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Your search keyword '"*DELAY differential equations"' showing total 2 results
2 results on '"*DELAY differential equations"'

1. A stability theorem for equilibria of delay differential equations in a critical case with application to a model of cell evolution.

Author

Amin, Karim, Badralexi, Irina, Halanay, Andrei, and Mghames, Ragheb

Subjects
*CELLULAR evolution, *TIME delay systems, *DELAY differential equations, *EQUILIBRIUM
Abstract

In this paper the stability of the zero equilibrium of a system with time delay is studied. The critical case of a multiple zero root of the characteristic equation of the linearized system is treated by applying a Malkin type theorem and using a complete Lyapunov-Krasovskii functional. An application to a model for malaria under treatment considering the action of the immune system is presented. [ABSTRACT FROM AUTHOR]

Published
2021
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2. Bifurcation Analysis of a Modified Tumor-immune System Interaction Model Involving Time Delay

Author

S. Kayan, Hüseyin Merdan, Serdar Göktepe, Radouane Yafia, TOBB ETU, Faculty of Science and Literature, Depertment of Mathematics, TOBB ETÜ, Fen Edebiyat Fakültesi, Matematik Bölümü, and Merdan, Hüseyin

Subjects
Hopf bifurcation, tumor immune system competition, Constant coefficients, delay differential equations, Differential equation, Applied Mathematics, periodic solutions, Delay differential equation, stability, reaction-diffusion system, 01 natural sciences, Biological applications of bifurcation theory, 010305 fluids & plasmas, symbols.namesake, Modeling and Simulation, 0103 physical sciences, symbols, Neumann boundary condition, Applied mathematics, 010301 acoustics, Center manifold, Bifurcation, Mathematics
Abstract

We study stability and Hopf bifurcation analysis of a model that refers to the competition between the immune system and an aggressive host such as a tumor. The model which describes this competition is governed by a reaction-diffusion system including time delay under the Neumann boundary conditions, and is based on Kuznetsov-Taylor's model. Choosing the delay parameter as a bifurcation parameter, we first show that Hopf bifurcation occurs. Second, we determine two properties of the periodic solution, namely its direction and stability, by applying the normal form theory and the center manifold reduction for partial functional differential equations. Furthermore, we discuss the effects of diffusion on the dynamics by analyzing a model with constant coefficients and perform some numerical simulations to support the analytical results. The results show that diffusion has an important effects on the dynamics of a mathematical model.

Published
2017

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