Eur. Phys. J. Spec. Top. (2022) 231: 1061-1070
https://doi.org/10.1140/epjs/s11734-021-00308-5

Regular Article

Fractional-order biological system: chaos, multistability and coexisting attractors

¹ Laboratory of Dynamical System and Control, University of Larbi Ben M’hidi, 04000, Oum El Bouaghi, Algeria
² Department of Mathematics and Computer Sciences, Larbi Ben M’hidi University, Oum El Bouaghi, Algeria
³ Nonlinear Dynamics Research Center (NDRC), College of Humanities and Sciences, Ajman University, Ajman, UAE
⁴ Department of Mathematics, Faculty of Science, University of Jordan, 11942, Amman, Jordan
⁵ Department of Innovation Engineering, University of Salento, 73100, Lecce, Italy
⁶ Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam

^e phamvietthanh@tdtu.edu.vn

Received: 18 January 2021
Accepted: 25 October 2021
Published online: 2 November 2021

Abstract

In this paper, the nonlinear dynamics of the biological system modeled by the fractional incommensurate order Van der Pol equations are investigated. The stability of the proposed fractional non-autonomous system is analyzed by varying both the fractional order derivative and system parameters. Moreover, very interesting phenomena such as symmetry, multi-stability and coexistence of attractors are discovered in the considered biological system. Numerical simulations are performed by considering the Caputo fractional derivative and results are reported by means of bifurcation diagrams, computation of the largest Lyapunov exponent, phase portraits in 2D and 3D projections.