Skip to main content
SpringerLink
Log in

Structural and stochastic transformations in a system of coupled populations

  • Regular Article
  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

A Correction to this article was published on 16 August 2023

This article has been updated

Abstract

A problem of the study of underlying mechanisms for structural transformations in coupled multicomponent biological systems is considered. We focus on the case of two coupled subunits, which, being isolated, exhibit chaotic modes. We use the Hassell map as a conceptual model for subunits. A variety of non-equilibrium mono- and multistable oscillatory regimes with in-phase and anti-phase synchronization in the coupled system is described. An impact of random disturbances on the these regimes is studied. High sensitivity to noise causing stochastic transformations from anti-phase to in-phase synchronization is investigated. We show how such transformations of the synchronization modes are accompanied by transitions from order to chaos.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Data availability statement

Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

Change history

References

  1. R.E. Amritkar, S. Jalan, Self-organized and driven phase synchronization in coupled map networks. Phys. A 321(1), 220–225 (2003). https://doi.org/10.1016/S0378-4371(02)01750-8

    Article  MathSciNet  MATH  Google Scholar 

  2. S. Boccaletti, A.N. Pisarchik, C.I. del Genio, A. Amann, Synchronization: From Coupled Systems to Complex Networks (Cambridge University Press, Cambridge, 2018)

    Book  MATH  Google Scholar 

  3. S. Jalan, A. Kumar, I. Leyva, Explosive synchronization in frequency displaced multiplex networks. Chaos 29(4), 041102 (2019). https://doi.org/10.1063/1.5092226

    Article  ADS  MathSciNet  MATH  Google Scholar 

  4. Y.A. Kuznetsov, Elements of Applied Bifurcation Theory (Springer, Berlin, 2004)

    Book  MATH  Google Scholar 

  5. G. Tanaka, M.A.F. Sanjuán, K. Aihara, Crisis-induced intermittency in two coupled chaotic maps: towards understanding chaotic itinerancy. Phys. Rev. E 71, 016219 (2005). https://doi.org/10.1103/PhysRevE.71.016219

    Article  ADS  Google Scholar 

  6. A. Pikovsky, M. Rosenblum, J. Kurths, Synchronization: A Universal Concept in Nonlinear Sciences (Cambridge University Press, Cambridge, 2001)

    Book  MATH  Google Scholar 

  7. F. Hellmann, P. Schultz, P. Jaros, R. Levchenko, T. Kapitaniak, J. Kurths, Y. Maistrenko, Network-induced multistability through lossy coupling and exotic solitary states. Nat. Commun. 11, 592 (2020). https://doi.org/10.1038/s41467-020-14417-7

    Article  ADS  Google Scholar 

  8. I. Bashkirtseva, L. Ryashko, Chaotic transients, riddled basins, and stochastic transitions in coupled periodic logistic maps. Chaos 31, 053101 (2021). https://doi.org/10.1063/5.0050613

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. N.F. Rulkov, Regularization of synchronized chaotic bursts. Phys. Rev. Lett. 86, 183–186 (2001). https://doi.org/10.1103/PhysRevLett.86.183

    Article  ADS  Google Scholar 

  10. G. Tanaka, B. Ibarz, M.A.F. Sanjuan, K. Aihara, Synchronization and propagation of bursts in networks of coupled map neurons. Chaos 16(1), 013113 (2006). https://doi.org/10.1063/1.2148387

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. Z. Wang, H. Tian, O. Krejcar, H. Namazi, Synchronization in a network of map-based neurons with memristive synapse. Eur. Phys. J. Spec. Top. (2022). https://doi.org/10.1140/epjs/s11734-022-00691-7

    Article  Google Scholar 

  12. M.N. Kuperman, M.F. Laguna, G. Abramson, J.A. Monjeau, J.L. Lanata, Metapopulation oscillations from satiation of predators. Phys. A 527, 121288 (2019). https://doi.org/10.1016/j.physa.2019.121288

    Article  MathSciNet  MATH  Google Scholar 

  13. A. Belyaev, I. Bashkirtseva, L. Ryashko, Stochastic variability of regular and chaotic dynamics in 2D metapopulation model. Chaos Solitons Fract. 151, 111270 (2021). https://doi.org/10.1016/j.chaos.2021.111270

    Article  MathSciNet  MATH  Google Scholar 

  14. D.S. Goldobin, A. Pikovsky, Synchronization and desynchronization of self-sustained oscillators by common noise. Phys. Rev. E 71, 045201 (2005). https://doi.org/10.1103/PhysRevE.71.045201

    Article  ADS  MathSciNet  Google Scholar 

  15. S. Gil, Y. Kuramoto, A.S. Mikhailov, Common noise induces clustering in populations of globally coupled oscillators. EPL 88(6), 60005 (2009). https://doi.org/10.1209/0295-5075/88/60005

    Article  ADS  Google Scholar 

  16. K.H. Nagai, H. Kori, Noise-induced synchronization of a large population of globally coupled nonidentical oscillators. Phys. Rev. E 81, 065202 (2010). https://doi.org/10.1103/PhysRevE.81.065202

    Article  ADS  Google Scholar 

  17. A. Buscarino, L.V. Gambuzza, M. Porfiri, L. Fortuna, M. Frasca, Robustness to noise in synchronization of complex networks. Sci. Rep. 3, 2026 (2013). https://doi.org/10.1038/srep02026

    Article  ADS  Google Scholar 

  18. A.N. Pisarchik, I.A. Bashkirtseva, L.B. Ryashko, Noise-induced quasiperiodicity in a ring of unidirectionally-coupled nonidentical maps. Phys. Lett. A 383(14), 1571–1577 (2019). https://doi.org/10.1016/j.physleta.2019.02.029

    Article  ADS  MathSciNet  MATH  Google Scholar 

  19. I. Bashkirtseva, L. Ryashko, Stochastic deformations of coupling-induced oscillatory regimes in a system of two logistic maps. Phys. D (2020). https://doi.org/10.1016/j.physd.2020.132589

    Article  MathSciNet  MATH  Google Scholar 

  20. S. Metta, A. Provenzale, E.A. Spiegel, On-off intermittency and coherent bursting in stochastically-driven coupled maps. Chaos Solitons Fract. 43(1), 8–14 (2010). https://doi.org/10.1016/j.chaos.2010.06.001

    Article  ADS  MathSciNet  MATH  Google Scholar 

  21. J. Emenheiser, A. Chapman, M. Pósfai, J.P. Crutchfield, M. Mesbahi, R.M. D’Souza, Patterns of patterns of synchronization: noise induced attractor switching in rings of coupled nonlinear oscillators. Chaos 26(9), 094816 (2016). https://doi.org/10.1063/1.4960191

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. I. Tsvetkov, I. Bashkirtseva, L. Ryashko, Stochastic transformations of multi-rhythmic dynamics and order-chaos transitions in a discrete 2D model. Chaos 31, 063121 (2021). https://doi.org/10.1063/5.0054679

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. I. Bashkirtseva, L. Ryashko, A.N. Pisarchik, Stochastic transitions between in-phase and anti-phase synchronization in coupled map-based neural oscillators. Commun. Nonlinear Sci. Numer. Simul. 95, 105611 (2021). https://doi.org/10.1016/j.cnsns.2020.105611

    Article  MathSciNet  MATH  Google Scholar 

  24. A.N. Pisarchik, A.E. Hramov, Multistability in Physical and Living Systems (Springer, Berlin, 2022)

    Book  MATH  Google Scholar 

  25. M.P. Hassell, Density-dependence in single-species populations. J. Anim. Ecol. 44, 283–295 (1975). https://doi.org/10.2307/3863

    Article  Google Scholar 

  26. M.P. Hassell, J.H. Lawton, R.M. May, Patterns of dynamical behaviour in single-species populations. J. Anim. Ecol. 45, 471–486 (1976). https://doi.org/10.2307/3886

    Article  Google Scholar 

  27. M. Vellekoop, G. Högnäs, A unifying framework for chaos and stochastic stability in discrete population models. J. Math. Biol. 35, 557–588 (1997). https://doi.org/10.1007/s002850050066

    Article  MathSciNet  MATH  Google Scholar 

  28. I. Bashkirtseva, Crises, noise, and tipping in the Hassell population model. Chaos 28, 033603 (2018). https://doi.org/10.1063/1.4990007

    Article  ADS  MathSciNet  MATH  Google Scholar 

  29. M. Anazawa, Inequality in resource allocation and population dynamics models. R. Soc. Open Science 6(7), 182178 (2019). https://doi.org/10.1098/rsos.182178

    Article  ADS  Google Scholar 

  30. G. Grebogi, E. Ott, J.A. Yorke, Crises, sudden changes in chaotic attractors, and transient chaos. Phys. D 7(1), 181–200 (1983). https://doi.org/10.1016/0167-2789(83)90126-4

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The research funding from the Ministry of Science and Higher Education of the Russian Federation (Ural Federal University Program of Development within the Priority-2030 Program) is gratefully acknowledged.

Author information

Author notes

  1. Irina Bashkirtseva and Lev Ryashko contributed equally to this work.

Authors and Affiliations

  1. Department of Theoretical and Mathematical Physics, Ural Federal University, Lenina, 51, Yekaterinburg, 620000, Russia

    Irina Bashkirtseva & Lev Ryashko

Authors
  1. Irina Bashkirtseva
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lev Ryashko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Irina Bashkirtseva.

Additional information

The original online version of this article was revised: The given and family names of the authors were interchanged.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bashkirtseva, I., Ryashko, L. Structural and stochastic transformations in a system of coupled populations. Eur. Phys. J. Spec. Top. 232, 1247–1252 (2023). https://doi.org/10.1140/epjs/s11734-022-00762-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjs/s11734-022-00762-9

Search

Navigation