Dynamic Analysis on Reaction-diffusion Genetic Regulatory Networks with Delays - Sun, Qingshan; Lin, Zhi; Wang, Guangwen (Journal of physics. Conference series, 2025)
In this paper, we propose a reaction-diffusion genetic regulatory network with Neumann boundary conditions. We incorporate the diffusion factors into the delayed mathematical model of genetic networks, and with the time delays, we demonstrate the local stability and Hopf bifurcation in accordance with the Hopf bifurcation theory. When the sum of the delays exceeds the critical value, a Hopf bifurcation occurs. Finally, we select the appropriate system parameters and present a numerical simulation to illustrate the theoretical analysis.