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Title: Rotating spirals in oscillatory media with nonlocal interactions and their normal form
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 paper 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 prove 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.  more » « less
Award ID(s):
1911742
PAR ID:
10337663
Author(s) / Creator(s):
Date Published:
Journal Name:
Discrete and Continuous Dynamical Systems - S
Volume:
0
Issue:
0
ISSN:
1937-1632
Page Range / eLocation ID:
0
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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