Resonantly forced inhomogeneous reaction-diffusion systems

When resonant forcing of an oscillatory medium causes phase-locking of the oscillations, typical spatiotemporal patterns observed involve spatially uniform domains within which the medium oscillates uniformly with the same phase. Phase fronts are the domain walls where the phase shifts from one locked value to another. Phase front dynamics in resonantly forced oscillatory reaction-diffusion systems are studied by means of computer simulations. Two models are investigated: the forced complex Ginzburg-Landau (FCGL) equation and a coupled map lattice (CML) with a superstable period-3 local map. Oscillatory systems may exhibit a regime of spatiotemporal turbulence called the Benjamin-Feir-unstable (BF-unstable) regime. The presence of resonant forcing locks the phase of the oscillations and suppresses the desynchronization associated with turbulence. Phase fronts in resonantly forced BF-unstable systems can exhibit complex turbulent dynamics. Systems at the 2:1 resonance in the BF-unstable regime are studied in one and two dimensions. The effect of spatially inhomogeneous forcing in 2:1 resonant systems is studied. The 3:1 BF-unstable FCGL equation is studied in one and two dimensions. In two dimensions a turbulent zone may form at a phase front. The width of this zone diverges at a critical forcing intensity. The critical properties of this "front explosion" nonequilibrium phase transition are studied. The two-dimensional CML model is known to exhibit a front explosion. The three-dimensional CML system is studied and a front explosion is found, but with substantially different properties than in the two-dimensional system. In three dimensions, in finite systems, the front explosion is a discontinuous transition. Evidence for a first order phase transition in the thermodynamic limit is discussed. In the 4:1 FCGL equation, "pacemaker turbulence" is studied. In this state there are many sources of expanding circular fronts, and new sources are formed when fronts collide. Another phenomenon studied is the formation of four-armed spirals with alternating thick and thin arms and an elongated core. In one dimension, the formation of bound structures containing multiple phase fronts is studied; the arms of the spirals are related to these structures., The phenomenology of spatiotemporal patterns in oscillatory reaction-diffusion systems subject to periodic external forcing with spatially random amplitude is explored and characterized using numerical simulations. Resonant forcing may cause phase locking of the local reaction kinetics, leading to multiple stable oscillatory states of differing phase. A spatially inhomogeneous form of the forced complex Ginzburg-Landau equation is used to study 2:1 and 3:1 resonantly forced systems with quenched disorder. Front roughening and spontaneous nucleation of target patterns are discussed. In 2:1 resonantly forced systems, local front reversals govern the pattern dynamics. Time-varying disorder is studied in the periodically forced FitzHugh-Nagumo system at the 3:1 resonance; it may lead to the breaking of the symmetry between phase locked states. Consequently, inequivalent fronts with different velocities exist, as do stable structures derived from multiple fronts bound by virtue of their different individual velocities. Spiral wave dynamics in these systems is studied.