Note on the Control of Trajectories of a Dynamical System Modeling Genetic Networks

The discussion of mathematical modeling of diseases in terms of disruptions in the corresponding genetic network is present in the literature. When modeling using dynamic systems, it is possible to observe the evolution of processes. The state trajectory of a genetic network can tend toward an attractor, conventionally called pathogenic. Treatment (in the mathematical model) can be associated with redirecting the trajectory to a conventionally normal attractor. In the model, this can be done by purposefully changing the adjustable parameters. This article considers this situation for an artificially constructed system. Changing one of the parameters is sufficient to redirect the necessary trajectory to the normal attractor, which solves the problem.