BIFURCATION ANALYSIS OF A CLASS OF DISCRETE THOMAS TYPE SYSTEM

Abstract

We often use differential equations to represent continuous dynamical systems and difference equations to represent discrete dynamical systems. In general, discrete dynamical systems have rich dynamic behaviors. Bifurcation problems of differential systems have been extensively studied.The dynamics of a discrete-time Thomas type system is investigated in the closed first quadrant. It is shown that the system undergoes flip bifurcation and Neimark–Sacker bifurcation in the interior by using a center manifold theorem and bifurcation theory. Numerical simulations are presented not only to illustrate our results with the theoretical analysis, but also to exhibit much more interesting dynamical behavior, including orbits of period 2, 4, 8 and chaotic sets. These results show far richer dynamics of the discrete model compared with the continuous model