System with Switchings as Models of Regulatory Modules in Genomic Cell Systems

In recent times there has been an increasing interest in switching control systems due to their ability to display simultaneously several types of dynamics in different modes of the analyzed system. Such models are used for many issues, both theoretical and practical, e.g. in control of mechanical systems and electric drives, in the automotive industry, in aircraft and air traffic control. In this paper, we present the application of switching systems in biological models of intercellular signal pathways. According to the type of biological system, switches in the model may be dependent on the state of the system or on time. The properties of the biological system can be partially characterized by searching for an analytical solution for the subsystems of the full model. Besides, transition graphs can describe the qualitative behaviour of the system by presenting jumps between subsystems. Moreover, in the systems with switching, we can find stationary points, which reflect specific system behaviour: stabilization or oscillation.