Exploring complexity in some simple nonlinear chemical kinetic schemes

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Abstract
We study two nonlinear chemical kinetic schemes which are arguably the simplest that can display chaotic behavior. These schemes model situations where precursor decay is neglected and included respectively and can represent both isothermal and thermokinetic processes. We make use of a consistent nondimensionalization that has the advantage of unifying all the previously published related models. A systematic investigation of the dynamical behavior within a subspace of the full parameter space reveals clearly distinguished regions where sequences of period doubling, chaos and mixed-mode oscillations exist. We find evidence for a sequence of mixed mode oscillations convolved with chaotic attractors in an extremely complex manner; in this region of parameter space our studies confirm that bistability, and period-doubling to chaos from both simple and mixed mode oscillations can occur, and support conclusions recently reported by Petrov et al. [J. Chem. Phys. 97, 6191 (1992)]. Detailed numerical work indicates that this complexity may be associated with the presence of a tangent homoclinic orbit biasymptotic to a periodic orbit. In addition, Lyapounov spectral analysis confirms the existence of low dimensional chaotic attractors. We suggest some typical experimental scenarios where such complex behavior might be expected.

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