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Localized Patterns on Ring Lattices

Fall 2021
Moyi Tian (Brown)

It has been observed that s-shaped curves, known as snaking, emerge as the existence branches of stationary localized patterns in spatially discrete systems posed on lattices. Little is known about how graph structure impacts the connection of stationary patterns in parameter space. To address this problem, we focus on ring lattices and discuss analytical results in different coupling regimes.