Long-time behavior of solutions and chaos in reaction-diffusion equations

Kamal N. Soltanov, Anatolij K. Prykarpatski and Denis Blackmore

Chaos, Solitons & Fractals, 2017, vol. 99, issue C, 91-100

Abstract: It is shown that members of a class (of current interest with many applications) of non-dissipative reaction-diffusion partial differential equations with local nonlinearity can have an infinite number of different unstable solutions traveling along an axis of the space variable with varying speeds, traveling impulses and also an infinite number of different states of spatio-temporal (diffusion) chaos. These solutions are generated by cascades of bifurcations governed by the corresponding steady states. The behavior of these solutions is analyzed in detail and, as an example, it is explained how space-time chaos can arise. Results of the same type are also obtained in the case of a nonlocal nonlinearity.

Keywords: Semilinear PDE; Reaction-diffusion equation; Behavior of solutions; Chaos (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:99:y:2017:i:c:p:91-100

DOI: 10.1016/j.chaos.2017.03.057

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