Dynamical Transition Theory of Hexagonal Pattern Formations
Taylan Şengül
Abstract:The main goal of this paper is to understand the formation of hexagonal patterns from the dynamical transition theory point of view. We consider the transitions from a steady state of an abstract nonlinear dissipative system. To shed light on the formation of mixed mode patterns such as the hexagonal pattern, we consider the case where the linearized operator of the system has two critical real eigenvalues, at a critical value λ c of a control parameter λ with associated eigenmodes having a roll and rectangula… Show more
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