Ionization waves: Hopf–Hopf bifurcations and nonlinear wave-wave interactions

Abstract

The nonlinear dynamics within the transition region between p and s waves is studied for a neon glow discharge. Starting from a Hopf–Hopf bifurcation, the normal form constants are determined and their dependence upon the plasma parameters is discussed. The coexisting state of both waves is a stable two torus in the limit of a large external resistance. Taking into account the extension of the plasma by using a coupled set of complex Ginzburg–Landau equations, the two torus becomes unstable for a system length greater than the typical wavelength of ionization waves. Any initial condition decays and as a rule, the asymptotic states are pure regular s waves or Benjamin–Feir unstable pure p waves. Intermittency is found for selected values of the control parameters. This coexisting regime represents a state of strong nonlinear wave-wave interaction that can only be described by the coupled system.