The Helmholtzian Equation: Stabilizing Mechanisms for Quadratic Nonlinear Fields

Price, Colin (1995) The Helmholtzian Equation: Stabilizing Mechanisms for Quadratic Nonlinear Fields.

View this record at http://eprints.worc.ac.uk/4903/
Official URL: 10.1016/0167-2789(95)00053-7

Abstract

Hexagonal Resonant Triad patterns are shown to exist as stable solutions of a particular type of nonlinear field where no cubic field nonlinearity is present. The zero ‘dc’ Fourier mode is shown to stabilize these patterns produced by a pure quadratic field nonlinearity. Closed form solutions and stability results are obtained near the critical point, complimented by numerical studies far from the critical point. These results are obtained using a neural field based on the Helmholtzian operator. Constraints on structure and parameters for a general pure quadratic neural field which supports hexagonal patterns are obtained.

Item Type: Article
Keywords: QC Physics
Members: University of Worcester
Depositing User: ULCC Admin
Date Deposited: 08 Nov 2016 13:17
Last Modified: 08 Nov 2016 13:17
URI: http://collections.crest.ac.uk/id/eprint/14189

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