Nonisospectral Lotka–Volterra Systems as a Candidate Model for Food Chain

Abstract

In this paper, we derive a generalized nonisospectral semi-infinite Lotka–Volterra equation, which possesses a determinant solution. We also give its a Lax pair expressed in terms of symmetric orthogonal polynomials. In addition, if the simplified case of the moment evolution relation is considered, that is, without the convolution term, we also give a generalized nonisospectral finite Lotka–Volterra equation with an explicit determinant solution. Finally, an application of the generalized nonisospectral continuous-time Lotka–Volterra equation in the food chain is investigated by numerical simulation. Our approach is mainly based on Hirota’s bilinear method and determinant techniques.