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Published on: September 27, 2019

Applying snapback repellers in resource budget models.

Shu-Ming Chang1, Hsun-Hui Chen

  • 1Department of Applied Mathematics, National Chiao Tung University, Hsinchu 300, Taiwan. smchang@math.nctu.edu.tw

Chaos (Woodbury, N.Y.)
|January 10, 2012
PubMed
Summary
This summary is machine-generated.

This study rigorously proves Satake

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Last Updated: May 26, 2026

Applying an eMASS Customization Program as a Research Tool to Evaluate Consumer Benefits
08:27

Applying an eMASS Customization Program as a Research Tool to Evaluate Consumer Benefits

Published on: September 27, 2019

Area of Science:

  • Ecology
  • Mathematical Biology
  • Chaos Theory

Background:

  • Satake's generalized resource budget model, a modification of Isagi's model, was previously suggested to exhibit chaos for depletion coefficients > 1 based on positive Lyapunov exponents.
  • A positive Lyapunov exponent alone indicates sensitivity (Devaney's chaos), not necessarily deterministic chaos.
  • Understanding the precise conditions and nature of chaos in ecological models is crucial for predicting population dynamics.

Purpose of the Study:

  • To rigorously prove that Satake's generalized resource budget model exhibits chaos in Devaney's sense.
  • To investigate the influence of odd versus even positive depletion coefficients on system behavior.
  • To provide a robust mathematical and numerical foundation for the chaotic nature of the model.

Main Methods:

  • Application of snapback repeller theory.
  • Utilizing topological entropy theory.
  • Conducting numerical analysis of the generalized resource budget model.

Main Results:

  • The generalized resource budget model is mathematically proven to be chaotic in Devaney's sense.
  • Numerical computations reveal distinct behaviors for positive odd and even depletion coefficients.
  • The study establishes a rigorous definition of chaos within this ecological model.

Conclusions:

  • Satake's generalized resource budget model demonstrates true chaos, going beyond mere sensitivity.
  • The parity of the depletion coefficient significantly impacts the model's dynamics.
  • This work provides a rigorous framework for understanding chaos in ecological resource budget models.