scholarly journals Permanence in Multispecies Nonautonomous Lotka-Volterra Competitive Systems with Delays and Impulses

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Xiaomei Feng ◽  
Fengqin Zhang ◽  
Kai Wang ◽  
Xiaoxia Li
Keyword(s):  
Sufficient Conditions ◽  
Fixed Time ◽  
Impulsive Effects ◽  
Competitive Systems ◽  
Integrable Form

This paper studies multispecies nonautonomous Lotka-Volterra competitive systems with delays and fixed-time impulsive effects. The sufficient conditions of integrable form on the permanence of species are established.

scholarly journals Stability and attractivity of solutions of differential equations with impulses at fixed times

2000 ◽  
Vol 13 (1) ◽  
pp. 77-84 ◽  
Author(s):  
S. Sivasundaram ◽  
S. Vassilyev
Keyword(s):  
Differential Equations ◽  
Lyapunov Functions ◽  
Dynamic Properties ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Fixed Time ◽  
Impulsive Effects ◽  
Comparison Methods ◽  
Vector Lyapunov Functions ◽  
Fixed Times

In this paper we consider the dynamics of solutions of impulsive differential equations with fixed time moments of impulsive effects on the basis of comparison methods and vector Lyapunov functions. We propose sufficient conditions on the following dynamic properties: stability, attractivity, and some combinations of them.

scholarly journals Almost Periodic Solution for an Epidemic Prey-Predator System with Impulsive Effects and Multiple Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-15
Author(s):  
Baodan Tian ◽  
Ning Chen ◽  
Yanhong Qiu
Keyword(s):  
Periodic Solution ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Impulsive Effects ◽  
Mean Value Theorem ◽  
Multiple Delays ◽  
Almost Periodic ◽  
Epidemic Disease ◽  
Multiple Variables ◽  
Predator System

A nonautonomous epidemic prey-predator system with impulsive effects and multiple delays is considered; further, there is an epidemic disease in the predator. By the mean-value theorem of multiple variables, integral inequalities, differential inequalities, and other mathematical analysis skills, sufficient conditions which guarantee the permanence of the system are obtained. Furthermore, by constructing a series of Lyapunov functionals it is proved that there exists a unique uniformly asymptotically stable almost periodic solution of the system.

Stability analysis for discrete-time stochastic neural networks with mixed time delays and impulsive effects

2010 ◽  
Vol 88 (12) ◽  
pp. 885-898 ◽  
Author(s):  
R. Raja ◽  
R. Sakthivel ◽  
S. Marshal Anthoni
Keyword(s):  
Neural Networks ◽  
Equilibrium Point ◽  
Discrete Time ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Impulsive Effects ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Mixed Time Delays ◽  
The Stability

This paper investigates the stability issues for a class of discrete-time stochastic neural networks with mixed time delays and impulsive effects. By constructing a new Lyapunov–Krasovskii functional and combining with the linear matrix inequality (LMI) approach, a novel set of sufficient conditions are derived to ensure the global asymptotic stability of the equilibrium point for the addressed discrete-time neural networks. Then the result is extended to address the problem of robust stability of uncertain discrete-time stochastic neural networks with impulsive effects. One important feature in this paper is that the stability of the equilibrium point is proved under mild conditions on the activation functions, and it is not required to be differentiable or strictly monotonic. In addition, two numerical examples are provided to show the effectiveness of the proposed method, while being less conservative.

scholarly journals Finite-Time Synchronization of Markovian Jumping Complex Networks with Non-Identical Nodes and Impulsive Effects

Entropy ◽  
2019 ◽  
Vol 21 (8) ◽  
pp. 779
Author(s):  
Tao Chen ◽  
Shiguo Peng ◽  
Zhenhua Zhang
Keyword(s):  
Complex Networks ◽  
Finite Time ◽  
Time Synchronization ◽  
Sufficient Conditions ◽  
Impulsive Effects ◽  
Markovian Jumping ◽  
Complex Dynamic Systems ◽  
Synchronization Problem ◽  
Analysis Technique ◽  
Lyapunov Function Method

In this paper, we investigate the finite-time synchronization problem for a class of Markovian jumping complex networks (MJCNs) with non-identical nodes and impulsive effects. Sufficient conditions for the MJCNs are presented based on an M-matrix technique, Lyapunov function method, stochastic analysis technique, and suitable comparison systems to guarantee finite-time synchronization. At last, numerical examples are exploited to illustrate our theoretical results, and they testify the effectiveness of our results for complex dynamic systems.

APPROXIMATE CONTROLLABILITY OF SECOND-ORDER STOCHASTIC DIFFERENTIAL EQUATIONS WITH IMPULSIVE EFFECTS

2010 ◽  
Vol 24 (14) ◽  
pp. 1559-1572 ◽  
Author(s):  
RATHINASAMY SAKTHIVEL ◽  
YONG REN ◽  
N. I. MAHMUDOV
Keyword(s):  
Biological Sciences ◽  
Differential Equations ◽  
Approximate Controllability ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Second Order ◽  
Impulsive Effects ◽  
Infinite Dimensional ◽  
Infinite Dimensional Dynamical Systems ◽  
Necessary And Sufficient

Many practical systems in physical and biological sciences have impulsive dynamical behaviors during the evolution process which can be modeled by impulsive differential equations. In this paper, the approximate controllability of nonlinear second-order stochastic infinite-dimensional dynamical systems with impulsive effects is considered. By using the Holder's inequality, stochastic analysis and fixed point strategy, a new set of necessary and sufficient conditions are formulated which guarantees the approximate controllability of the nonlinear second-order stochastic system. The results are obtained under the assumption that the associated linear system is approximately controllable.

SKOROKHOD EMBEDDINGS IN BOUNDED TIME

2011 ◽  
Vol 11 (02n03) ◽  
pp. 215-226 ◽  
Author(s):  
STEFAN ANKIRCHNER ◽  
PHILIPP STRACK
Keyword(s):  
Brownian Motion ◽  
Time Horizon ◽  
Sufficient Conditions ◽  
Stopping Time ◽  
Fixed Time ◽  
Stopping Times ◽  
Embedding Problem ◽  
Brownian Motion With Drift ◽  
Necessary And Sufficient ◽  
Skorokhod Embedding Problem

This article deals with the Skorokhod embedding problem in bounded time for the Brownian motion with drift Xt = κt + Wt: Given a probability measure μ we aim at finding a stopping time τ such that the law of Xτ is μ, and τ is almost surely smaller than some given fixed time horizon T > 0. We provide necessary and sufficient conditions on the distribution μ for the existence of such bounded stopping times.

scholarly journals Global Property in a Delayed Periodic Predator-Prey Model with Stage-Structure in Prey and Density-Independence in Predator

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Xiaolin Fan ◽  
Zhidong Teng ◽  
Haijun Jiang
Keyword(s):  
Sufficient Conditions ◽  
Stage Structure ◽  
Global Property ◽  
Predator Density ◽  
Predator Prey ◽  
Density Independence ◽  
Predator Prey Model ◽  
Prey Model ◽  
Density Dependency ◽  
Integrable Form

We study the global property in a delayed periodic predator-prey model with stage-structure in prey and density-independence in predator. The sufficient conditions on the ultimate boundedness of all positive solutions are obtained, and the sufficient conditions of the integrable form for the permanence and extinction are further established, respectively. Some well-known results on the predator density-dependency are improved and extended to the predator density-independent cases. The theoretical results are confirmed by the special examples and the numerical simulations.

scholarly journals An Impulsive Periodic Single-Species Logistic System with Diffusion

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Chenxue Yang ◽  
Mao Ye ◽  
Zijian Liu
Keyword(s):  
Periodic Solution ◽  
Lyapunov Function ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Single Species ◽  
Patchy Environment ◽  
Estimation Technique ◽  
Numerical Examples ◽  
Integrable Form

We study a single-species periodic logistic type dispersal system in a patchy environment with impulses. On the basis of inequality estimation technique, sufficient conditions of integrable form for the permanence and extinction of the system are obtained. By constructing an appropriate Lyapunov function, conditions for the existence of a unique globally attractively positive periodic solution are also established. Numerical examples are shown to verify the validity of our results and to further discuss the model.

scholarly journals PERIODIC SOLUTIONS OF A MODEL OF LOTKA-VOLTERRA WITH VARIABLE STRUCTURE AND IMPULSES

2015 ◽  
Vol 11 (6) ◽  
pp. 5317-5325
Author(s):  
Katya Dishlieva ◽  
Katya Dishlieva
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Variable Structure ◽  
Impulsive Effects ◽  
Volterra Model ◽  
Right Hand

We consider a generalized version of the classical Lotka Volterra model with differential equations. The version has a variable structure (discontinuous right hand side) and the solutions are subjected to the discrete impulsive effects. The moments of right hand side discontinuity and the moments of impulsive effects coincide and they are specific for each solution. Using the Brouwer fixed point theorem, sufficient conditions for the existence of periodic solution are found.

scholarly journals Robust set stabilization of Boolean control networks with impulsive effects

2018 ◽  
Vol 23 (4) ◽  
pp. 553-567 ◽  
Author(s):  
Xiaojing Xu ◽  
Yansheng Liu ◽  
Haitao Li ◽  
Fuad E. Alsaadi
Keyword(s):  
Feedback Control ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
State Feedback Control ◽  
Impulsive Effects ◽  
Algebraic Form ◽  
Control Networks ◽  
Set Stabilization ◽  
Necessary And Sufficient

This paper addresses the robust set stabilization problem of Boolean control networks (BCNs) with impulsive effects via the semi-tensor product method. Firstly, the closed-loop system consisting of a BCN with impulsive effects and a given state feedback control is converted into an algebraic form. Secondly, based on the algebraic form, some necessary and sufficient conditions are presented for the robust set stabilization of BCNs with impulsive effects under a given state feedback control and a free-form control sequence, respectively. Thirdly, as applications, some necessary and sufficient conditions are presented for robust partial stabilization and robust output tracking of BCNs with impulsive effects, respectively. The study of two illustrative examples shows that the obtained new results are effective.

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