Applying snapback repellers in resource budget models

Abstract

In Satake's generalized resource budget model of ecology, which was modified from Isagi's resource budget model, Satake and Iwasa illustrated, by computing the positive Lyapunov exponent, that if the depletion coefficient is greater than one, then the system is chaotic. However, a positive Lyapunov exponent implies only sensitivity in Devaney's chaos. Therefore, this work presents mathematical viewpoints and numerical analysis on Satake's generalized resource budget model to rigorously prove that the generalized resource budget model is chaotic in Devaney's sense by using the snapback repeller theory and the topological entropy theory. Moreover, this work also investigates that there is a significant difference between the behaviors of positive odd depletion coefficients and positive even depletion coefficients under numerical computations.