Bifurcation in the almost periodic $ 2 $D Ricker map

Abstract

<p style='text-indent:20px;'>This paper studies bifurcations in the coupled <inline-formula><tex-math id="M2">\begin{document}$ 2 $\end{document}</tex-math></inline-formula> dimensional almost periodic Ricker map. We establish criteria for stability of an almost periodic solution in terms of the Lyapunov exponents of a corresponding dynamical system and use them to find a bifurcation function. We find that if the almost periodic coefficients of all the maps are identical, then the bifurcation function is the same as the one obtained in the one dimensional case treated earlier, and that this result holds in <inline-formula><tex-math id="M3">\begin{document}$ N $\end{document}</tex-math></inline-formula> 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.</p>