scholarly journals An impulsive delay differential inequality and applications

2012 ◽  
Vol 64 (6) ◽  
pp. 1875-1881 ◽  
Author(s):  
Xiaodi Li ◽  
Martin Bohner
Keyword(s):  
Differential Inequality ◽  
Impulsive Delay ◽  
Delay Differential ◽  
Delay Differential Inequality

Impulsive and Diffusive Effects on Stability of BAM Neural Networks with Delays

2011 ◽  
Vol 219-220 ◽  
pp. 896-899
Author(s):  
Qing Hua Zhou ◽  
Li Wan
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Differential Inequality ◽  
Bam Neural Networks ◽  
Bidirectional Associative Memory ◽  
Diffusion Effects ◽  
Impulsive Delay ◽  
Diffusive Effects ◽  
Delay Differential ◽  
Delay Differential Inequality

Although the results on exponential stability of delayed bidirectional associative memory (BAM) neural networks with impulse or diffusion were reported by some researchers, impulsive and diffusive effects should simultaneously be taken account into consideration since diffusion and impulses are ubiquitous in both nature and manmade systems, which reflects a more realistic dynamics than the former results. By using the impulsive delay differential inequality, some new sufficient criteria on exponential stability are established. Our criteria are independent of diffusion effects and dependent on the magnitude of the delays and impulses, which shows that diffusion effects are harmless and the magnitude of the delays and impulses needs enough small in the stabilization.

scholarly journals Stability Analysis of Impulsive Stochastic Functional Differential Equations with Delayed Impulses via Comparison Principle and Impulsive Delay Differential Inequality

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Pei Cheng ◽  
Fengqi Yao ◽  
Mingang Hua
Keyword(s):  
Comparison Principle ◽  
Differential Inequality ◽  
Functional Differential Equations ◽  
Stochastic Functional Differential Equations ◽  
Impulsive Delay ◽  
Functional Differential ◽  
Delay Differential ◽  
Delayed Impulses ◽  
Stochastic Functional ◽  
Delay Differential Inequality

The problem of stability for nonlinear impulsive stochastic functional differential equations with delayed impulses is addressed in this paper. Based on the comparison principle and an impulsive delay differential inequality, some exponential stability and asymptotical stability criteria are derived, which show that the system will be stable if the impulses’ frequency and amplitude are suitably related to the increase or decrease of the continuous stochastic flows. The obtained results complement ones from some recent works. Two examples are discussed to illustrate the effectiveness and advantages of our results.

scholarly journals Attracting and Quasi-Invariant Sets of Cohen-Grossberg Neural Networks with Time Delay in the Leakage Term under Impulsive Perturbations

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Guiying Chen ◽  
Linshan Wang
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Differential Inequality ◽  
Invariant Sets ◽  
Leakage Term ◽  
Impulsive Perturbations ◽  
Delay Differential ◽  
Delay Differential Inequality

A class of impulsive Cohen-Grossberg neural networks with time delay in the leakage term is investigated. By using the method ofM-matrix and the technique of delay differential inequality, the attracting and invariant sets of the networks are obtained. The results in this paper extend and improve the earlier publications. An example is presented to illustrate the effectiveness of our conclusion.

scholarly journals Necessary and sufficient conditions for oscillations of delay differential inequalities

1989 ◽  
Vol 39 (2) ◽  
pp. 161-165
Author(s):  
Jurang Yan
Keyword(s):  
Differential Inequality ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Differential Inequalities ◽  
Necessary And Sufficient Condition ◽  
First Order ◽  
Linear Delay ◽  
Delay Differential ◽  
Necessary And Sufficient ◽  
Delay Differential Inequality

A necessary and sufficient condition is obtained for a first order linear delay differential inequality to be oscillatory. Our main result improves and extends some known results.

scholarly journals Synchronization Analysis of a Class of Neural Networks with Multiple Time Delays

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Changyou Wang ◽  
Qiang Yang ◽  
Tao Jiang ◽  
Nan Li
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Lyapunov Function ◽  
Differential Inequality ◽  
Time Delays ◽  
Multiple Delays ◽  
Multiple Time ◽  
Multiple Time Delays ◽  
Delay Differential ◽  
Delay Differential Inequality

In this paper, we study the synchronization of a new fractional-order neural network with multiple delays. Based on the control theory of linear systems with multiple delays, we get the controller to analyse the synchronization of the system. In addition, a suitable Lyapunov function is constructed by using the theory of delay differential inequality, and some criteria ensuring the synchronization of delay fractional neural networks with Caputo derivatives are obtained. Finally, the accuracy of the method is verified by a numerical example.

scholarly journals Stability of linear neutral delay-differential systems

1988 ◽  
Vol 38 (3) ◽  
pp. 339-344 ◽  
Author(s):  
Li-Ming Li
Keyword(s):  
Differential Inequality ◽  
Sufficient Conditions ◽  
Neutral Delay ◽  
Differential Systems ◽  
Delay Differential Systems ◽  
The Stability ◽  
Delay Differential ◽  
Delay Differential Inequality

Sufficient conditions are obtained for the stability of linear neutral delay-differential systems by using a delay-differential inequality.

scholarly journals Oscillation criteria for second order nonlinear delay inequalities

1976 ◽  
Vol 14 (3) ◽  
pp. 331-341 ◽  
Author(s):  
S. Nababan ◽  
E.S. Noussair
Keyword(s):  
Differential Inequality ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Second Order ◽  
Oscillation Criteria ◽  
All Solutions ◽  
Sufficient And Necessary Conditions ◽  
Delay Differential ◽  
Nonlinear Delay ◽  
Delay Differential Inequality

Oscillation criteria are obtained, for the nonlinear delay differential inequality u(u″+f(t, u(t), u(g(t)))) ≤ 0. The main theorems give sufficient conditions (and in some cases sufficient and. necessary conditions) for all solutions u(t) to have arbitrary large zeros. Generalizations to more general cases are discussed.

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