Abstract:
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.
Citation:
M. P. Kulakov, E. Ya. Frisman, “Clustering and chimeras in the model of the spatial-temporal dynamics of agestructured populations”, Nelin. Dinam., 14:1 (2018), 13–31
\Bibitem{KulFri18}
\by M.~P.~Kulakov, E.~Ya.~Frisman
\paper Clustering and chimeras in the model of the spatial-temporal dynamics of agestructured populations
\jour Nelin. Dinam.
\yr 2018
\vol 14
\issue 1
\pages 13--31
\mathnet{http://mi.mathnet.ru/nd593}
\crossref{https://doi.org/10.20537/nd1801002}
\elib{https://elibrary.ru/item.asp?id=32773033}
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https://www.mathnet.ru/eng/nd593
https://www.mathnet.ru/eng/nd/v14/i1/p13
This publication is cited in the following 4 articles:
E. Ya. Frisman, O. L. Zhdanova, M. P. Kulakov, G. P. Neverova, O. L. Revutskaya, “Mathematical modeling of population dynamics based on recurrent equations: results and prospects. Part II”, Biol. Bull, 48:3 (2021), 239–250
M. P. Kulakov, E. Ya. Frisman, “Approaches to study of multistability in spatio-temporal dynamics of two-age population”, Izv. Vyss. Uchebn. Zaved.-Prikl. Nelineynaya Din., 28:6 (2020), 653–678
E. Ya. Frisman, M. P. Kulakov, O. L. Revutskaya, O. L. Zhdanova, G. P. Neverova, “Osnovnye napravleniya i obzor sovremennogo sostoyaniya issledovanii dinamiki strukturirovannykh i vzaimodeistvuyuschikh populyatsii”, Kompyuternye issledovaniya i modelirovanie, 11:1 (2019), 119–151
M. P. Kulakov, E. Ya. Frisman, “Modelirovanie prostranstvenno-vremennoi dinamiki populyatsii s vozrastnoi strukturoi i dalnodeistvuyuschimi vzaimodeistviyami: sinkhronizatsiya i klasterizatsiya”, Matem. biologiya i bioinform., 14:1 (2019), 1–18
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