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Switching-induced Turing instability.

J Buceta1, Katja Lindenberg

  • 1Department of Chemistry and Biochemistry and Institute for Nonlinear Science, University of California, San Diego, 9500 Gilman Drive, La Jolla 92093-0340, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 22, 2002
PubMed
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We found a new way to create patterns in homogeneous systems by alternating between two dynamics. This Turing instability is driven by external forcing and internal dynamics, influencing pattern formation in biological models.

Area of Science:

  • Theoretical Biology
  • Mathematical Biology
  • Morphogenesis

Background:

  • Many biological systems start as homogeneous and pattern-free.
  • Inducing pattern formation is key to understanding development and morphogenesis.
  • Existing models often require specific initial conditions or complex interactions.

Purpose of the Study:

  • To propose a novel mechanism for inducing Turing instability.
  • To explore pattern formation in systems with a single homogeneous stable state.
  • To identify conditions for driving Turing instability via dynamic alternation.

Main Methods:

  • Theoretical analysis of system dynamics.
  • Investigating global alternation between two homogeneous stable states.
  • Numerical simulations on established biological models.

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Main Results:

  • A mechanism for inducing Turing instability through dynamic alternation was proposed.
  • The type of alternation required to drive instability was determined.
  • Spatiotemporal structure appearance depends on the ratio of external forcing and short-time instability dynamics.

Conclusions:

  • Global alternation of dynamics can induce Turing instability and pattern formation.
  • This mechanism offers a new route to pattern generation in biological systems.
  • The findings are relevant to understanding morphogenesis and developmental processes.