Modified Predator-Prey System with Nonlinear Predation and Human Disturbance
Keywords:
Lotka-Volterra, Newton-Raphson, Nonlinear, StabilityAbstract
This article presents a nonlinear mathematical model of predator-prey dynamics incorporating human disturbance. Building on the classical Lotka-Volterra framework, the model includes functional responses and modified growth parameters influenced by anthropogenic factors. Stability analysis using Jacobian matrices reveals conditions for coexistence, particularly the inequality alpha < 1 + beta. Numerical solutions were obtained using the Newton-Raphson method, yielding equilibrium populations of N* approx 95.66 for prey and P*= 0.25 for predators. Phase portrait analysis confirms the local stability of the equilibrium point. The findings underscore the ecological importance of regulating human impact to maintain balanced predator-prey relationships.
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