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Investigating the effect of circularly polarized electric field on spatially extended Gray-Scott Model

Authors : Amitava Giri and Sandip Kar*



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Abstract

According to Turing’s hypothesis, the spatially heterogeneous pattern emerges from a reaction-diffusion system due to the diffusion driven instability caused by the difference in diffusivities of the activator and inhibitor like reactant species. However, reaction-diffusion systems consisting of ionic reactants often lead to interesting spatiotemporal structures under the influence of constant external electric or magnetic field even in absence of diffusion driven instability. Unfortunately, only stripe like pattern arises in presence of such kind of external electric field. Herein, we explored the effect of circularly polarized electric field on a spatially extended model reaction-diffusion system (Gray-Scott model), and showed that under the influence of such kind of periodic perturbation, a diverse range of spatial patterns can be obtained both in presence and absence of diffusion driven instability. Interestingly, the long time limit spatiotemporal structures emerged under the presence of circularly polarized electric field are found to be evolving with time due to the intrinsic time dependent nature of the external perturbation. Thus, our numerical study provides a way to obtain diverse spatiotemporal patterns by circumventing the stringent condition of diffusion-driven instability, which can be easily verified by performing experiments with ionic reaction-diffusion system.

 

Keyword

Turing pattern, Gray-Scott model, electric field, periodic perturbation.