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Numerical Study of Biological Problems in a Predator- Prey System Mathematical biology
English
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The logistic Lotka-Volterra predator-prey equations §with diffusion based on Luckinbill's experiment with §Didinium nasutum as predator and Paramecium aurelia §as prey, have been solved numerically along with a §third equation to include prey-taxis in the system. §The effect of prey-taxis on the dynamics of the §population has been examined using three initial §conditions, four response functions and three data §sets. The stability of the points of equilibria have §been established for each model using Routh-Hurwitz §conditions and the variational matrix criteria. This §has further been verified through numerical §simulations. The effect of bifurcation value of the§prey-taxis coefficient on the numerical solution has §been examined in each case. It has been observed §that as the value of the prey-taxis coefficient §becomes considerably higher than the bifurcation §value, chaotic dynamics develop. As diffusion in §predator velocity is incorporated in the system, it §returns to a cyclic pattern. A brief study of §coexistence of low population densities both with and§without prey-taxis has also been done.
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