Abstract
In this article, we study complex spatio-temporal solutions in nonlinear time-fractional reaction-diffusion systems. The main attention is paid to nonlinear dynamics near a bifurcation point. Despite the fact that the homogeneous state is stable at the parameters lower than bifurcation ones, a variety of complex solutions can also form in the subcritical domain. As an example, we consider a generalized fractional FitzHugh-Nagumo model. Depending on the given standard bifurcation parameters and the order of fractional derivative, the new types of steady auto-wave solutions in such systems have revealed. By computer simulation, it is shown that fractional reaction-diffusion possess much more complex nonlinear dynamics than their integer counterparts even at a subcritical bifurcation.
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Datsko, B., Gafiychuk, V. Complex spatio-temporal solutions in fractional reaction-diffusion systems near a bifurcation point. FCAA 21, 237–253 (2018). https://doi.org/10.1515/fca-2018-0015
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DOI: https://doi.org/10.1515/fca-2018-0015