Clustering and chimeras in the model of the spatial-temporal dynamics of agestructured populations

M. P. Kulakov ; E. Ya. Frisman

Russian journal of nonlinear dynamics, Tome 14 (2018) no. 1, pp. 13-31.

Résumé

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.

Détail

Mots-clés : population, chimera
Keywords: multistability, coupled map lattice, synchronization, clustering, basin of attraction.

Bibliographie

[1] Bogomolov S. A., Strelkova G. I., Schöll E., Anishchenko V. S., “Amplitude and phase chimeras in an ensemble of chaotic oscillators”, Tech. Phys. Lett., 42:7 (2016), 765–768 | DOI

[2] Kuznetsov S. P., “Universality and scaling in behavior of coupled Feigenbaum systems”, Radiophys. Quantum El., 28:8 (1985), 681–695 | DOI

[3] Kuznetsov A. P., Kuznetsov S. P., “Critical dynamics of coupled map lattices at the onset of chaos”, Radiophys. Quantum El., 34:10–12 (1991), 845–868

[4] Kulakov M. P., Neverova G. P., Frisman E. Ya., “Multistability in dynamic models of migration coupled populations with an age structure”, Nelin. Dinam., 10:4 (2014), 407–425 (Russian)

[5] Kulakov M. P., Frisman E. Ya., “Attraction basins of clusters in coupled map lattices”, Nelin. Dinam., 11:1 (2015), 51–76 (Russian)

[6] Kulakov M. P., Frisman E. Ya., “Clustering and chimera in the spatial-temporal dynamics of populations with age structure in the ring habitat”, Regional’nye problemy, 19:4 (2016), 5–11 (Russian)

[7] Semenova N. I., Anishchenko V. S., “Coherence-incoherence transition with appearance of chimera states in a one-dimensional ensemble”, Nelin. Dinam., 12:3 (2016), 295–309 (Russian)

[8] Frisman E. Ya., Neverova G. P., Kulakov M. P., Zhigalskii O. A., “Multimode phenomenon in the population dynamics of animals with short live cycles”, Dokl. Biol. Sci., 460:1 (2015), 42–47 | DOI | DOI

[9] Frisman E. Ya., Neverova G. P., Revutskaya O. L., Kulakov M. P., “Dynamic modes of two-age population model”, Izv. Vyssh. Uchebn. Zaved. Prikl. Nelin. Dinam., 18:2 (2010), 111–130 (Russian)

[10] Abrams D. M., Strogatz S. H., “Chimera states for coupled oscillators”, Phys. Rev. Lett., 93:17 (2004), 174102, 4 pp. | DOI

[11] Bogomolov S. A., Slepnev A. V., Strelkova G. I., Schöll E., Anishchenko V. S., “Mechanisms of appearance of amplitude and phase chimera states in ensembles of nonlocally coupled chaotic systems”, Commun. Nonlinear Sci. Numer. Simul., 43 (2016), 25–36 | DOI

[12] Frisman E. Ya., Neverova G. P., Revutskaya O. L., “Complex dynamics of the population with a simple age structure”, Ecol. Model., 222:12 (2011), 1943–1950 | DOI

[13] Kuramoto Y., Battogtokh D., “Coexistence of coherence and incoherence in nonlocally coupled phase oscillators”, Nonl. Phen. Compl. Sys., 5:4 (2002), 380–385

[14] Omelchenko I., Maistrenko Yu., Hövel Ph., Schöll E., “Loss of coherence in dynamical networks: Spatial chaos and chimera states”, Phys. Rev. Lett., 106:23 (2011), 234102, 4 pp. | DOI

[15] Omelchenko I., Riemenschneider B., Hövel Ph., Schöll E., “Transition from spatial coherence to incoherence in coupled chaotic systems”, Phys. Rev. E, 85:2 (2012), 026212, 9 pp. | DOI

[16] Salmon J. K., Moraes M. A., Dror R. O., Shaw D. E., “Parallel random numbers: as easy as $1, 2, 3$”, Proc. of 2011 Internat. Conf. for High Performance Computing, Networking, Storage and Analysis (Seatle, Wash., Nov 2011), 16, 12 pp.

[17] Semenova N. I., Rybalova E. V., Strelkova G. I., Anishchenko V. S., “«Coherence – incoherence» transition in ensembles of nonlocally coupled chaotic oscillators with nonhyperbolic and hyperbolic attractors”, Regul. Chaotic Dyn., 22:2 (2017), 148–162 | DOI

[18] Shepelev I. A., Vadivasova T. E., Bukh A. V., Strelkova G. I., Anishchenko V. S., “New type of chimera structures in a ring of bistable FitzHugh – Nagumo oscillators with nonlocal interaction”, Phys. Lett. A, 381:16 (2017), 1398–1404 | DOI

[19] Tsigkri-DeSmedt N. D., Hizanidis J., Hövel P., Provata A., “Multi-chimera states and transitions in the Leaky Integrate-and-Fire model with nonlocal and hierarchical connectivity”, Eur. Phys. J. Spec. Top., 225:6–7 (2016), 1149–1164 | DOI

[20] Viana R. L., Batista A. M., Batista C. A. S., Iarosz K. C., “Lyapunov spectrum of chaotic maps with a long-range coupling mediated by a diffusing substance”, Nonlinear Dynam., 87:3 (2017), 1589–1601 | DOI

[21] Zhang Y.-Q., Wang X.-Y., “Spatiotemporal chaos in mixed linear–nonlinear coupled logistic map lattice”, Phys. A, 402 (2014), 104–118 | DOI