Mathematical modelling

Description of real-world systems of interacting units by the means of network model is an effective method of research both in macro- and microscale. In addition, using the simple onelayer networks with one type of connections between the nodes when describing real-world networks is inefficiently because of their complex structural and dynamical nature.

Mathematical model of Volume Free Electron Lasers (VFEL) is described. Some aspects and origins of VFEL chaotic dynamics are examined.

Several mathematical models of volume free electron lasers are described with the aim of investigation of their nonlinear dynamics. This review includes models of beams of charged particles moving through spatially­periodic systems (photonic crystals). In simulation of volume free electron lasers on the base of photonic crystals made from metallic threads or foils working in the microwave range it was shown the necessity of taking into account dispersion of electromagnetic waves on resonator threads.