Using Differential Equations with Time Delay on a Hexagonal Lattice for Modeling Immunosensors

被引：0
作者：
Martsenyuk, V [1 ]
Sverstiuk, A. [2 ]
Gvozdetska, I. S. [2 ]
机构：
[1] Univ Bielsko Biala, Bielsko Biala, Poland
[2] I Horbachevsky Ternopil State Med Univ, Ternopol, Ukraine
来源：
CYBERNETICS AND SYSTEMS ANALYSIS | 2019年 / 55卷 / 04期
关键词：
biosensor; immunosensor; differential equation on a hexagonal lattice; differential equation with time delay; asymptotic stability; Lyapunov functional; STABILITY;
D O I：
10.1007/s10559-019-00171-2
中图分类号：
TP3 [计算技术、计算机技术];
学科分类号：
0812 ;
摘要：
A model of an immunosensor is proposed based on a system of differential equations with time delay on a hexagonal lattice. The presented main result consists of conditions of local asymptotic stability of an endemic state. To obtain this result, the method of Lyapunov functionals is used. It combines the general approach to constructing Lyapunov functionals for predator-prey models and differential equations with time delay on a hexagonal lattice. A numerical example shows the influence of time delays on stability, namely, the transition from a stable focus to a limit cycle through a Hopf bifurcation occurs.
引用
收藏
页码：625 / 637
页数：13
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