A Reaction–Diffusion System of General Gene Expression with Delays
Abstract
In this paper, a complete analysis is presented to study a reaction–diffusion system of general gene expression with two time delays and with Neumann boundary conditions. The global existence of a unique strong solution and the existence of an attractor are established. Using delays as bifurcation parameters, we obtain critical values so that the Hopf bifurcation occurs at a unique equilibrium point. Numerical simulations are provided to illustrate both the stability of the equilibrium point and the emergence of bifurcations. For steady-state solutions, the Maximum Principle is used to obtain the bounds of positive solutions. The conditions for the system to have constant solutions are also investigated.
Fields of Study & Subjects
Mathematical and Theoretical Epidemiology and Ecology Models
Mathematical Biology Tumor Growth
Nonlinear Differential Equations Analysis
Publication details
- Journal / source
- Mathematics
- Volume
- 14
- Issue
- 3
- Pages
- 563–563
- Publication date
- 4 February 2026
- Language
- EN