MATLAB environment are executed for illustrating the efficacy and correctness of considered CDAS approach. Remarkably, our attained analytical outcomes have been in outstanding conformity with the numerical outcomes. The investigated CDAS strategy has numerous significant applications to the fields of encryption and secure communication.

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