| dc.description.abstract | The predator-prey equations were developed and used by Lotka and Volterra to analyze the dynamics of biological systems in which two species interact, one as a predator and the other as prey [3]. Several attempts have been made in finding the exact solutions of these models using both numerical and analytical techniques [5]. Lie symmetry analysis has had applications in solving mathematical models involving non-linear differential equations; both ordinary and partial. In this paper, we have solved a modified diffusive predator-prey competition model of the form:2220,,30txxtxxuuu uuv and vvvvuv − − + + =− − + +=; using Lie symmetry approach and obtained its general symmetry solutions. This method makes use of generator, prolongations, infinitesimal generators, symmetries and invariant solutions. The solutions obtained may be used to describe the long-term growth or decline of species in an ecosystem. | en_US |
