Chaotic hidden attractor in a fractional order system modelling the interaction between dark matter and dark energy

Abstract

In this paper the dynamics of a fractional order system modelling the interaction between dark matter and dark energy is analytically and numerically studied. It is shown for the first time that systems modelling the interaction between dark matter and dark energy, chaotic hidden attractors can be present. The chaotic attractor co-exists with two asymptotically stable equilibria. Equilibria of the linearized system exhibit a center-like behavior. The numerical integration is done by means of the Adams-Bashforth-Moulton scheme and the finite Lyapunov exponents are numerically determined with a dedicated Matlab code. The 3D representation of the chaotic hidden attractor reveals the fact it is not connected with the equilibria, being `hidden` somewhere in the considered phase space.