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Adapting to a changing environment: non-obvious thresholds in multi-scale systems.

Clare Perryman1, Sebastian Wieczorek2

  • 1Mathematics Research Institute, University of Exeter , Exeter EX4 4QF, UK.

Proceedings. Mathematical, Physical, and Engineering Sciences
|October 9, 2014
PubMed
Summary

Systems fail to adapt when conditions change too rapidly, a phenomenon explained by a new nonlinear threshold. This non-obvious threshold, identified through singular perturbation theory, is crucial for understanding adaptation failures in diverse multi-scale systems.

Keywords:
canardsfolded singularityrate-induced bifurcationsthresholds

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Area of Science:

  • Nonlinear dynamics
  • Complex systems science
  • Applied mathematics

Background:

  • Many natural and technological systems struggle to adapt to rapid environmental changes.
  • These 'non-adiabatic' processes, where systems fail to adjust smoothly, are widespread but poorly understood.
  • Traditional stability theory often fails to capture these adaptation failures.

Purpose of the Study:

  • To identify and characterize the underlying nonlinear phenomenon responsible for adaptation failure in systems experiencing rapid external changes.
  • To develop a theoretical framework for understanding these 'non-adiabatic' processes.
  • To explain the ubiquity of adaptation failures across diverse scientific domains.

Main Methods:

  • Identification of a novel nonlinear phenomenon: a threshold where systems fail to follow changing stable states adiabatically.
  • Derivation of existence conditions for these thresholds in multi-scale systems.
  • Application of concepts from modern singular perturbation theory, including folded singularities and canard trajectories.

Main Results:

  • Demonstrated that adaptation failure thresholds are generic in multi-scale systems but non-obvious to traditional analysis.
  • Showcased the utility of singular perturbation theory in analyzing these complex thresholds.
  • Provided a unified explanation for adaptation failures across various systems.

Conclusions:

  • The identified non-obvious thresholds are key to understanding why multi-scale systems fail to adapt to rapid environmental shifts.
  • This framework offers new insights into phenomena such as climate tipping points, ecosystem regime shifts, and neural excitability.
  • The findings bridge theoretical dynamics with practical implications in climate science, ecology, neuroscience, and technology.