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How a responsive reproduction factor is determinant in a prey-predator dynamics: A numerical and analytical study in
M S Bittencourt1, E L Brugnago1, Z O Guimarães-Filho1
1Physics Institute, University of São Paulo, 05508-090 São Paulo, SP, Brazil.
This study explores a discrete-time prey-predator model where prey reproduction depends on predation risk. Results show complex dynamics, including chaos and coexistence, depending on prey growth parameters.
Area of Science:
- Ecology
- Mathematical Biology
- Dynamical Systems
Background:
- Prey-predator models are fundamental in ecology.
- Understanding how predation risk influences prey reproduction is crucial for population dynamics.
- Discrete-time models offer unique insights into complex ecological interactions.
Purpose of the Study:
- To investigate the dynamics of a discrete-time prey-predator model with a prey reproductive response to predation risk.
- To analyze the impact of two prey population growth parameters on system stability and behavior.
- To identify conditions leading to species coexistence, extinction, or complex dynamical phenomena.
Main Methods:
- Analytical determination of equilibrium points based on growth parameter ranges.
- Numerical simulations to explore quasiperiodic, chaotic, and hyperchaotic behaviors.
- Investigation of Arnold tongue-like structures and specific topological patterns.
Main Results:
- Identified all equilibrium points analytically, contingent on growth parameter values.
- Observed quasiperiodic, chaotic, and hyperchaotic dynamics through numerical analysis.
- Confirmed analytical findings with numerical simulations, revealing complex population behaviors.
Conclusions:
- The discrete-time prey-predator model exhibits diverse dynamics, including coexistence and extinction.
- Prey's adaptive reproductive strategies (increasing or decreasing reproduction under threat) are compatible with coexistence.
- The model demonstrates rich dynamical behaviors, such as chaos and hyperchaos, influenced by ecological parameters.
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