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Chaos in a periodically forced predator-prey ecosystem model
1Faculty of Engineering and Applied Science, Memorial University of Newfoundland, St. John's, Canada.
Mathematical Biosciences
|January 1, 1993
Summary
Periodic forcing of the Volterra predator-prey model reveals complex dynamics. The ecosystem exhibits chaotic behavior through period-doubling bifurcations or frequency locking, impacting ecological stability.
Area of Science:
- Ecology
- Mathematical Biology
- Dynamical Systems
Background:
- The classical Volterra predator-prey model describes ecological interactions.
- Unforced models typically exhibit stable equilibrium points.
Purpose of the Study:
- To investigate the impact of periodic forcing on the Volterra predator-prey model.
- To identify and characterize complex dynamical behaviors, including chaos.
Main Methods:
- Periodic variation was introduced to the prey's intrinsic growth rate.
- Numerical simulations explored parameter space, analyzing control parameters like forcing amplitude and frequency.
- Poincaré maps, Lyapunov exponents, and fractal dimensions were calculated to analyze strange attractors.
Main Results:
- The forced system demonstrated a wide range of steady-state chaotic solutions.
- Transitions to chaos were observed via Feigenbaum cascades of period-doubling bifurcations.
- Frequency locking was identified as an alternative route to chaotic dynamics.
Conclusions:
- Periodic forcing can destabilize stable predator-prey equilibria, leading to complex dynamics.
- The study highlights diverse pathways to chaos in ecological models.
- Understanding these chaotic regimes is crucial for predicting ecosystem behavior.