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Dynamics of a Predator-Prey Model with Numerical Integration

This document explores a predator-prey model characterized by the Lotka-Volterra equations, revealing the interactions of two species in a computational simulation. The model utilizes parameters including growth rates and carrying capacity to analyze stability and population dynamics. With specified initial conditions and parameter values, the simulation generates phase portraits using vector fields to illustrate the behavior of the populations over time. The model is essential for understanding ecological balance and species interaction in varying environments.

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Dynamics of a Predator-Prey Model with Numerical Integration

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  1. %% PPLANE file %% H.name = 'RMmodel.pps'; H.xvar = 'x'; H.yvar = 'y'; H.xder = '(alpha.*(1-x./K) - beta.*y./(b+x)).*x'; H.yder = '(delta.*x./(b+x) - gamma)*y'; H.pname = {'alpha','delta','beta','K','gamma','b'}; H.pval = {'0.5','1/6','1/3','10','0.1','1/15'}; H.fieldtype = 'arrows'; H.npts = 20; H.wind = [0 1 0 1];

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