Global Asymptotic Stability and Nonlinear Analysis of the Model of the Square Immunopixels Array Based on Delay Lattice Differential Equations

Autor: Tomasz Gancarczyk, Lukasz Wieclaw, Joanna Nikodem, Mikolaj Karpinski, Vasyl Martsenyuk, Kornel Warwas, Stanislaw Rajba
Jazyk: angličtina
Rok vydání: 2019
Předmět:
Zdroj: Symmetry
Volume 12
Issue 1
Symmetry, Vol 12, Iss 1, p 40 (2019)
ISSN: 2073-8994
DOI: 10.3390/sym12010040
Popis: Biosensors and immunosensors show an increasing attractiveness when developing current cheap and fast monitoring and detecting devices. In this work, a model of immunosensor in a class of delayed lattice differential equations is offered and studied. The spatial operator describes symmetric diffusion processes of antigenes between pixels. The main results are devoted to the qualitative research of the model. The conditions of global asymptotic stability, which are constructed with the help of Lyapunov functionals, determine a lower estimate of the time of immune response. Nonlinear analysis of the model is performed with help of a series of numerical characteristics including autocorrelation function, mutual information, embedding, and correlation dimensions, sample entropy, the largest Lyapunov exponents. We consider the influence of both symmetric and unsymmetric diffusion of antigens between pixels on the qualitative behavior of the system. The outcomes are verified with the help of numerical simulation in cases of 4 ×
4 - and 16 ×
16 - arrays of immunopixels.
Databáze: OpenAIRE
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