Abstract
Березанский Леонид, отделение математики, Университет имени Бен-Гуриона, Беэр-Шева, Израиль; brznsky@cs.bgu.ac.il. Leonid Berezansky, brznsky@cs.bgu.ac.il Ben-Gurion University of the Negev, Beer-Sheva, Israel
Highlights
One of the main motivations to study nonlinear delay differential systems is their importance in investigations of artificial neural network models and more generally in Mathematical Biology
In this review paper we will discuss a global stability problem for linear and nonlinear systems of FDE. Such investigations one can divide by the form of a system: vector o scalar form and by the method of investigation
The main methods are: constructing of Lyapunov functionals, applications of special matrices such as M-matrix or special matrix functions such as matrix measure, method of matrix inequalities, which is very popular in papers on Control Theory, fixed point approach and using a notion of nonlinear Volterra operator
Summary
We give a review on recent results for global stability for nonlinear functional differential equations. Such equations include delay differential equations, integro-differential equations and equations with distributed delay and are applied as mathematical models in Population Dynamics and other sciences. We consider methods used to study global stability: constructing of Lyapunov functional, applications of special matrices such as M-matrix or special matrix functions such as matrix measure, method of matrix inequalities, which is very popular in papers on Control Theory, fixed point approach and using a notion of nonlinear Volterra operator
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