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 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 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 Stability analysis of linear conformable fractional differential equations system with time delays

2019 ◽  
Vol 38 (6) ◽  
pp. 159-171 ◽  
Author(s):  
Vahid Mohammadnezhad ◽  
Mostafa Eslami ◽  
Hadi Rezazadeh
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Differential Equations ◽  
Laplace Transform ◽  
Fractional Differential Equations ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Euler’S Method ◽  
Fractional Differential ◽  
Theoretical Results

In this paper, we first study stability analysis of linear conformable fractional differential equations system with time delays. Some sufficient conditions on the asymptotic stability for these systems are proposed by using properties of the fractional Laplace transform and fractional version of final value theorem. Then, we employ conformable Euler’s method to solve conformable fractional differential equations system with time delays to illustrate the effectiveness of our theoretical results

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