Attraction basins of clusters in coupled map lattices

    2015, Vol. 11, No. 1, pp.  51-76

    Author(s): Kulakov M. P., Frisman E. Y.

    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.
    Keywords: metapopulation, multistability, coupled map lattices, clustering, basin of attraction
    Citation: Kulakov M. P., Frisman E. Y., Attraction basins of clusters in coupled map lattices, Rus. J. Nonlin. Dyn., 2015, Vol. 11, No. 1, pp.  51-76

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