Comparative analysis of results of numerical simulation of cyber-physical biosensor systems on the basis of lattice differential equations https://doi.org/10.33108/visnyk_tntu2019.03.123
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Abstract
The article deals with the comparative analysis of the results of numerical modeling of
mathematical models of cyber-physical biosensor systems on hexagonal and rectangular lattices using lattice
differential equations. The main attention is given to the mathematical description of the discrete population
dynamics in combination with the dynamic logic of the studied models. The lattice differential equations with delay
are proposed to simulate antigen-antibody interaction within hexagonal and rectangular biopixels. Appropriate
spatial operators have been used to model the interaction between biopixels similar to the phenomenon of
diffusion. The paper presents the results of numerical simulations in the form of phase plane images and lattice
images of the probability of antigen to antibody binding in the biopixels of cyberphysical biosensor systems for
antibody populations relative to antigen populations. The obtained experimental results make it possible to carry
out a comparative analysis of the stability of mathematical models of cyberphysical immunosensory systems on
hexagonal and rectangular lattices using lattice differential equations. It is concluded that at a constant delay
value [0, 0.25) for the model on the hexagonal lattice and [0, 0.22] when using a rectangular lattice,
respectively, the solutions of the mathematical models studied tend to non-identical endemic states, which in this
case are stable foci. The results of the phase diagrams of antigen populations, antibodies and lattice images of the
likelihood of antigen binding to antibodies in the biopixels of cyberphysical biosensor systems conclude that at a
constant delay value 0,25 (in the case of a hexagonal lattice) and 0.23 (in the case of a rectangular lattice), Hopf
bifurcation occurs and all subsequent trajectories correspond to stable boundary cycles for all pixels. The obtained
experimental results make it possible to perform a comparative analysis of the stability of mathematical models of
cyberphysical biosensor systems on hexagonal and rectangular lattices using lattice differential equations.
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