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Pattern Formation in a Three-Species Cyclic Competition Model.

Kalyan Manna1, Vitaly Volpert2,3,4, Malay Banerjee5

  • 1Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, 208016, Uttar Pradesh, India.

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|March 29, 2021
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Summary
This summary is machine-generated.

This study examines cyclic competition models, revealing how spatial patterns and nonlocality influence biodiversity. Nonlocal competition can stabilize dynamics but may initially reduce biodiversity, which can be restored with increased nonlocality.

Keywords:
Cyclic competition modelDiffusionHopf bifurcationNonlocal interactionsPattern formationTuring instability

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Area of Science:

  • Ecology
  • Mathematical Biology
  • Theoretical Ecology

Background:

  • Species compete for resources, making biodiversity maintenance a key ecological question.
  • Cyclic competition, where dominance follows a circular pattern, is observed in nature.
  • Understanding spatial dynamics is crucial for predicting population distributions and biodiversity.

Purpose of the Study:

  • To investigate spatiotemporal pattern formation in a three-species cyclic competition model.
  • To analyze the impact of two distinct cyclic orderings on population dynamics.
  • To explore the role of nonlocal intra-specific competition on biodiversity.

Main Methods:

  • Analysis of a diffusive Lotka-Volterra type three-species cyclic competition model.
  • Employing analytical and numerical methods to study pattern formation.
  • Incorporating nonlocal intra-specific competition terms to assess their effects.

Main Results:

  • Non-spatial models predict species extinction via global bifurcations.
  • Turing patterns are possible for one cyclic ordering but not the other.
  • Nonlocality can stabilize dynamics, initially reducing biodiversity, but restoring it at larger scales.

Conclusions:

  • Spatial structure and cyclic competition significantly shape population distributions.
  • Nonlocal competition offers a mechanism to control biodiversity, with potential for both loss and restoration.
  • The study highlights complex interactions between competition, spatial dynamics, and biodiversity maintenance.