Efim Frisman

    Sholom-Aleikhem St., 4, Birobidzhan, 679016, Russia
    Institute for Complex Analysis of Regional Problems, Far Eastern Branch of RAS


    Kulakov M. P., Frisman E. Y.
    The article is devoted to the model of spatial-temporal dynamics of age-structured populations coupled by migration. The dynamics of a single population is described by a two-dimensional nonlinear map demonstrating multistability, and a coupling is a nonlocal migration of individuals. An analysis is made of the problem of synchronization (complete, cluster and chaotic), chimera states formation and transitions between different types of dynamics. The problem of dependence of the space-time regimes on the initial states is discussed in detail. Two types of initial conditions are considered: random and nonrandom (special, as defined ratios) and two cases of single oscillator dynamics — regular and irregular fluctuations. A new cluster synchronization mechanism is found which is caused by the multistability of the local oscillator (population), when different clusters differ fundamentally in the type of their dynamics. It is found that nonrandom initial conditions, even for subcritical parameters, lead to complex regimes including various chimeras. A description is given of the space-time regime when there are several single nonsynchronous elements with large amplitude in a cluster with regular or chaotic dynamics. It is found that the type of spatial-temporal dynamics depends considerably on the distribution parameters of random initial conditions. For a large scale factor and any coupling parameters, there are no coherent regimes at all, and coherent states are possible only for a small scale factor.
    Keywords: population, multistability, coupled map lattice, synchronization, clustering, chimera, basin of attraction
    Citation: Kulakov M. P., Frisman E. Y.,  Clustering and chimeras in the model of the spatial-temporal dynamics of agestructured populations, Rus. J. Nonlin. Dyn., 2018, Vol. 14, no. 1, pp.  13-31
    Shlufman K. V., Neverova G. P., Frisman E. Y.
    The paper studies dynamic modes of the Ricker model with the periodic Malthusian parameter. The equation parametric space is shown to have multistability areas in which different dynamic modes are possible depending on the initial conditions. In particular, the model trajectory can asymptotically tend either to a stable cycle or to a chaotic attractor. Oscillation synchronization of the 2-cycles and the Malthusian parameter of the model are studied. Fluctuations in population size and environmental factors can be either synchronous or asynchronous. The structural features of attraction basins in phase space are investigated for possible stable dynamic modes.
    Keywords: recurrence equation, Ricker model, periodic Malthusian parameter, stability, bifurcation, dynamic modes, phase space, basins of attraction, multistability
    Citation: Shlufman K. V., Neverova G. P., Frisman E. Y.,  Dynamic modes of the Ricker model with periodic Malthusian parameter, Rus. J. Nonlin. Dyn., 2017, Vol. 13, No. 3, pp.  363-380
    Revutskaya O. L., Neverova G. P., Kulakov M. P., Frisman E. Y.
    This paper is concerned with the model of dynamics for population with a simple age structure. It is assumed that the growth of population size is regulated by limiting the survival rate of younger individuals. It is shown that the density-dependent regulation of offspring survival can lead to fluctuations in population size. Moreover, there are multistability areas in which the type of dynamic regimes depends on the initial conditions. These aspects of dynamic behavior can explain the changes in the oscillation period, and the appearance and disappearance of population size fluctuations.
    Keywords: mathematical modeling, population dynamics, age structure, density-dependent regulation, stability, bifurcations, dynamic modes, multistability, chaos
    Citation: Revutskaya O. L., Neverova G. P., Kulakov M. P., Frisman E. Y.,  Model of age-structured population dynamics: stability, multistability, and chaos, Rus. J. Nonlin. Dyn., 2016, Vol. 12, No. 4, pp.  591–603
    Shlufman K. V., Neverova G. P., Frisman E. Y.
    This paper investigates the emergence and stability of 2-cycles for the Ricker model with the 2-year periodic Malthusian parameter. It is shown that the stability loss of the trivial solution occurs through the transcritical bifurcation resulting in a stable 2-cycle. The subsequent tangent bifurcation leads to the appearance of two new 2-cycles: stable and unstable ones. As a result, there is multistability. It is shown that the coexistence of two different stable 2-cycles is possible in a narrow area of the parameter space. Further stability loss of the 2-cycles occurs according to the Feigenbaum scenario.
    Keywords: recurrence equation, Ricker model, periodic Malthusian parameter, stability, bifurcation, multistability
    Citation: Shlufman K. V., Neverova G. P., Frisman E. Y.,  Two-cycles of the Ricker model with the periodic Malthusian parameter: stability and multistability, Rus. J. Nonlin. Dyn., 2016, Vol. 12, No. 4, pp.  553-565
    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
    Kulakov M. P., Neverova G. P., Frisman E. Y.
    This article researches model of two coupled an age structured populations. The model consists of two identical two-dimensional maps demonstrating the Neimark – Sacker and period-doubling bifurcations. The “bistability” of dynamic modes is found which is expressed in a co-existence the nontrivial fixed point and periodic points (stable 3-cycle). The mechanism of loss stability and formation of complex hierarchy for multistable states are investigated.
    Keywords: metapopulation, multistability, maps, synchronization, basin of attraction
    Citation: Kulakov M. P., Neverova G. P., Frisman E. Y.,  Multistability in dynamic models of migration coupled populations with an age structure, Rus. J. Nonlin. Dyn., 2014, Vol. 10, No. 4, pp.  407-425

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