Attraction basins of clusters in coupled map lattices

This paper researches a phenomenon of clustering and multistability in a non-global coupled Ricker maps. To construct attraction basins for some phases of clustering we propose a method. For this purpose we consider the several simultaneously possible and fundamentally different trajectories of the system corresponding to different phases of clustering. As a result these phases or trajectories have the unique domains of attraction (basins) in the phase space and stability region in the parametric space. The suggested approach consists in that each a trajectory is approximated the non-identical asymmetric coupled map lattices consisting of fewer equations and equals the number of clusters. As result it is shown the formation and transformation of clusters is the same like a bifurcations leading to birth of asynchronous modes in approximating systems.