Sentence examples for by functional differential equations from inspiring English sources

This paper considers the class of systems described by functional differential equations involving the sup-operator.

In this paper, we extend a recently developed approximation method to nonlinear systems given by functional differential equations.

The Lotka-Volterra system described by functional differential equations is one of the most famous and important population dynamics models.

In many practical systems, the system models can be described by functional differential equations of neutral type, the models of which depend on both state and state derivatives.

The theory has been focused, in particular, on systems possessing internal lags, those being described by functional differential equations, those being characterized as hybrid dynamic systems and those being described by coupled continuous-time and discrete-time dynamics, [6 10].

Functional differential equations with impulse effect occur in many applications, such as population dynamics, biology, biotechnology, industrial robotic, pharmacokinetics, optimal control, etc., and can be expressed by functional differential equations with impulses, see [1 5].

It has been realized that the synaptic transmission is a noisy process brought on by random fluctuations from the release of neurotransmitters and other probabilistic causes, and it is of great significance to consider stochastic effects on the stability of neural networks or dynamical system described by stochastic functional differential equations (see [12 23]).

It has been realized that the synaptic transmission is a noisy process brought about by random fluctuations from the release of neurotransmitters and other probabilistic causes, and it is of great significance to consider stochastic effects on the stability of neural networks described by stochastic functional differential equations.

A general mathematical representation of delayed dynamics is given by Retarded Functional Differential Equations (RFDE) [ 13].

The principle below was for the first time introduced by Ważewski [21] for ordinary differential equations and later extended to retarded functional differential equations by Rybakowski [22].

In recent years, the Halanay inequality has been extended to more general type and used for investigating the stability and dissipativity of various functional differential equations by several researchers (see, e.g., [3 7]).