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UNSTABLE WAVE-TRAINS AND CHAOTIC WAKES IN REACTION-DIFFUSION SYSTEMS OF LAMBDA-OMEGA TYPE
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UNSPECIFIED (1995) UNSTABLE WAVE-TRAINS AND CHAOTIC WAKES IN REACTION-DIFFUSION SYSTEMS OF LAMBDA-OMEGA TYPE. PHYSICA D, 82 (1-2). pp. 165-179. ISSN 0167-2789.
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Abstract
Periodic wavetrains are the one-dimensional equivalent of spiral waves and target patterns, and play a crucial role in the dynamics of oscillatory reaction-diffusion equations. I consider the behaviour of a lambda-omega system of reaction-diffusion equations on a one-dimensional finite spatial domain with boundary conditions corresponding to the forcing of a particular periodic wavetrain. I derive a condition for the wavetrain itself to be a stable solution, and present numerical evidence for a complex sequence of bifurcations in the unstable region of parameter space. Finally I discuss the implications of the results for the phenomenon of irregular wakes behind transition waves in reaction-diffusion equations.
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: | PHYSICA D | ||||
Publisher: | ELSEVIER SCIENCE BV | ||||
ISSN: | 0167-2789 | ||||
Official Date: | 1 April 1995 | ||||
Dates: |
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Volume: | 82 | ||||
Number: | 1-2 | ||||
Number of Pages: | 15 | ||||
Page Range: | pp. 165-179 | ||||
Publication Status: | Published |
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