UDC 602.1:519.85:53.082.9:616-07
АPPLICATION OF DIFFERENTIAL EQUATIONS WITH TIME DELAY
ON A HEXAGONAL LATTICE FOR IMMUNOSENSOR MODELING
Abstract. A model of immunosensor is proposed, which is based on the system of differential equations with time delay on a hexagonal lattice. The main result is conditions of local asymptotic stability of endemic state. To this end, the method of Lyapunov functionals is used. It combines the general approach to construction of Lyapunov functionals for the predator-prey models and differential equations with time delay on a hexagonal lattice. A numerical example shows the influence of time delay on stability, namely, we have transition from stable focus to the limit cycle through the Hopf bifurcation.
Keywords: biosensor, immunosensor, differential equations on a hexagonal lattice, differential equations with delay, asymptotic stability, Lyapunov functional
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