Dynamics of oscillatory and excitable fields with nanlocal coupling

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In this research project, a variety of new types of pattern dynamics exhibited by self-oscillatory media with effective non-local coupling were studied theoretically. A specific 3-component reaction-diffusion model as well as its reduced form near the Hopf bifurcation were analyzed mathematically and numerically1. Existence of rotating spiral waves without phase singularity was demonstrated. This occurs when a group of oscillators near the spiral core, which experience relatively weak internal field, fails to synchronize with this field. Our reaction-diffusion model and its reduction were confirmed to exhibit this behavior2. Existence of soft-mode turbulence was confirmed. Soft-mode turbulence is a type of spatio-temporal chaos which arises when a spatially uniform state becomes Turing unstable under the condition that the system already breaks a certain continuous symmetry. A linear stability analysis for our reduced equation (non-locally coupled complex GL equation) was carried out, which revealed that the type of eigenvalue spectrum peculiar to soft-mode turbulence appear under suitable condition. Direct numerical simulation of the equation confirmed the occurrence of the expected turbulent behavior