A new discrete chaotic system with rational fraction and its dynamical behaviors

A new discrete chaotic system with rational fraction is introduced in this paper. The dynamical behaviors, including the symmetry, value domain, equilibrium point, route to chaos, period-doubling bifurcation, and Lyapunov exponents spectrum, are further investigated. Moreover, we study the tracking and control problems of this new system. Also, numerical simulations are presented to show the effectiveness and feasibility of the developed controller.