scholarly journals Permanence and Periodic Solutions for a Two-Patch Impulsive Migration PeriodicN-Species Lotka-Volterra Competitive System

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Zijian Liu ◽  
Chenxue Yang
Keyword(s):  
Periodic Solution ◽  
Lyapunov Function ◽  
Function Method ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Analysis Method ◽  
Competitive System ◽  
Numerical Examples ◽  
Lyapunov Function Method ◽  
Globally Stable

We study a two-patch impulsive migration periodicN-species Lotka-Volterra competitive system. Based on analysis method, inequality estimation, and Lyapunov function method, sufficient conditions for the permanence and existence of a unique globally stable positive periodic solution of the system are established. Some numerical examples are shown to verify our results and discuss the model further.

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 Hub-Induced Synchronization in Scale-Free Networks with Cluster Structure

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Jianbao Zhang ◽  
Zhongjun Ma ◽  
Jinde Cao
Keyword(s):  
Lyapunov Function ◽  
Function Method ◽  
Cluster Structure ◽  
Sufficient Conditions ◽  
Cluster Synchronization ◽  
Numerical Examples ◽  
Scale Free ◽  
Lyapunov Function Method ◽  
Scale Free Networks ◽  
Theoretical Results

A recent research indicated that the corticocortical connectivity network of the cat possesses cluster structure and that each cluster in the network is scale-free and has a most connected hub. Motivated by that research, we slightly modify the network model and derive sufficient conditions for cluster synchronization of the modified network based on Lyapunov function method. The obtained results indicate that cluster synchronization can be induced by the hubs of the scale-free networks. In our opinion, the concept of hub-induced synchronization provides a better understanding of cluster synchronization in scale-free networks. Numerical examples are provided to demonstrate the effectiveness of the theoretical results.

scholarly journals Global Attractivity of a Periodic DelayedN-Species Model of Facultative Mutualism

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Ahmadjan Muhammadhaji ◽  
Zhidong Teng
Keyword(s):  
Lyapunov Function ◽  
Periodic Solutions ◽  
Function Method ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Positive Periodic Solutions ◽  
Facultative Mutualism ◽  
Lyapunov Function Method

Two classes of periodicN-species Lotka-Volterra facultative mutualism systems with distributed delays are discussed. Based on the continuation theorem of the coincidence degree theory developed by Gaines and Mawhin and the Lyapunov function method, some new sufficient conditions on the existence and global attractivity of positive periodic solutions are established.

scholarly journals Almost anti-periodic solution of inertial neural networks model on time scales

2022 ◽  
Vol 355 ◽  
pp. 02006
Author(s):  
Adnène Arbi ◽  
Najeh Tahri
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Lyapunov Function ◽  
Time Scales ◽  
Differential Inequality ◽  
Function Method ◽  
Lyapunov Function Method ◽  
Existence And Stability ◽  
Inertial Neural Networks ◽  
Inequality Techniques

In this work, since the importance of investigation of oscillators solutions, an methodology for proving the existence and stability of almost anti-periodic solutions of inertial neural networks model on time scales are discussed. By developing an approach based on differential inequality techniques coupled with Lyapunov function method. A numerical example is given for illustration.

scholarly journals A Mathematical Model of Cancer Treatment by Radiotherapy

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Zijian Liu ◽  
Chenxue Yang
Keyword(s):  
Mathematical Model ◽  
Periodic Solution ◽  
Asymptotic Stability ◽  
Cancer Treatment ◽  
Cancer Cells ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Numerical Examples ◽  
Globally Asymptotic Stability

A periodic mathematical model of cancer treatment by radiotherapy is presented and studied in this paper. Conditions on the coexistence of the healthy and cancer cells are obtained. Furthermore, sufficient conditions on the existence and globally asymptotic stability of the positive periodic solution, the cancer eradication periodic solution, and the cancer win periodic solution are established. Some numerical examples are shown to verify the validity of the results. A discussion is presented for further study.

EXISTENCE AND GLOBAL ATTRACTIVITY OF A POSITIVE PERIODIC SOLUTION FOR A NON-AUTONOMOUS PREDATOR-PREY MODEL UNDER VIRAL INFECTION

2009 ◽  
Vol 02 (04) ◽  
pp. 419-442 ◽  
Author(s):  
FENGYAN ZHOU
Keyword(s):  
Numerical Simulation ◽  
Periodic Solution ◽  
Lyapunov Function ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Positive Periodic Solution ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System

A new non-autonomous predator-prey system with the effect of viruses on the prey is investigated. By using the method of coincidence degree, some sufficient conditions are obtained for the existence of a positive periodic solution. Moreover, with the help of an appropriately chosen Lyapunov function, the global attractivity of the positive periodic solution is discussed. In the end, a numerical simulation is used to illustrate the feasibility of our results.

scholarly journals Existence and Global Attractivity of Positive Periodic Solutions for a Two-Species Competitive System with Stage Structure and Impulse

2011 ◽  
Vol 2011 ◽  
pp. 1-28 ◽  
Author(s):  
Changjin Xu ◽  
Daxue Chen
Keyword(s):  
Periodic Solution ◽  
Lyapunov Functional ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Stage Structure ◽  
Positive Periodic Solution ◽  
Positive Periodic Solutions ◽  
Competitive System

A class of nonautonomous two-species competitive system with stage structure and impulse is considered. By using the continuation theorem of coincidence degree theory, we derive a set of easily verifiable sufficient conditions that guarantee the existence of at least a positive periodic solution, and, by constructing a suitable Lyapunov functional, the uniqueness and global attractivity of the positive periodic solution are presented. Finally, an illustrative example is given to demonstrate the correctness of the obtained results.

scholarly journals Input-to-State Stability and Stabilization of Nonlinear Impulsive Positive Systems

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1663
Author(s):  
Yiqing Xue ◽  
Ping Zhao
Keyword(s):  
Lyapunov Function ◽  
Function Method ◽  
State Feedback ◽  
Sufficient Condition ◽  
Positive Systems ◽  
Numerical Examples ◽  
Lyapunov Function Method ◽  
Stability And Stabilization

This paper focuses on the problems of input-to-state stability (ISS) and stabilization for nonlinear impulsive positive systems (NIPS). Using the max-separable ISS Lyapunov function method, a sufficient condition on ISS is given for general NIPS. On that basis, the ISS criteria for linear impulsive positive systems (LIPS) and affine nonlinear impulsive positive systems (ANIPS) are given. Through them, ISS properties can be directly judged from the algebraic and differential characteristics of the systems. Then, utilizing the ISS criteria, state-feedback and impulsive controllers are designed for LIPS and ANIPS, respectively, which make the systems input-to-state stabilizable. Lastly, some numerical examples are given to verify the effectiveness of our results.

PERMANENCE AND GLOBAL STABILITY FOR NONLINEAR DISCRETE MODEL

2006 ◽  
Vol 09 (01n02) ◽  
pp. 31-40 ◽  
Author(s):  
CHEN XIAOXING
Keyword(s):  
Periodic Solution ◽  
Lyapunov Function ◽  
Global Stability ◽  
Periodic Solutions ◽  
Nonlinear Model ◽  
Discrete Model ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Existence Of Periodic Solutions

A discrete nonlinear model is studied and sufficient conditions which guarantee the permanence of the model are obtained. Assuming that the coefficients in the model are periodic, the existence of periodic solutions are obtained. Sufficient conditions are obtained to ensure the global stability of the positive periodic solution by constructing a suitable Lyapunov function.

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