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Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior
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Published on: January 31, 2020

Extreme multistability in a chemical model system.

Calistus N Ngonghala1, Ulrike Feudel, Kenneth Showalter

  • 1Department of Mathematics, West Virginia University, Morgantown, West Virginia 26506-6310, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 7, 2011
PubMed
Summary
This summary is machine-generated.

Coupled chemical systems can display extreme multistability, featuring infinite coexisting attractors. This phenomenon arises from a conserved quantity that slices the state space, with attractors in each slice.

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Area of Science:

  • Chemical kinetics
  • Nonlinear dynamics
  • Complex systems

Background:

  • Coupled systems can exhibit complex behaviors, including multistability.
  • Understanding the conditions leading to extreme multistability is crucial for predicting system dynamics.

Purpose of the Study:

  • To demonstrate extreme multistability in coupled chemical model systems.
  • To identify the underlying mechanisms responsible for this phenomenon.
  • To investigate the influence of coupling and parameter mismatch.

Main Methods:

  • Simulation of coupled chemical model systems.
  • Analysis of system dynamics and attractor coexistence.
  • Identification of conserved quantities in the long-term limit.

Main Results:

  • Extreme multistability, characterized by infinitely many coexisting attractors, was observed.
  • The emergence of a conserved quantity was linked to extreme multistability.
  • This conserved quantity effectively 'slices' the state space into distinct manifolds.
  • At least one attractor was found within each state space slice as time approached infinity.

Conclusions:

  • Extreme multistability in coupled chemical systems is driven by the long-term emergence of conserved quantities.
  • Conserved quantities lead to a state space partitioning, enabling infinite attractor coexistence.
  • The degree of coupling and parameter mismatch significantly influence the manifestation of extreme multistability.