Homoclinic orbits and mixed-mode oscillations in far-from-equilibrium systems

Journal Article · Wed Jul 01 00:00:00 EDT 1987 · J. Stat. Phys.; (United States)

DOI:https://doi.org/10.1007/BF01010405· OSTI ID:6094465

Gaspard, P; Wang, X h

Nonlinear autonomous dynamicay systems with a homoclinic tangency to a periodic orbit are investigated. We study the bifurication sequences of the mixed mode oscillations generated by the homoclinicity, which are shown to belong to two different types, depending on the nature of the Liapunov numbers of the basic periodic orbit. A detailed numerical analysis is carried out to show how the existence of a tangent homoclinic orbit allows us to understand in a quantative way a particular and regular sequence of cool flame-ignition oscillations observed in a thermokinetic model of hydrocarbon oxidation. Chaotic cool flame oscillations are also observed in the same model. When the control parameter crosses a critical value, this chaotic set of trajectories becomes globally unstable and forms a Cantor-like hyperbolic repellor, and the ingition mechansim generates a homoclinic tangency to the Cantor set of trajectories.

• Research Organization: Faculte des Sciences, Universite Libre de Bruxelles, B-1050 Brussels, Belgium
• OSTI ID: 6094465
• Journal Information: J. Stat. Phys.; (United States), Journal Name: J. Stat. Phys.; (United States) Vol. 48:1; ISSN JSTPB
• Country of Publication: United States
• Language: English

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37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CHEMICAL REACTION KINETICS
CHEMICAL REACTIONS
COMBUSTION
COMBUSTION KINETICS
FLAMES
HYDROCARBONS
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KINETICS
LYAPUNOV METHOD
MATHEMATICAL SPACE
NONLINEAR PROBLEMS
ORGANIC COMPOUNDS
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