A new approach on the modelling, chaos control and synchronization of a fractional biological oscillator

Advances in Difference Equations

article

Alshomrani, Ali Saleh¹  Ullah, Malik Zaka¹  Baleanu, Dumitru² 

[1] Mathematical Modelling and Applied Computation Research Group (MMAC), Department of Mathematics, Faculty of Science, King Abdulaziz University;Department of Mathematics, Faculty of Arts and Sciences, Çankaya University;Institute of Space Sciences

关键词: Fractional model;    Biological system;    Chaotic attractors;    Chaos control;    Synchronization;   

DOI  :  10.1186/s13662-021-03224-z

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

This research aims to discuss and control the chaotic behaviour of an autonomous fractional biological oscillator. Indeed, the concept of fractional calculus is used to include memory in the modelling formulation. In addition, we take into account a new auxiliary parameter in order to keep away from dimensional mismatching. Further, we explore the chaotic attractors of the considered model through its corresponding phase-portraits. Additionally, the stability and equilibrium point of the system are studied and investigated. Next, we design a feedback control scheme for the purpose of chaos control and stabilization. Afterwards, we introduce an efficient active control method to achieve synchronization between two chaotic fractional biological oscillators. The efficiency of the proposed stabilizing and synchronizing controllers is verified via theoretical analysis as well as simulations and numerical experiments.

【 授权许可】

CC BY