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Mathematical Sciences Analysis and PDE Seminar: "Rotating Waves in Oscillatory Media with Nonlocal Coupling". Gabriela Jaramillo, University of Houston

Wednesday, December 01, 2021
11:00 am to 11:50 am

Zoom Meeting ID: 980 0579 2992

Speaker: Gabriela Jaramillo (University of Houston)

Title: Rotating Waves in Oscillatory Media with Nonlocal Coupling

Abstract: Biological and physical systems that can be classified as oscillatory media give rise to interesting phenomena like target patterns and spiral waves. The existence of these structures has been proven in the case of systems with local diffusive interactions. In this talk the more general case of oscillatory media with nonlocal coupling is considered. We model these systems using evolution equations where the nonlocal interactions are expressed via a diffusive convolution kernel, and explore the existence of rotating wave solutions for these systems. Since the nonlocal nature of the equations precludes the use of standard techniques from spatial dynamics, the method we use relies instead on a combination of a multiple-scales analysis and a construction similar to Lyapunov-Schmidt. This approach then allows us to derive a normal form, or reduced equation, that captures the leading order behavior of these solutions.