Abstract
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.
Highlights
Chaos is one of the most prominent features of complex dynamical systems whose state variables are highly dependent on their initial conditions
In [6], a parameter observer was designed in order to identify unknown parameters in hyperchaotic systems, which was needed for designing a state-feedback controller
We study the stability and equilibrium of the new system and analyse its chaotic behaviour by using phase-portrait responses
Summary
Chaos is one of the most prominent features of complex dynamical systems whose state variables are highly dependent on their initial conditions. We propose a state-feedback control to stabilize the fractional model and apply an active control strategy to synchronize two identical chaotic oscillators. 3, the new mathematical fractional model of a chaotic biological oscillator is introduced, and its stability and equilibrium point are investigated. Afterwards, a state-feedback control is designed to stabilize the new model, and an active controller is introduced in order to achieve synchronization. The integer-order model (5) suffers from the lack of memory effect, while hereditary property is the intrinsic feature of many complex biological systems. To overcome this drawback, the concept of fractional calculus is used to include memory in the model formulation.
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