scholarly journals Permanence and Extinction for a Nonautonomous Malaria Transmission Model with Distributed Time Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-15
Author(s):  
Xiaohong Zhang ◽  
Jianwen Jia ◽  
Xinyu Song
Keyword(s):  
Time Delay ◽  
Asymptotic Stability ◽  
Malaria Transmission ◽  
Global Asymptotic Stability ◽  
Sufficient Conditions ◽  
Analytical Techniques ◽  
Functional Method ◽  
Transmission Model ◽  
Distributed Time Delay ◽  
Lyapunov Functional Method

We study the permanence, extinction, and global asymptotic stability for a nonautonomous malaria transmission model with distributed time delay. We establish some sufficient conditions on the permanence and extinction of the disease by using inequality analytical techniques. By a Lyapunov functional method, we also obtain some sufficient conditions for global asymptotic stability of this model. A numerical analysis is given to explain the analytical findings.

scholarly journals Analysis of a delay nonautonomous predator-prey system with disease in the prey

2010 ◽  
Vol 15 (1) ◽  
pp. 97-108 ◽  
Author(s):  
G. P. Samanta
Keyword(s):  
Time Delay ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Policy Makers ◽  
Predator Prey ◽  
Analytical Technique ◽  
Predator Prey Model ◽  
Lyapunov Functional Method

In this paper we have considered a nonautonomous predator-prey model with time delay due to gestation, in which a disease that can be transmitted by contact spreads among the prey only. Here, we have established some sufficient conditions on the permanence of the system by using inequality analytical technique. By Lyapunov functional method, we have also obtained some sufficient conditions for global asymptotic stability of this model. We have observed that the time delay has no effect on the permanence of the system but it has an effect on the global asymptotic stability of this model. The aim of the analysis of this model is to identify the parameters of interest for further study, with a view to informing and assisting policy-makers in targeting prevention and treatment resources for maximum effectiveness.

PERMANENCE AND EXTINCTION OF A NONAUTONOMOUS STAGE-STRUCTURED EPIDEMIC MODEL WITH DISTRIBUTED TIME DELAY

2010 ◽  
Vol 18 (02) ◽  
pp. 377-398
Author(s):  
G. P. SAMANTA
Keyword(s):  
Time Delay ◽  
Epidemic Model ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Analytical Technique ◽  
Distributed Time Delay ◽  
Lyapunov Functional Method ◽  
Varying Total Population Size ◽  
Model Computer ◽  
Two Stages

In this paper, we have considered a nonautonomous stage-structured epidemic model having two stages of the period of infection according to the progressing process of some infectious diseases (e.g. Chagas' disease, hepatitis C, etc.) with varying total population size and distributed time delay to become infectious. The infected persons in the different stages have different ability of transmitting disease. We have established some sufficient conditions on the permanence and extinction of the disease by using inequality analytical technique. We have obtained the explicit formula of the eventual lower bounds of infected persons. We have introduced some new threshold values R0 and R* and further obtained that the disease will be permanent when R0 > 1 and the disease will be going to extinct when R* < 1. By Lyapunov functional method, we have also obtained some sufficient conditions for global asymptotic stability of this model. Computer simulations are carried out to explain the analytical findings. The aim of the analysis of this model is to identify the parameters of interest for further study, with a view to informing and assisting policy-maker in targeting prevention and treatment resources for maximum effectiveness.

Mean Square Asymptotic Stability of Neutral Stochastic Neutral Networks with Multiple Time-Varying Delays

2013 ◽  
Vol 684 ◽  
pp. 579-582
Author(s):  
Xiang Dong Shi
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Stochastic Neural Networks ◽  
Multiple Time ◽  
Time Varying ◽  
Lyapunov Functional Method ◽  
Inequality Techniques ◽  
Neutral Stochastic Neural Networks

The paper considers the problems of almost surely asymptotic stability for neutral stochastic neural networks with multiple time-varying delays. By applying Lyapunov functional method and differential inequality techniques, new sufficient conditions ensuring the existence and almost surely asymptotic stability of neutral stochastic neural networks with multiple time-varying delays are established. The results are shown to be generalizations of some previously published results and are less conservative than existing results.

The Globally Asymptotic Stability Analysis of the Delayed Recurrent Neural Networks Stability Criterion via LMI Technique and Nonsmooth Analysis

2013 ◽  
Vol 380-384 ◽  
pp. 2030-2033
Author(s):  
Zhen Cai Li ◽  
Yang Wang
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Recurrent Neural Networks ◽  
Nonsmooth Analysis ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Linear Matrix ◽  
Time Varying ◽  
Globally Asymptotic Stability ◽  
Lyapunov Functional Method

This paper considers the problem of globally asymptotic stability of the recurrent neural networks with time-varying delays. A linear matrix inequality (LMI) technology and Lyapunov functional method is employed by combing the means of the nonsmooth analysis. A few new sufficient conditions and criterions were proposed to ensure the delayed recurrent neural networks are uniqueness and globally asymptotic stability of their equilibrium point. A few simulation examples are presented to demonstrate the effectiveness of the results and to improve feasibility.

Stability for Hopfield Neural Networks With Time Delay

2002 ◽  
Vol 8 (1) ◽  
pp. 13-18 ◽  
Author(s):  
Linshan Wang ◽  
Daoyi Xu
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Asymptotic Stability ◽  
Equilibrium Point ◽  
Global Asymptotic Stability ◽  
Sufficient Conditions ◽  
Hopfield Neural Networks ◽  
Unique Equilibrium ◽  
Transmission Delays

In this paper, the global asymptotic stability of the equilibrium point of Hopfield neural networks with interneuronal transmission delays is studied. Some sufficient conditions related to the existence of a unique equilibrium point and its global asymptotic stability are derived.

scholarly journals Periodic solution for inertial neural networks with variable parameters

2021 ◽  
Vol 6 (12) ◽  
pp. 13580-13591
Author(s):  
Lingping Zhang ◽  
◽  
Bo Du
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Asymptotic Stability ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Mawhin’S Continuation Theorem ◽  
Variable Parameters ◽  
Inertial Neural Networks ◽  
Lyapunov Functional Method

<abstract><p>We discuss periodic solution problems and asymptotic stability for inertial neural networks with $ D- $operator and variable parameters. Based on Mawhin's continuation theorem and Lyapunov functional method, some new sufficient conditions on the existence and asymptotic stability of periodic solutions are established. Finally, a numerical example verifies the effectiveness of the obtained results.</p></abstract>

scholarly journals ANALYSIS OF A NONAUTONOMOUS HIV/AIDS EPIDEMIC MODEL WITH DISTRIBUTED TIME DELAY

2010 ◽  
Vol 15 (3) ◽  
pp. 327-347 ◽  
Author(s):  
Guruprasad P. Samanta
Keyword(s):  
Time Delay ◽  
Epidemic Model ◽  
Horizontal Transmission ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Infected People ◽  
Analytical Technique ◽  
Aids Epidemic ◽  
Distributed Time Delay ◽  
Hiv Aids

In this paper, we have considered a nonautonomous stage‐structured HIV/AIDS epidemic model through vertical and horizontal transmissions of infections, having two stages of the period of infection according to the developing progress of infection before AIDS defined would be detected, with varying total population size and distributed time delay to become infectious (through horizontal transmission) due to intracellular delay between initial infection of a cell by HIV and the release of new virions. The infected people in the different stages have different ability of transmitting disease. We have established some sufficient conditions on the permanence and extinction of the disease by using inequality analytical technique. We have obtained the explicit formula of the eventual lower bounds of infected people. We have introduced some new threshold values _Ro and R* and further obtained that the disease will be permanent when _Ro > 1 and the disease will be going to extinct when R* < 1. By Lyapunov functional method, we have also obtained some sufficient conditions for global asymptotic stability of this model. Computer simulations are carried out to explain the analytical findings.

Global asymptotic stability of an SIR epidemic model with distributed time delay

2001 ◽  
Vol 47 (6) ◽  
pp. 4107-4115 ◽  
Author(s):  
Edoardo Beretta ◽  
Tadayuki Hara ◽  
Wanbiao Ma ◽  
Yasuhiro Takeuchi
Keyword(s):  
Time Delay ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Epidemic Model ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Distributed Time Delay

NOVEL STABILITY CONDITIONS FOR CELLULAR NEURAL NETWORKS WITH TIME DELAY

2001 ◽  
Vol 11 (07) ◽  
pp. 1853-1864 ◽  
Author(s):  
XIAOFENG LIAO ◽  
KWOK-WO WONG ◽  
JUEBANG YU
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Research Work ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Lyapunov Functionals ◽  
Time Varying ◽  
Time Varying Delay

In this paper, the global asymptotic stability of cellular neural networks with time delay is discussed using some novel Lyapunov functionals. Novel sufficient conditions for this type of stability are derived. They are less restrictive and more practical than those currently used. As a result, the design of cellular neural networks with time delay is refined. Our work can also be generalized to cellular neural networks with time-varying delay, a topic on which little research work has been done. By means of several different Lyapunov functionals, some sufficient conditions related to the global asymptotic stability for cellular neural networks with perturbations of time-varying delays are derived.

ON THE GLOBAL ASYMPTOTIC STABILITY ANALYSIS OF DELAYED NEURAL NETWORKS

2005 ◽  
Vol 15 (12) ◽  
pp. 4019-4025 ◽  
Author(s):  
ZHAOHUI YUAN ◽  
DEWEN HU ◽  
LIHONG HUANG ◽  
GUOHUA DONG
Keyword(s):  
Neural Network ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Hopfield Neural Network ◽  
Cellular Neural Network ◽  
Functional Method ◽  
Activation Functions ◽  
Delayed Neural Networks ◽  
System Parameters ◽  
Lyapunov Functional Method

In this paper, the problem of the global asymptotic stability (GAS) of a class of delayed neural network is investigated. Under the generalization of dropping the boundedness and differentiability hypotheses for activation functions, using some existing results for the existence and uniqueness of the equilibrium point, we obtain a couple of general results concerning GAS by means of Lyapunov functional method without the assumption of symmetry of interconnection matrix. Our results improve and extend some previous works of other researchers. Moreover, our conditions are presented in terms of system parameters, which have leading significance in designs and applications of GAS for Hopfield neural network (HNNs) and delayed cellular neural network (DCNNs).

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