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

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.