V. MARTSENYUK, A. SVERSTIUK CYBER-PHYSICAL MODEL OF THE IMMUNOSENSOR SYSTEM AT THE HEXAGONAL LATTICE WITH THE USE OF DIFFERENCE EQUATIONS OF THE POPULATION DYNAMICS

The subject matter of the study is a model of cyber-physical immunosensory systems. The goal of the work is to create and to study the stability of the cyber-physical model of the immunosensory system at the hexagonal lattice using difference equations. The following tasks are solved in the article: development of functional scheme and cyber-physical model of immunosensory system; creation of discrete dynamics of the studied system; development of dynamic logical simulation of the cyber-physical immune system; definition of permanent states for studying the stability of a model of an immunosensor at the hexagonal lattice; the analysis of the results of numerical simulation of the cyber-physical model of the immunosensory system in the form of image of phase planes, the probability of contact of antigens with antibodies, lattice images of the probability of antibody bonds and an electron signal from the converter, that characterizes the number of fluorescing pixels. The following methods are used: methods of mathematical statistics and random processes, methods of the theory of optimization and operations research. The following results were obtained: The cyber-physical model of the immunosensory system at the hexagonal lattice using the difference equations that takes into account the presence of colonies of antigens and antibodies localized in pixels as well as the diffusion of colonies of antigens between pixels was developed. Discrete dynamics of populations in conjunction with dynamic logic is described. A class of delay time difference equations was introduced to simulate the interaction of "antigen-antibody" in the pixels of the immunosensor. The stability of the cyber-physical model of the immunosensory system with the help of the R package is researched. The results of numerical simulation in the form of phase planes image, the probability of contact of antigens with antibodies, lattice images of the probability of antibody bonds and an electron signal from the converter, that characterizes the number of fluorescing pixels, are obtained. The identical and endemic stable states of the cyber-physical model of the immunosensory system at the hexagonal lattice using differential equations of population dynamics are proposed. Conclusions: The numerical simulation of the developed cyber-physical model of the immunosensory system was conducted. It is established that its qualitative behavior significantly depends on the time of the immune response r . An electrical signal, modeled by the number of fluorescent immunopips, is important in the design of cyberphysiological immunosensory systems and studies of their resilience. Limit cycle or steady focus determine the appropriate form of immunosensory electrical signal. The conclusion on the stability of immunosensors is based on the grid image of the pixels that are fluorescing. The obtained experimental results allowed to perform a complete analysis of the stability of the immunosensor model, taking into account the delay in time.