ISSN:
1572-9613
Keywords:
Homoclinic tangency
;
bifurcation theory
;
periodic attractors
;
chaos
;
hyperbolic repellor
;
symbolic dynamics
;
chemical thermokinetics
;
cool flame-ignition oscillations
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract Nonlinear autonomous dynamical systems with ahomoclinic tangency to a periodic orbit are investigated. We study the bifurcation 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 quantitative 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 ignition mechanism generates ahomoclinic tangency to the Cantor set of trajectories. The complex bifurcation diagram may be globally reconstructed from a one-dimensional dynamical system, thanks to the strong contractivity of thermokinetics. It is found that a symbolic dynamics with three symbols is necessary to classify the periodic windows of the complex bifurcation sequence observed numerically in this system.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01010405
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