
Abstract The behaviour of a modified autocatalator model: P + C → A + C, rate = k0pc, A + 2B → 3B, rate = k1ab2, B → C, rate = k2b, C → D , rate = k3c, is studied in a batch system with the 'pool chemical approximation’ applied to the precursor P (i.e. we assume p = p0 = constant for all time). Only for the special case k0p0 = k3, for which there is a reduction to a two variable system, are ‘classical’ nonlinear dynamical responses exhibited, with multiple stationary states, Hopf bifurcation to stable or unstable limit cycles and extinction of oscillations via homoclinic orbit formation. Under limiting parameter values, the locus of homoclinic bifurcations can be obtained analytically. For the general cases of k0p0 < k3 and k3p0 > k3 the system is contracting or expanding respectively. For the contracting case, there may be an initial period of sustained but strictly transient bistability or oscillation, and a clear three-time period emerges, before the reaction dies out completely, with b and c tending to zero. For the expanding case, the reaction either dies out as above or follows a continuous growth in intermediate species concentrations and overall reaction rate. The behaviour in these general cases can be readily understood in great detail from a consideration of the stationary state and dynamic bifurcation structure for the reduced case.
chemical wave propagation, multistability, double zero eigenvalue degeneracy, Hopf bifurcation, product-feedback autocatalator scheme, homoclinic orbit bifurcations, Classical flows, reactions, etc. in chemistry, extinction of oscillations, stationary state, limit cycle structure
chemical wave propagation, multistability, double zero eigenvalue degeneracy, Hopf bifurcation, product-feedback autocatalator scheme, homoclinic orbit bifurcations, Classical flows, reactions, etc. in chemistry, extinction of oscillations, stationary state, limit cycle structure
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