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Emergent Spatial–Temporal Patterns in a Ring of Locally Coupled Population Oscillators

Author

Listed:
  • Alexey V. Rusakov

    (Institute of Theoretical and Experimental Biophysics, 142290 Pushchino, Russia)

  • Dmitry A. Tikhonov

    (Institute of Theoretical and Experimental Biophysics, 142290 Pushchino, Russia
    Institute of Mathematical Problems of Biology, Keldysh Institute of Applied Mathematics, Professor Vitkevich St. 1, 142290 Pushchino, Russia)

  • Nailya I. Nurieva

    (Institute of Theoretical and Experimental Biophysics, 142290 Pushchino, Russia)

  • Alexander B. Medvinsky

    (Institute of Theoretical and Experimental Biophysics, 142290 Pushchino, Russia)

Abstract

A closed chain of oscillators can be considered a model for ring-shaped ecosystems, such as atolls or the coastal zones of inland reservoirs. We use the logistic map, which is often referred to as an archetypical example of how complex dynamics can arise from very simple nonlinear equations, as a model for a separate oscillator in the chain. We present an original algorithm that allows us to find solutions to the spatiotemporal logistic equation quite efficiently or to state with certainty that there are no such solutions. Based on the Shannon formula, we propose formulas for estimating the spatial and temporal entropy, which allow us to classify our solutions as regular or irregular. We show that regular solutions can occur within the Malthus parameter region that corresponds to the irregular dynamics of a solitary logistic map.

Suggested Citation

  • Alexey V. Rusakov & Dmitry A. Tikhonov & Nailya I. Nurieva & Alexander B. Medvinsky, 2023. "Emergent Spatial–Temporal Patterns in a Ring of Locally Coupled Population Oscillators," Mathematics, MDPI, vol. 11(24), pages 1-15, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:24:p:4970-:d:1301197
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    References listed on IDEAS

    as
    1. Rajvaidya, Bhakti Parag & Deshmukh, Ankosh D. & Gade, Prashant M. & Sahasrabudhe, Girish G., 2020. "Transition to coarse-grained order in coupled logistic maps: Effect of delay and asymmetry," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    2. Abta, Refael & Schiffer, Marcelo & Ben-Ishay, Avishag & Shnerb, Nadav M., 2008. "Stabilization of metapopulation cycles: Toward a classification scheme," Theoretical Population Biology, Elsevier, vol. 74(3), pages 273-282.
    3. Benjamin Kerr & Claudia Neuhauser & Brendan J. M. Bohannan & Antony M. Dean, 2006. "Local migration promotes competitive restraint in a host–pathogen 'tragedy of the commons'," Nature, Nature, vol. 442(7098), pages 75-78, July.
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