Open AccessBifurcation in the almost periodic $ 2 $D Ricker map
Author(s) -
Brian Ryals,
Robert J. Sacker
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021089
Subject(s) - mathematics , lyapunov exponent , bifurcation , dimension (graph theory) , function (biology) , stability (learning theory) , mathematical analysis , combinatorics , pure mathematics , physics , nonlinear system , computer science , quantum mechanics , evolutionary biology , machine learning , biology
This paper studies bifurcations in the coupled \begin{document}$ 2 $\end{document} dimensional almost periodic Ricker map. We establish criteria for stability of an almost periodic solution in terms of the Lyapunov exponents of a corresponding dynamical system and use them to find a bifurcation function. We find that if the almost periodic coefficients of all the maps are identical, then the bifurcation function is the same as the one obtained in the one dimensional case treated earlier, and that this result holds in \begin{document}$ N $\end{document} dimension under modest coupling constraints. In the general two-dimensional case, we compute the Lyapunov exponents numerically and use them to examine the stability and bifurcations of the almost periodic solutions.