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The Helmholtzian Equation: Stabilizing Mechanisms for Quadratic Nonlinear Fields

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Price, Colin ORCID: https://orcid.org/0000-0002-2173-9897 (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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Official URL: http://www.sciencedirect.com/science/article/pii/0...

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
Additional Information:	The full-text cannot be supplied for this item. Please check availability with your local library or Interlibrary Requests Service.
Uncontrolled Discrete Keywords:	Helmholtzian Equation, Quadratic Nonlinear Fields
Subjects:	Q Science > QC Physics
Divisions:	College of Business, Psychology and Sport > Worcester Business School
Related URLs:	http://www.sciencedirect.com
Depositing User:	Tanya Buchanan
Date Deposited:	20 Sep 2016 13:16
Last Modified:	17 Jun 2020 17:13
URI:	https://eprints.worc.ac.uk/id/eprint/4903

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