scholarly journals Synchronization in Time-Varying and Evolving Complex Networks

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1939
Author(s):  
Gualberto Solís-Perales ◽  
José Luis Zapata ◽  
Guillermo Obregón-Pulido
Keyword(s):  
Complex Networks ◽  
Exponential Stability ◽  
Coupling Strength ◽  
Interconnected Systems ◽  
Time Varying ◽  
Numerical Examples ◽  
Dynamical Complex Networks

In this contribution, we present the synchronization in dynamical complex networks with varying couplings. We identify two kinds of variations—(i) Non autonomous (Time-varying) couplings: where the coupling strength depends exclusively on time, (ii) Autonomous or Varying couplings (evolution) where the coupling strength depends on the behavior of the interconnected systems. The coupling strength in (i) is exogenous whereas in (ii) the coupling strength is endogenous and is defined by the states of the systems in the nodes. The exponential stability of the synchronization is ensured for the non autonomous couplings, due to the imposition of the coupling strength. Whereas, in the case of evolutionary couplings the exponential stability of the synchronization is not guaranteed for all time, due to the couplings are not controlled or imposed. We present an overview of these features in complex networks and illustrated by means of numerical examples.

scholarly journals Exponential Stability Results of Discrete-Time Stochastic Neural Networks with Time-Varying Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Yajun Li
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Exponential Stability ◽  
Discrete Time ◽  
Computational Efficiency ◽  
Model Transformation ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Numerical Examples ◽  
Stability Results

An innovative stability analysis approach for a class of discrete-time stochastic neural networks (DSNNs) with time-varying delays is developed. By constructing a novel piecewise Lyapunov-Krasovskii functional candidate, a new sum inequality is presented to deal with sum items without ignoring any useful items, the model transformation is no longer needed, and the free weighting matrices are added to reduce the conservatism in the derivation of our results, so the improvement of computational efficiency can be expected. Numerical examples and simulations are also given to show the effectiveness and less conservatism of the proposed criteria.

Exponential Stability Criteria for Neutral System with Mixed Time-Varying Delays and Nonlinear Perturbations

2013 ◽  
Vol 787 ◽  
pp. 891-895 ◽  
Author(s):  
Shao Ying Wang ◽  
Fang Qiu ◽  
Xue Gang Tian
Keyword(s):  
Exponential Stability ◽  
Sufficient Conditions ◽  
Neutral System ◽  
Time Varying ◽  
Nonlinear Perturbations ◽  
Stability Criteria ◽  
Neutral Systems ◽  
Numerical Examples

This paper focuses on the issue of robustly exponential stability for uncertain neutral systems with mixed time-varying delays and nonlinear perturbations. Some new sufficient conditions dependent on the delays are derived in terms of Lyapunov-Krasovskii functionals combined with free-weighting matrices. Two numerical examples are given to show the effectiveness of the proposed method.

Robust Stability of Switched Interconnected Systems With Time-Varying Delays

2017 ◽  
Vol 13 (2) ◽  
Author(s):  
Huanbin Xue ◽  
Jiye Zhang ◽  
Hong Wang ◽  
Baoshan Jiang
Keyword(s):  
Exponential Stability ◽  
Lyapunov Functions ◽  
Nonlinear Dynamical Systems ◽  
Sufficient Conditions ◽  
Interconnected Systems ◽  
Time Varying ◽  
Differential Inequalities ◽  
Interconnected System ◽  
Robust Exponential Stability ◽  
Arbitrary Switching

The problem of robust exponential stability for a class of switched nonlinear dynamical systems with uncertainties and time-varying delays is investigated. On the assumption that each isolated subsystem of the interconnected system can be exponentially stabilized and the corresponding Lyapunov functions are available, using M-matrix property, the differential inequalities with time-varying delays are constructed. By the stability analysis of the differential inequalities, the sufficient conditions to ensure the robust exponential stability of the switched interconnected systems (SIS) under arbitrary switching are obtained. The proposed method, which neither requires the individual subsystems to share a common Lyapunov function (CLF), nor needs to know the values of individual Lyapunov functions at each switching time, would provide a new mentality for studying stability of arbitrary switching. In addition, by resorting to average dwell time approach, conditions for guaranteeing the robust exponential stability of SIS under constrained switching are derived. The proposed criteria are explicit, and they are convenient for practical applications. Finally, two numerical examples are given to illustrate the validity and correctness of the proposed theories.

Equilibrium-pinning control for complex networks with inter-node coupling strength saturation improvement

2019 ◽  
Vol 31 (01) ◽  
pp. 2050013
Author(s):  
Chen Huang ◽  
Xinbiao Lu ◽  
Jun Zhou ◽  
Huimin Qian ◽  
Haoqian Huang ◽  
...  
Keyword(s):  
Complex Networks ◽  
Control Strategy ◽  
Coupling Strength ◽  
Pinning Control ◽  
Network Equilibrium ◽  
Node Number ◽  
Network Nodes ◽  
Numerical Examples ◽  
Practical Applications ◽  
Saturation Threshold

In most conventional complex network equilibrium-pinning control, all the network nodes are usually balanced by attaching at least one controller to each node of the concerned network. When the node number is huge and the inter-node connections are complex, this control strategy requires the ability to manipulate the inter-node coupling strength to grow rapidly and intensively. In practical applications, however, the inter-node coupling strength cannot be increased unlimitedly; as a matter of fact, the coupling strength cannot be further changed after reaching some saturation threshold. In this paper, by exploiting the improved coupling strength saturation function, we suggest a new pinning control strategy that makes the network reach its equilibrium-pinning point more effectively than the network with saturated coupling strength. Numerical examples are illustrated to show the effectiveness of the main results.

scholarly journals New Pinning Synchronization of Complex Networks with Time-Varying Coupling Strength and Nondelayed and Delayed Coupling

2015 ◽  
Vol 2015 ◽  
pp. 1-13
Author(s):  
Guoliang Wang ◽  
Zhongbao Yue ◽  
Feng Wang
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Coupling Strength ◽  
Time Varying ◽  
Numerical Example ◽  
Synchronization Problem ◽  
Delayed Coupling

The pinning synchronization problem for a class of complex networks is studied by a stochastic viewpoint, in which both time-varying coupling strength and nondelayed and delayed coupling are included. Different from the traditionally similar methods, its interval is separated into two subintervals and described by a Bernoulli variable. Both bounds and switching probability of such subintervals are contained. Particularly, the nondelayed and delayed couplings occur alternately in which another independent Bernoulli variable is introduced. Then, a new kind of pinning controller without time-varying coupling strength signal is developed, in which only its bounds and probabilities are contained. When such probabilities are unavailable, two different kinds of adaption laws are established to make the complex network globally synchronous. Finally, the validity of the presented methods is proved through a numerical example.

scholarly journals Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays

2011 ◽  
Vol 21 (4) ◽  
pp. 649-658 ◽  
Author(s):  
Qianhong Zhang ◽  
Lihui Yang ◽  
Daixi Liao
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Exponential Stability ◽  
Differential Inequality ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Cellular Neural Networks ◽  
Time Varying ◽  
Fuzzy Cellular Neural Networks ◽  
Inequality Technique

Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays Fuzzy cellular neural networks with time-varying delays are considered. Some sufficient conditions for the existence and exponential stability of periodic solutions are obtained by using the continuation theorem based on the coincidence degree and the differential inequality technique. The sufficient conditions are easy to use in pattern recognition and automatic control. Finally, an example is given to show the feasibility and effectiveness of our methods.

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