Abstract: Critical phenomena – such as hysteresis of steady states, kinetic and thermokinetic self-oscillations of the chemical transformation rate, and regular and chaotic selfoscillations – are observed in various catalytic systems. The nonlinear effects in the dynamics of heterogeneous catalytic reactions were intensively studied since the last third of the twentieth century. Under study is a nonlinear dynamical system of autonomous ordinary differential equations with two fast variables x and y and one slow variable z. The equation for z contains a small parameter µ, and for µ = 0 the system of fast motions is included in a one-parameter family of two-dimensional subsystems with parameter z. Let us assume that each subsystem has a rough periodic solution lz and, moreover, the complete system has a rough periodic solution L which, as µ → 0, tends to the periodic solution lz0 for some z = z0. Taking a plane (y, z) transversal to L, we construct a point Poincar´e map and prove the existence of an invariant manifold for the steady point corresponding to the periodic solution L. Note that L has an invariant manifold on a guaranteed interval with respect to y, and this interval is separated from zero as µ → 0. The proved theorem allows us to give some sufficient conditions for the existence and absence of multipeak self-oscillations in the dynamical system under consideration. As an example, we consider a kinetic model of the heterogeneous catalytic reaction of hydrogen oxidation over nickel.

Cite: Chumakov G.A. , Chumakova N.A.
Differential Equations with a Small Parameter and Multipeak Self-Oscillations
Dynamics in Siberia 26 Feb - 2 Mar 2024