Applying snapback repellers in resource budget models

Shu-Ming Chang*, Hsun Hui Chen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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.

Original languageAmerican English
Article number043126
Number of pages9
JournalChaos
Volume21
Issue number4
DOIs
StatePublished - 18 Nov 2011

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