Vector Lyapunov functions for practical stability of nonlinear impulsive functional differential equations

AbstractThis paper studies the practical stability of the solutions of nonlinear impulsive functional differential equations. The obtained results are based on the method of vector Lyapunov functions and on differential inequalities for piecewise continuous functions. Examples are given to illustrate our results

Second Method of Lyapunov and Existence of Integral Manifolds for Impulsive Differential-Difference Equations

AbstractBy means of piecewise continuous functions which are analogues of Lyapunov's functions, sufficient conditions are obtained for the existence of integral manifolds for impulsive differential-difference equations with variable impulsive perturbations

Razumikhin–type theorems on stability in terms of two measures for impulsive functional differential systems

This paper studies the stability problems for impulsive functional differential equations with finite delay and fixed moments of impulse effect. By using the Lyapunov functions and Razumikhin technique sufficient conditions for stability in terms of two different piecewise continuous measures of such equations are found

An Impulsive Delay Discrete Stochastic Neural Network Fractional-Order Model and Applications in Finance

In this paper, we propose a new tool for modeling and analysis in finance, introducing an impulsive discrete stochastic neural network (NN) fractional-order model. The main advantages of the proposed approach are: (i) Using NNs which can be trained without the restriction of a model to derive parameters and discover relationships, driven and shaped solely by the nature of the data; (ii) using fractional-order differences, whose nonlocal property makes the fractional calculus a suitable tool for modeling actual financial systems; (iii) using impulsive perturbations, which give an opportunity to control the dynamic behavior of the model; (iv) including a stochastic term, which allows to study the effect of noise disturbances generally existing in financial assets; (v) taking into account the existence of time delayed influences. The modeling approach proposed in this paper can be applied to investigate macroeconomic systems

Fractional-like derivative of Lyapunov-type functions and applications to stability analysis of motion

This article discusses the application of a fractional-like derivative of Lyapunov-type functions in the stability analysis of solutions of perturbed motion equations with a fractional-like derivative of the state vector. The main theorems of the direct Lyapunov method for this class of motion equations are established