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Thus, the derived sufficient condition includes diffusion terms.
Cross diffusion terms are not taken into account.
In [32 36], unfortunately, reaction-diffusion terms were omitted in the deductions, which result in that the criteria of obtained stability do not contain the diffusion terms.
The diffusion terms are treated with a penalty method.
We consider the transient drift-diffusion model with fast diffusion terms.
We observe reduced heat and mass transfer in the presence of cross diffusion terms.
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Further numerical simulations show that: (I) Interactional GRNs without reaction-diffusion terms cannot reach a steady state, because of the defection of information from reaction-diffusion terms.
Interactional GRNs without reaction-diffusion terms cannot reach a steady state, because of the defection of information from reaction-diffusion terms.
Moreover, we derive a sufficient asymptotic synchronization condition for the neural networks with reaction-diffusion terms if reaction-diffusion terms satisfy a weaker condition.
The influence of the reaction-diffusion terms on the synchronization of neural networks cannot be found.
In other words, reaction-diffusion terms are important and indispensable for interactional GRNs.
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