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NORMAL-FORM FOR HOPF-BIFURCATION OF PARTIAL-DIFFERENTIAL EQUATIONS ON THE SQUARE
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UNSPECIFIED (1995) NORMAL-FORM FOR HOPF-BIFURCATION OF PARTIAL-DIFFERENTIAL EQUATIONS ON THE SQUARE. NONLINEARITY, 8 (5). pp. 715-734. ISSN 0951-7715.
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Abstract
We derive and analyse a normal form governing dynamics of Hopf bifurcations of partial differential evolution equations on a square domain. We assume that the differential operator for the linearized problem decomposes into two one-dimensional self-adjoint operators and a local 'reaction' operator; this gives a basis of i.e. of the form u(x(1),x(2)) = f(1)(x(1))f(2)(x(2)). The normal form reduces to that investigated by Swift [23] for bifurcation of modes with odd parity but is new for modes with even parity where the centre eigenspace carries a reducible action of D-4 x S-1. We consider the Brusselator equations as an example and discover that a separable linearization introduces a degeneracy which causes the three` new third order terms in the normal form to be related in an unexpected but simple way.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Journal or Publication Title: | NONLINEARITY | ||||
Publisher: | IOP PUBLISHING LTD | ||||
ISSN: | 0951-7715 | ||||
Official Date: | September 1995 | ||||
Dates: |
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Volume: | 8 | ||||
Number: | 5 | ||||
Number of Pages: | 20 | ||||
Page Range: | pp. 715-734 | ||||
Publication Status: | Published |
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