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Chaos in a nonautonomous eco-epidemiological model with delay
Sudip Samanta1, Pankaj Kumar Tiwari2, Abdullah K Alzahrani3
1Department of Mathematics, Bankura University, Bankura 722155, West Bengal, India.
Applied Mathematical Modelling
|April 15, 2020
Summary
This study analyzes a predator-prey model with disease and incubation delay. Incubation delay impacts stability but not permanence, potentially leading to chaotic dynamics in nonautonomous systems.
Area of Science:
- Mathematical Biology
- Ecology
- Epidemiology
Background:
- Predator-prey models are fundamental in ecology.
- Incorporating disease dynamics and time delays enhances realism.
- Understanding disease incubation periods is crucial for population dynamics.
Purpose of the Study:
- To analyze a nonautonomous predator-prey model with disease in prey.
- To investigate the impact of discrete time delay for disease incubation on system permanence and stability.
- To explore the transition to complex dynamics like chaos.
Main Methods:
- Differential inequalities for permanence analysis.
- Lyapunov's functional method for global asymptotic stability.
- Numerical simulations and nonlinear dynamics tools (Poincaré section, Lyapunov exponent) for complex dynamics.
Main Results:
- Sufficient conditions for system permanence were established.
- Incubation delay does not affect system permanence.
- Incubation delay influences the global stability of periodic solutions.
- Autonomous systems show Hopf-bifurcation with delay; nonautonomous systems exhibit chaos.
Conclusions:
- Incubation delay is a critical factor in predator-prey dynamics, especially in nonautonomous settings.
- The model demonstrates a transition from stable periodic solutions to chaotic behavior influenced by incubation delay.
- Nonlinear dynamics tools confirm the emergence of chaos in complex ecological models.
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