Chaotic Behavior in a Novel Fractional Order System with No Equilibria

This article takes into consideration a novel chaotic system of four dimensional fractional order having no equilibria. We cannot use mathematical methods such as Melnikov’s and Shilnikov’s method to prove that the given system is chaotic. We shall analyse the dynamical features of the fractional order system by using predictor-corrector algorithm. This method reports chaotic dynamics. We shall apply the basic ideas of non linear dynamical analysis such as bifurcation diagrams and Lyapunov exponents to recognise the chaotic behavior for the given system. One interesting phenomena for the system is that it has cascade of period doubling bifurcations and chaotic attractors without having any equilibrium points.