On the Fractional-Order Complex Cosine Map: Fractal Analysis, Julia Set Control and Synchronization

In this paper, we introduce a generalized complex discrete fractional-order cosine map. Dynamical analysis of the proposed complex fractional order map is examined. The existence and stability characteristics of the map’s fixed points are explored. The existence of fractal Mandelbrot sets and Julia sets, as well as their fractal properties, are examined in detail. Several detailed simulations illustrate the effects of the fractional-order parameter, as well as the values of the map constant and exponent. In addition, complex domain controllers are constructed to control Julia sets produced by the proposed map or to achieve synchronization of two Julia sets in master/slave configurations. We identify the more realistic synchronization scenario in which the master map’s parameter values are unknown. Finally, numerical simulations are employed to confirm theoretical results obtained throughout the work

Chaos and bifurcation of a nonlinear discrete preypredator system

Abstract The discrete-time Prey-predator system obtained by two dimensional map was studied in present study. The fixed points and their stability were analyzed. Bifurcation diagram has been obtained for selected range of different parameters. As some parameters varied, the model exhibited chaos as a long time behavior. Lyapunov exponents and fractal dimension of the chaotic attractor of our map were also calculated. Complex dynamics such as cycles and chaos were observed