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The Helmholtzian Equation: Stabilizing Mechanisms for Quadratic Nonlinear Fields

Price, Colin (1995) The Helmholtzian Equation: Stabilizing Mechanisms for Quadratic Nonlinear Fields. Physica D: Nonlinear Phenomena, 83 (4). pp. 374-382. ISSN 0167-2789

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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.

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Uncontrolled Keywords: Helmholtzian Equation, Quadratic Nonlinear Fields
Subjects: Q Science > QC Physics
Divisions: Academic Departments > Worcester Business School
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Depositing User: Tanya Buchanan
Date Deposited: 20 Sep 2016 13:16
Last Modified: 20 Sep 2016 13:16
URI: https://eprints.worc.ac.uk/id/eprint/4903

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