Quantifying chaos and transient chaos in nonlinear chemically reacting systems

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Abstract
In the chemical literature of recent years, there has been considerable interest in the study of deterministic chaos within the context of nonlinear kinetic schemes. However, dynamical systems theory admits a rather strict definition of ‘‘chaos’’ which has seldom been confirmed in the many cases where it is claimed that chaos exists in coupled chemical kinetic models. In this paper we carry out a systematic study of the dynamical properties of two such model systems, computing Lyapunov exponents, fractal dimensions, and power spectra from the (time) series arising from the associated differential equations. In both cases, the analyses presented here provide strong support for the existence of chaotic dynamics for certain values of the appropriate control parameters. In view of the potential difficulty of resolving stochastic fluctuations from chaotic temporal behavior in experimental situations, it is recommended that, wherever possible, authors report estimates of Lyapunov exponents and fractal dimensions of associated chaotic attractors.

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