The propagation of travelling waves in an open cubic autocatalytic chemical system

The reaction-diffusion travelling waves that can be initiatedin an open isothermal chemical system governed by cubic autocatalytickinetics are discussed. The system is shown to be capable ofsustaining up to three spatially uniform steady states, the(trivial) unreacted state, which is always stable (a node),and two nontrivial states, one of which is always unstable (asaddle point). The third state can change its stability throughHopf bifurcation (both subcritical and supercritical). Thisallows the possibility of two sorts of travelling wave beingestablished; there are wave profiles which connect the unreactedstate ahead to the nontrivial state at the rear, and wave profiles(pulse waves) which have the unreacted state at both the frontand rear. The conditions under which a particular wave is initiatedare considered by both a discussion of the (ordinary) differentialequations governing the travelling waves and by numerical integrationsof an initial-value problem. This treatment also reveals thepossibility of a stable travelling wave propagating throughthe system, leaving behind a temporally unstable stationarystate. Under these conditions, spatiotemporal chaotic behaviouris seen to develop after the passage of the wave.