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Bifurcation, chaos, multistability, and organized structures in a predator-prey model with vigilance
Mainul Hossain1, Shilpa Garai1, Sajad Jafari2
1Department of Mathematics, Visva-Bharati, Santiniketan 731235, India.
Chaos (Woodbury, N.Y.)
|July 1, 2022
Summary
Prey species use vigilance as an anti-predator strategy, significantly impacting predator-prey dynamics. This study models how prey growth rate and vigilance strength create complex system behaviors and rare Wada basin boundaries.
Area of Science:
- Ecology
- Mathematical Biology
- Theoretical Ecology
Background:
- Species survival relies on anti-predator strategies.
- Vigilance is a key anti-predator behavior influencing predator-prey interactions.
- Predator-prey models are crucial for understanding ecological dynamics.
Purpose of the Study:
- To investigate the complex dynamics of a discrete-time predator-prey model.
- To analyze the effects of prey growth rate and vigilance strength on system behavior.
- To explore emergent phenomena such as period-adding and Wada basin boundaries.
Main Methods:
- Developed a discrete-time predator-prey model incorporating prey vigilance.
- Utilized isoperiodic and Lyapunov exponent diagrams for biparameter analysis.
- Conducted extensive numerical simulations to explore system dynamics.
Main Results:
- Observed diverse organized periodic structures and period-adding phenomena.
- Identified period-bubbling near a shrimp-shaped periodic structure.
- Detected the presence of multiple heterogeneous attractors and rare Wada basin boundaries.
Conclusions:
- Vigilance significantly alters predator-prey system dynamics.
- Complex and rare dynamical behaviors arise from variations in prey growth and vigilance.
- The model provides insights into the intricate ecological interactions driven by anti-predator strategies.
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