Four-phase patterns in forced oscillatory systems

Abstract

We investigate pattern formation in self-oscillating systems forced by an external periodic perturbation. Experimental observations and numerical studies of reaction-diffusion systems and an analysis of an amplitude equation are presented. The oscillations in each of these systems entrain to rational multiples of the perturbation frequency for certain values of the forcing frequency and amplitude. We focus on the subharmonic resonant case where the system locks at one fourth the driving frequency, and four-phase rotating spiral patterns are observed at low forcing amplitudes. The spiral patterns are studied using an amplitude equation for periodically forced oscillating systems. The analysis predicts a bifurcation (with increasing forcing) from rotating four-phase spirals to standing two-phase patterns. This bifurcation is also found in periodically forced reaction-diffusion equations, the FitzHugh-Nagumo and Brusselator models, even far from the onset of oscillations where the amplitude equation analysis is not strictly valid. In a Belousov-Zhabotinsky chemical system periodically forced with light we also observe four-phase rotating spiral wave patterns. However, we have not observed the transition to standing two-phase patterns, possibly because with increasing light intensity the reaction kinetics become excitable rather than oscillatory.

11 pages

References in corpus (7)

• Complex Patterns in a Simple System
• Pattern Formation in Dissipative Nonvariational Systems: The Effects of Front Bifurcations
• From Labyrinthine Patterns to Spiral Turbulence
• Complex Patterns in Reaction-Diffusion Systems: A Tale of Two Front Instabilities
• Interface Proliferation and the Growth of Labyrinths in a Reaction-Diffusion System
• A Phase Front Instability in Periodically Forced Oscillatory Systems
• Multi-Phase Patterns in Periodically Forced Oscillatory Systems

Cited by in corpus (13)

• Evolutionary games on graphs
• Dynamics of Turing patterns under spatio-temporal forcing
• Local versus global interactions in nonequilibrium transitions: A model of social dynamics
• Resonance tongues and patterns in periodically forced reaction-diffusion systems
• Frequency Locking in Spatially Extended Systems
• Stripe-hexagon competition in forced pattern forming systems with broken up-down symmetry
• Transition from oscillatory to excitable regime in a system forced at three times its natural frequency
• Front explosion in a periodically forced surface reaction
• Harmonic forcing of an extended oscillatory system: Homogeneous and periodic solutions
• Emergence of patterns in driven and in autonomous spatiotemporal systems
• Synchronization in driven versus autonomous coupled chaotic maps
• Traveling spatially periodic forcing of phase separation
• Superlattice Patterns in the Complex Ginzburg-Landau Equation with Multi-Resonant Forcing