Earn, D.J.D., Rohani, P., Bolker, B.G., Stefan, A.H. and Kisdi, é. (2004) On the Mechanistic Underpinning of Discrete-Time Population Models with Complex Dynamics. Journal of Theoretical Biology, 228, 261-269.
https://doi.org/10.1016/j.jtbi.2004.01.003

has been cited by the following article:

• 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.