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Delay induced stability switch, multitype bistability and chaos in an intraguild predation model.

Hongying Shu1, Xi Hu2, Lin Wang3

  • 1Department of Mathematics, Tongji University, Shanghai, 200092, P. R. China.

Journal of Mathematical Biology
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Summary

In intraguild predation models, time delays can surprisingly stabilize or destabilize populations, leading to complex dynamics like bistability and potentially chaos. This research explores these intricate ecological interactions.

Keywords:
BistabilityChaosIntraguild predationStability switchTime delay

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Area of Science:

  • Ecology
  • Mathematical Biology
  • Population Dynamics

Background:

  • Predator-prey models often show destabilizing effects from time delays, inducing oscillations.
  • Competition models typically do not exhibit oscillations due to delays.
  • Intraguild predation combines both predator-prey and competition dynamics.

Purpose of the Study:

  • To analyze a delayed intraguild predation model combining predator-prey and competition.
  • To investigate the complex dynamics induced by time delays in such models.
  • To identify the roles of delay in promoting stability or instability.

Main Methods:

  • Analysis of a delayed intraguild predation model.
  • Mathematical modeling of ecological interactions.
  • Numerical simulations to explore dynamic behaviors.

Main Results:

  • Time delays can induce stability switches, acting as both a destabilizing and stabilizing factor.
  • Three types of bistability were identified: node-node, node-cycle, and cycle-cycle.
  • Numerical simulations indicated that delays can lead to chaotic dynamics.

Conclusions:

  • Time delays play a crucial role in the complex dynamics of intraguild predation.
  • The presence of delay can lead to diverse stable states and potentially chaotic behavior.
  • Intraguild predation models with delays exhibit richer dynamics than traditional predator-prey or competition models.