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Exploring the complexity and chaotic behavior in plankton-fish system with mutual interference and time delay.

Archana Ojha1, Nilesh Kumar Thakur1

  • 1Department of Mathematics, National Institute of Technology, Raipur (CG) 492010, India.

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|November 6, 2020
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Summary

Anti-predator defense in plankton can lead to top predator extinction. Time delays and high phytoplankton inhibition can cause chaotic dynamics and double Hopf-bifurcations in plankton-fish models.

Keywords:
DefenseDouble Hopf-bifurcationHopf-bifurcationMutual interferencePlanktonTime delay

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Area of Science:

  • Ecology
  • Mathematical Biology
  • Population Dynamics

Background:

  • Prey anti-predator defense is an evolved survival mechanism against predation.
  • Plankton-fish interactions are crucial in aquatic ecosystems.
  • Time delays, such as gestation, can significantly impact population dynamics.

Purpose of the Study:

  • To investigate the dynamics of a three-tier plankton-fish model with anti-predator defense.
  • To analyze the effects of inhibitory effects, mutual interference, and gestation delay.
  • To explore the emergence of complex behaviors like chaos and bifurcations.

Main Methods:

  • Theoretical analysis of a discrete-time delayed plankton-fish model.
  • Stability analysis, including local stability and Hopf-bifurcation conditions.
  • Numerical simulations to demonstrate periodic, chaotic solutions, and bifurcation diagrams.

Main Results:

  • Top predator extinction observed due to phytoplankton defense.
  • High phytoplankton inhibition or gestation periods induce irregular system behavior.
  • Time delays combined with defense mechanisms promote chaotic phenomena.
  • Double Hopf-bifurcation occurs with variations in predator interference and time delay.

Conclusions:

  • Anti-predator defense can have profound, sometimes detrimental, effects on higher trophic levels.
  • Time delays are critical drivers of complex and chaotic dynamics in ecological models.
  • The model provides insights into the intricate interplay between defense, delay, and population stability.