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Periodic and traveling wave solutions to Volterra-Lotka equations with diffusion

✍ Scribed by P.L. Chow; W.C. Tam

Publisher
Springer
Year
1976
Tongue
English
Weight
621 KB
Volume
38
Category
Article
ISSN
1522-9602

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✦ Synopsis

Analytic and numerical solutions to two coupled nonlinear diffusion equations are studied. They are the modified equations of Volterra and Lotka for the spatially stratified predatorprey population model. In a bounded domain with the reflecting boundary, equilibrium, stability, and transition to time-periodic solutions are analyzed. For a,wide class of initial states, the solutions to the initial boundary-value problem evolve into their corresponding stable, space-homogeneous, periodic oscillations. In an unbounded domain, a family of traveling wave solutions is found for certain exponential, initial distributions in the limit as the diffusion coefficient vl of the prey tends to zero. In the presence of both diffusions, • the results of a numerical simulation to an initial-value problem showed the rapid formation of the Pursuit-Evasion Waves whose speed of propagation and amplitudes increase with the diffusion coefficient vl.

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