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

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.