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• W4242329267 abstract "To understand the spatiotemporal pattern formation in the random networked system, a general activator–substrate model with network structure is introduced. Firstly, we investigate the boundedness of the non-constant steady state of the elliptic system of the continuous medium system. It is found that the non-constant steady state admits their upper and lower bounds under certain conditions. Then, we establish some properties and nonexistence of the non-constant steady state with the no-flux boundary conditions. The main results show that the diffusion rate of the activator should be less than that of the substrate. Otherwise, there might be no pattern formation of the system. Afterward, a general random networked activator–substrate model is presented. Conditions of the stability, the Hopf bifurcation, the Turing instability and the co-dimensional-two Turing–Hopf bifurcation are yielded by the method of stability analysis and bifurcation theory. Finally, a suitable sub-system of the general activator–substrate model is chosen to verify the theoretical results, and full numerical simulations have well verified these results. Especially, an interesting finding is that the stability of the positive equilibrium will switch from unstable to stable one with the change of the connection probability of the nodes, which is different from the pattern formation in the continuous medium systems." @default.
• W4242329267 created "2022-05-12" @default.
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• W4242329267 date "2021-10-08" @default.
• W4242329267 modified "2023-09-26" @default.
• W4242329267 title "Spatiotemporal patterns in a general networked activator–substrate model" @default.
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• W4242329267 doi "https://doi.org/10.1007/s11071-021-06938-7" @default.
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