Differential System Approach to Gene Regulatory Network Modeling

The system of ordinary differential equations that arises in models of genetic networks is considered. This system has both nonlinear and linear parts. As a nonlinear part, we use a piecewise linear function. This allows us to treat systems with multiple (up to ten) equations. Special attention is paid to the four-dimensional systems that have an attractor in the form of a periodic solution. In the final part, the 10th-dimensional system is considered, which describes a subnetwork of a larger network that arises in a practical biomedical problem.