MODELING OF THE CYBER-PHYSICAL IMMUNOSENSOR SYSTEM IN THE RECTANGULAR LATTICE BY USING LATTICE DIFFERENTIAL EQUATIONS WITH DELAY

Abstract

The purpose of the work is to develop a mathematical and computer model of the cyber-physical immunosensory system using lattice differential equations with delay on a rectangular lattice and study their stability.The article is devoted to the problem of developing new mathematical and computational tools for obtaining and analyzing the results of numerical simulation in the design of cyberphysical immunosensory systems. The mathematical and computer models of the cyber-physical immunosensory system on a rectangular lattice using delay lattice differential equations are developed. Dynamic logic of the first order is used to simulate discrete events. The results of numerical modeling of the studied model in the form of image of phase planes, lattice images of the probability of bonds antigens with antibody and an electron signal with a transformer, which characterizes the number of fluorescing pixels, are presented. Computer simulation of cyber-physical immunosensory system was carried out. It is established that its qualitative behavior significantly depends on the time of the immune response. The conclusion on the stability of immunosensors can be made on the basis of the grid image of the pixels that are fluorescing. An electrical signal, modeled by the number of fluorescent immunopicles, is important in the design of cyberphysical immunosensory systems and studies of their resistance. Limit cycle or steady focus determine the appropriate form of immunosensory electrical signal. The experimental results obtained made it possible to carry out a complete analysis of the stability of the cyber-physical model of the immunosensor on a rectangular grid, taking into account the latency in time.