TITLE:
Chaos Synchronization in Discrete-Time Dynamical Systems with Application in Population Dynamics
AUTHORS:
Tahmineh Azizi, Gabriel Kerr
KEYWORDS:
Chaos Synchronization, Synchronization Threshold, Period-Doubling Bifurcation, Convex Link Function, Nonlinear Dynamics
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.8 No.3,
February
28,
2020
ABSTRACT: Study of chaotic synchronization as a fundamental phenomenon in the nonlinear dynamical systems theory has been recently raised many interests in science, engineering, and technology. In this paper, we develop a new mathematical framework in study of chaotic synchronization of discrete-time dynamical systems. In the novel drive-response discrete-time dynamical system which has been coupled using convex link function, we introduce a synchronization threshold which passes that makes the drive-response system lose complete coupling and synchronized behaviors. We provide the application of this type of coupling in synchronized cycles of well-known Ricker model. This model displays a rich cascade of complex dynamics from stable fixed point and cascade of period-doubling bifurcation to chaos. We also numerically verify the effectiveness of the proposed scheme and demonstrate how this type of coupling makes this chaotic system and its corresponding coupled system starting from different initial conditions, quickly get synchronized.