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Related Concept Videos

Entropy02:39

Entropy

Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
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In the field of chemistry, the terms "component" and "phase" hold significant importance. A component refers to a chemically distinct substance in a system that has specific properties. It is chemically homogeneous, meaning it has the same properties throughout. For example, in a mixture of salt and water, both salt and water are considered separate components because they have different chemical properties.On the other hand, a phase is a form of matter that has a consistent chemical...
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Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior
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Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior

Published on: January 31, 2020

Simple chemical systems with chaos.

Tomislav Plesa1, Julien Clinton Sprott2

  • 1Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom.

Chaos (Woodbury, N.Y.)
|May 15, 2026
PubMed
Summary

Researchers identified simpler chaotic chemical dynamical systems (CDSs) by proving properties of chaotic CDSs. This discovery shows that complex chaotic dynamics in chemical reactions are more common than previously thought.

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Area of Science:

  • Chemical Dynamics
  • Chaos Theory
  • Dynamical Systems

Background:

  • Existing simple chaotic three-dimensional dynamical systems (DSs) with quadratic polynomials are not chemical dynamical systems (CDSs).
  • Few three-dimensional quadratic CDSs exhibiting chaos have been reported, typically requiring complex structures (≥9 monomials, ≥3 quadratics, ≥7 reactions).
  • A gap exists in understanding simpler chaotic CDSs modeling mass-action chemical reaction networks (CRNs).

Purpose of the Study:

  • To establish fundamental properties of chaotic CDSs, particularly in three dimensions.
  • To bridge the gap by identifying simpler chaotic three-dimensional CDSs.
  • To quantify the structural complexity of chaotic CDSs.

Main Methods:

  • Theoretical analysis to prove basic properties of chaotic CDSs.
  • Numerical identification of chaotic three-dimensional CDSs using positive Lyapunov exponents.
  • Analysis of monomial and quadratic term counts in identified systems and their corresponding CRNs.

Main Results:

  • Chaotic three-dimensional CDSs must possess at least six monomials, including at least one negative quadratic term.
  • Twenty new chaotic three-dimensional CDSs were numerically identified.
  • These systems exhibit reduced complexity, with some having six monomials (four quadratic terms) or seven monomials (two quadratic terms), corresponding to CRNs with four (three quadratic) or five (two quadratic) reactions.

Conclusions:

  • The structural complexity of chaotic chemical dynamical systems is quantifiable.
  • Simpler chaotic CDSs are more prevalent than previously assumed, indicating their ubiquity.
  • These findings open new avenues for studying chaos in chemical reaction networks.