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Kulakov M. P., Frisman E. Y. Approaches to study of multistability in spatio-temporal dynamics of two-age population. *Izvestiya VUZ. Applied Nonlinear Dynamics*, 2020, vol. 28, iss. 6, pp. 653-678. DOI: 10.18500/0869-6632-2020-28-6-653-678

# Approaches to study of multistability in spatio-temporal dynamics of two-age population

Purpose of the work is to study spatio-temporal dynamics of limited two-age structured populations that populate a 2D habitat and capable of long-range displacement of individuals. We proposed the model that is the network of nonlocally coupled nonlinear maps with nonlinear coupling function. Conditions for the emergence of different types of heterogeneous spatial distribution, combining coherent and incoherent regimes in different sites and solitary states are studied. Methods. In order to study the multistability of the dynamics in space and time, we used the synchronization factor and the order parameter. In addition, the method for estimating a number of solitary states is proposed. During numerical experiments, we generated many random initial conditions and computed these indicators for asymptotic space-time regime, and estimated the probability of a specific scenario. Results. Three typical regimes of spatio-temporal dynamics are described. The first one is a homogeneous distribution with full or partial synchronization. The probability of this scenario decreases as the strength and/or radius of coupling decreases. The second is a heterogeneous distribution with spots, stripes or labyrinths patterns, corresponding to cluster synchronization. The last one is highly fragmented spots, but in general with coherent dynamics. It was shown that these regimes coexist under certain conditions. Moreover, in most cases, the spatio-temporal dynamics contains randomly located single elements with outbreak of population size (solitary states) regardless of the observed regime of most others. Conclusion. The following paradoxical situation was revealed. As the elements become less coupled and the dynamics more incoherent, the number of solitary states increases. As a result, the elements with outbreak are more often synchronized with each other and form clusters of solitary states mixed with clusters of synchronous populations, or with highly fragmented clusters, or such clusters appear against the background of absolutely non-synchronous dynamics.

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