Maximal families of periodic solutions in a kinetic model of heterogeneous catalytic reaction

E. A. Lashina ; G. A. Chumakov ; N. A. Chumakova

Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 5 (2005) no. 4, pp. 42-59

Résumé

In the paper a two-variable kinetic model of heterogeneous catalytic hydrogen oxidation on metallic catalysts is presented. The dynamical system that depends continuously on a set of real parameters is under study, i.e., we consider continuous families of dynamical systems. Our attention focusses on the description of the changes observed in flows depending upon one parameter, primarily, on the maximal families of periodic solutions. We deal with the global bifurcation properties of periodic orbits which can not be deduced from the local information and which engender in the flow the sensitive dependence on the initial conditions. The simplest of these involves the occurrence of planar homoclinic orbits. Studying the one-parameter family of two-variable systems with fast and slow variables it has become clear that the parametric sensitivity appears due to existence of stable and unstable canard cycles which occur close to the Hopf bifurcation. We describe some specific bundles of trajectories such as tunnels, whirlpools, and showers which illustrate a high sensitivity to the initial conditions. A new algorithm for refinement of a homoclinic orbit in one-parameter family of planar vector fields is proposed in the paper.