scholarly journals Evolutionary Dynamics of Stochastic SEIR Models with Migration and Human Awareness in Complex Networks

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Yue Zhang ◽  
Yuxuan Li
Keyword(s):  
Complex Networks ◽  
Numerical Experiments ◽  
Evolutionary Dynamics ◽  
Sufficient Conditions ◽  
Deterministic System ◽  
Stochastic Solution ◽  
Epidemic Dynamic ◽  
Theoretical Results ◽  
Disease Persistence ◽  
Human Awareness

In this paper, a stochastic SEIR (Susceptible-Exposed-Infected-Removed) epidemic dynamic model with migration and human awareness in complex networks is constructed. The awareness is described by an exponential function. The existence of global positive solutions for the stochastic system in complex networks is obtained. The sufficient conditions are presented for the extinction and persistence of the disease. Under the conditions of disease persistence, the distance between the stochastic solution and the local disease equilibrium of the corresponding deterministic system is estimated in the time sense. Some numerical experiments are also presented to illustrate the theoretical results. Although the awareness introduced in the model cannot affect the extinction of the disease, the scale of the disease will eventually decrease as human awareness increases.

scholarly journals Cluster Synchronization for Linearly Coupled Complex Networks with Identical and Nonidentical Nodes

2012 ◽  
Vol 2012 ◽  
pp. 1-17
Author(s):  
Yi Zhao ◽  
Jianwen Feng ◽  
Jingyi Wang
Keyword(s):  
Lyapunov Function ◽  
Complex Networks ◽  
Sufficient Conditions ◽  
Pinning Control ◽  
Cluster Synchronization ◽  
Adaptive Feedback ◽  
Numerical Examples ◽  
Control Schemes ◽  
Nonidentical Nodes ◽  
Theoretical Results

The cluster synchronization of linearly coupled complex networks with identical and nonidentical nodes is studied. Without assuming symmetry, we proved that these linearly coupled complex networks could achieve cluster synchronization under certain pinning control schemes. Sufficient conditions guaranteeing cluster synchronization for any initial values are derived by using Lyapunov function methods. Moreover, the adaptive feedback algorithms are proposed to adjust the control strength. Several numerical examples are given to illustrate our theoretical results.

scholarly journals Stability of stochastic model for Hepatitis C transmission with an isolation stage

Filomat ◽  
2020 ◽  
Vol 34 (14) ◽  
pp. 4795-4809
Author(s):  
Vuk Vujovic ◽  
Marija Krstic
Keyword(s):  
Hepatitis C ◽  
Existence And Uniqueness ◽  
Lyapunov Functions ◽  
Deterministic Model ◽  
Reliable Data ◽  
Deterministic System ◽  
Stochastic Perturbations ◽  
Stochastic Solution ◽  
Theoretical Results ◽  
Disease Free

In this paper we construct and investigate stability features of two stochastic hepatitis C models with an isolation stage which are obtained by an introduction of stochastic perturbations into the deterministic model for hepatitis C with an isolation stage. One of the stochastic models has only disease- free equilibrium and the other endemic equilibrium state. Aforementioned equilibriums belong to the equilibriums of corresponding deterministic system. For both of models, first of all, we prove the existence and uniqueness of global positive stochastic solution. Thereafter, by using suitable Lyapunov functions, we investigate stability properties of both models. We close the paper with numerical simulation with reliable data of hepatitis C transmission to illustrate our theoretical results.

scholarly journals Alternate Event-triggered Aperiodically Intermittent Control for Synchronization of Multi-weighted Complex Networks

2021 ◽  
Author(s):  
Dongsheng Xu ◽  
Huan Su ◽  
Chenfei Guo
Keyword(s):  
Complex Networks ◽  
Sufficient Conditions ◽  
Exponential Synchronization ◽  
Intermittent Control ◽  
Real Time Control ◽  
Practical Applications ◽  
Time Control ◽  
Theoretical Results ◽  
Event Triggered ◽  
Weighted Complex Networks

Abstract In this paper, the exponential synchronization problem for multi-weighted complex networks via alternate event-triggered aperiodically intermittent control (AETAIC) is considered. Different from existing literature, the proposed AETAIC is triggered alternatively by two pre-defined conditions, which can fast react to asynchronous external events and show better real-time control performance. Meanwhile, AETAIC removes the restrictions of traditional intermittent control on the lower bound of control intervals and upper bound of control periods or the maximum proportion of rest intervals. Though graph theory and Lyapunov method, several sufficient conditions are given to ensure exponential synchronization of the studied networks and Zeno behaviors can be excluded. Moreover, the theoretical results demonstrate that the control gain affects the control widths and exponential convergence rate, which shows that AETAIC can further reduce the frequency of controller updates and release the computation burdens. Finally, in order to illustrate the theoretical results, two practical applications about Chua's circuits and coupled oscillators are presented. Meanwhile, numerical simulations are provided to validate the effectiveness of the results.

scholarly journals Cluster Synchronization of Impulsive Complex Networks with Stochastic Perturbations and Time-Varying Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Yi Zhao ◽  
Jianwen Feng ◽  
Jingyi Wang
Keyword(s):  
Complex Networks ◽  
Sufficient Conditions ◽  
Stochastic Perturbation ◽  
Lyapunov Stability Theory ◽  
Cluster Synchronization ◽  
Linear Matrix ◽  
Time Varying ◽  
Stochastic Perturbations ◽  
Analysis Theory ◽  
Theoretical Results

This paper investigates the cluster synchronization of impulsive complex networks with stochastic perturbation and time-varying delays. Besides, the nodes in the complex networks are nonidentical. By utilizing the Lyapunov stability theory, stochastic analysis theory, and linear matrix inequalities (LMI), sufficient conditions are derived to guarantee the cluster synchronization. The numerical simulation is provided to show the effectiveness of the theoretical results.

scholarly journals Cluster Synchronization of Nonlinearly Coupled Complex Networks via Pinning Control

2011 ◽  
Vol 2011 ◽  
pp. 1-23 ◽  
Author(s):  
Jianwen Feng ◽  
Jingyi Wang ◽  
Chen Xu ◽  
Francis Austin
Keyword(s):  
Complex Networks ◽  
Numerical Simulations ◽  
Coupling Strength ◽  
Topological Structure ◽  
Sufficient Conditions ◽  
Pinning Control ◽  
Cluster Synchronization ◽  
General Complex ◽  
Coupling Strengths ◽  
Theoretical Results

We consider a method for driving general complex networks into prescribed cluster synchronization patterns by using pinning control. The coupling between the vertices of the network is nonlinear, and sufficient conditions are derived analytically for the attainment of cluster synchronization. We also propose an effective way of adapting the coupling strengths of complex networks. In addition, the critical combination of the control strength, the number of pinned nodes and coupling strength in each cluster are given by detailed analysis cluster synchronization of a special topological structure complex network. Our theoretical results are illustrated by numerical simulations.

Nonlinear stochastic synchronization of complex dynamical networks with delays

2019 ◽  
Vol 41 (16) ◽  
pp. 4590-4598 ◽  
Author(s):  
Fei Tan ◽  
Lili Zhou
Keyword(s):  
Complex Networks ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Adaptive Controller ◽  
Functional Theory ◽  
Adaptive Controllers ◽  
Feedback Factor ◽  
Numerical Examples ◽  
Random Uncertainties ◽  
Theoretical Results

This paper investigates the problem of synchronization for complex networks with time delays and stochastic uncertainties. Based on Lyapunov-Krasovskii functional theory, some sufficient conditions are derived. To deal with random uncertainties in networks, some suitable nonlinear adaptive controllers are designed, and some updating laws are used to deal with the feedback factor. The designed nonlinear adaptive controller can be used not only for synchronization of networks with delayed nodes, but also for the synchronization of networks with delayed random noises and delayed nodes. Finally, numerical examples illustrating the effectiveness of the proposed theoretical results are provided.

scholarly journals Adaptive Pinning Synchronization of Complex Networks with Stochastic Perturbations

2010 ◽  
Vol 2010 ◽  
pp. 1-21 ◽  
Author(s):  
Xinsong Yang ◽  
Jinde Cao
Keyword(s):  
Stability Analysis ◽  
Complex Networks ◽  
Stochastic Stability ◽  
Sufficient Conditions ◽  
Vector Form ◽  
Stochastic Perturbations ◽  
Analysis Theory ◽  
Stochastic Stability Analysis ◽  
Theoretical Results ◽  
Partial States

The adaptive pinning synchronization is investigated for complex networks with nondelayed and delayed couplings and vector-form stochastic perturbations. Two kinds of adaptive pinning controllers are designed. Based on an Lyapunov-Krasovskii functional and the stochastic stability analysis theory, several sufficient conditions are developed to guarantee the synchronization of the proposed complex networks even if partial states of the nodes are coupled. Furthermore, three examples with their numerical simulations are employed to show the effectiveness of the theoretical results.

scholarly journals SOR-like methods for solving the Sylvester equation

2015 ◽  
Author(s):  
Jakub Kierzkowski
Keyword(s):  
Iterative Methods ◽  
Numerical Experiments ◽  
Sufficient Conditions ◽  
Sylvester Equation ◽  
Modification Method ◽  
Stationary Iterative Methods ◽  
Theoretical Results

We present the SOR-like methods and highlight some of their known properties. We give the SOR-like method as proposed by Z. Wo źnicki and propose two similar methods based upon it. All three are stationary iterative methods for solving the Sylvester equation (AX-XB=C). We form two sufficient conditions under which one of those methods will converge. In addition, we present a modification method, based on the following fact: if X is a solution of AX-XB=C, it is also a solution of (A-αIm)X-X(B-αIn)=C. We also present numerical experiments to illustrate the theoretical results and some properties of the methods.

scholarly journals Near-optimal control and threshold behavior of an avian influenza model with spatial diffusion on complex networks

2021 ◽  
Vol 18 (5) ◽  
pp. 6452-6483
Author(s):  
Keguo Ren ◽  
◽  
Xining Li ◽  
Qimin Zhang ◽  
Keyword(s):  
Optimal Control ◽  
Avian Influenza ◽  
Complex Networks ◽  
Sufficient Conditions ◽  
Hamiltonian Function ◽  
Threshold Dynamics ◽  
Threshold Behavior ◽  
Necessary And Sufficient ◽  
Theoretical Results ◽  
Near Optimality

<abstract><p>Near-optimization is as sensible and important as optimization for both theory and applications. This paper concerns the near-optimal control of an avian influenza model with saturation on heterogeneous complex networks. Firstly, the basic reproduction number $ \mathcal{R}_{0} $ is defined for the model, which can be used to govern the threshold dynamics of influenza disease. Secondly, the near-optimal control problem was formulated by slaughtering poultry and treating infected humans while keeping the loss and cost to a minimum. Thanks to the maximum condition of the Hamiltonian function and the Ekeland's variational principle, we establish both necessary and sufficient conditions for the near-optimality by several delicate estimates for the state and adjoint processes. Finally, a number of examples presented to illustrate our theoretical results.</p></abstract>

Conditions for the local and global asymptotic stability of the time–fractional Degn–Harrison system

2020 ◽  
Vol 21 (7-8) ◽  
pp. 749-759
Author(s):  
Rachida Mezhoud ◽  
Khaled Saoudi ◽  
Abderrahmane Zaraï ◽  
Salem Abdelmalek
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Linearization Method ◽  
Direct Lyapunov Method ◽  
Fractional Systems ◽  
Reaction Diffusion Model ◽  
Theoretical Results

AbstractFractional calculus has been shown to improve the dynamics of differential system models and provide a better understanding of their dynamics. This paper considers the time–fractional version of the Degn–Harrison reaction–diffusion model. Sufficient conditions are established for the local and global asymptotic stability of the model by means of invariant rectangles, the fundamental stability theory of fractional systems, the linearization method, and the direct Lyapunov method. Numerical simulation results are used to illustrate the theoretical results.

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