A variant of the multi-species Lotka–Volterra model is studied in which species competing for fixed finite resources are replaced by new randomly chosen species whenever they become extinct. The model exhibits chaos, punctuated equilibria, leptokurtosis, and self-organized criticality. It has application to ecology, finance, and possibly other diverse systems.  2004 Elsevier B.V. All rights re...

Abstract This paper aims to developed a high-order and accurate method for the solution of one-dimensional Lotka-Volterra-diffusion with Numman boundary conditions. A fourth-order compact finite difference scheme spatial part combined implicit-explicit Runge Kutta in temporal are proposed. Furthermore, points discretized by using terms fourth order accuracy. key idea proposed is take full advan...