Global Synchronization in Complex Networks with Adaptive Coupling

Global synchronization in adaptive coupling networks is studied in this paper. A new simple adaptive controller is proposed based on a concept of asymptotically stable led by partial state variables. Under the proposed adaptive update law, the network can achieve global synchronization without calculating the eigenvalues of the outer coupling matrix. The update law is only dependent on partial state variables of individual oscillators. Numerical simulations are given to show the effectiveness of the proposed method, in which the unified chaotic system is chosen as the nodes of the network with different topologies.

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GLOBAL SYNCHRONIZATION IN AN ARRAY OF LINEARLY COUPLED DELAYED NEURAL NETWORKS WITH AN ARBITRARY COUPLING MATRIX

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127406016847 ◽

2006 ◽

Vol 16 (11) ◽

pp. 3357-3368 ◽

Cited By ~ 3

Author(s):

HONGTAO LU ◽

GUANRONG CHEN

Keyword(s):

Neural Networks ◽

Numerical Simulations ◽

Output Coupling ◽

Sufficient Condition ◽

Global Synchronization ◽

Coupling Matrix ◽

Delayed Neural Networks ◽

Arbitrary Coupling ◽

General Sufficient Condition ◽

Theoretical Results

In this paper, we investigate global synchronization in an array of linearly coupled identical delayed neural networks. We consider the array with an arbitrary coupling matrix without assuming it to be symmetric, irreducible and diffusive. Moreover, we consider the array being connected through two different coupling schemes, state-coupling and output-coupling, respectively. For state-coupling, we derive a more general sufficient condition ensuring global synchronization, which is an extension of some existing results in the literature. For output-coupling, we derive a new sufficient condition for global synchronization. Numerical simulations are given to illustrate the theoretical results.

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Synchronization of time-varying coupled complex networks via adaptive pinning control

International Journal of Modern Physics C ◽

10.1142/s0129183121501643 ◽

2021 ◽

pp. 2150164

Author(s):

Hai Lin ◽

Jincheng Wang

Keyword(s):

Lyapunov Function ◽

Complex Networks ◽

Complex Network ◽

Function Theory ◽

Pinning Control ◽

Time Varying ◽

Control Parameters ◽

State Variables ◽

Network Time ◽

Adaptive Coupling

Pinning synchronization of complex networks with two different kinds of time-varying coupling are studied in this paper. Inner coupling of the state variables and outer coupling in the complex network are taken into consideration. Based on the Lyapunov function theory, some general criteria and a simplified corollary for ensuring network synchronization are proposed. Linear pinning controllers, adaptive pinning controllers and adaptive coupling strength are designed for achieving complex network time-varying synchronization. Furthermore, the analytic relationship between control parameters is studied. Numerical simulations further illustrate the effectiveness of conclusions.

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Fully Distributed Synchronization of Complex Networks With Adaptive Coupling Strengths

IEEE Transactions on Cybernetics ◽

10.1109/tcyb.2021.3062039 ◽

2021 ◽

pp. 1-13

Author(s):

Qiang Song ◽

Guanghui Wen ◽

Wenwu Yu ◽

Deyuan Meng ◽

Wenlian Lu

Keyword(s):

Complex Networks ◽

Distributed Synchronization ◽

Adaptive Coupling ◽

Coupling Strengths

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Topology Identification of Complex Network via Chaotic Ant Swarm Algorithm

Mathematical Problems in Engineering ◽

10.1155/2013/401983 ◽

2013 ◽

Vol 2013 ◽

pp. 1-5 ◽

Cited By ~ 2

Author(s):

Haipeng Peng ◽

Lixiang Li ◽

Jürgen Kurths ◽

Shudong Li ◽

Yixian Yang

Keyword(s):

Complex Networks ◽

Numerical Simulations ◽

Complex Network ◽

Parameter Optimization ◽

Ant Algorithm ◽

Structure Parameters ◽

Topology Identification ◽

Unknown Structure ◽

Swarm Algorithm ◽

Scientific Fields

Nowadays, the topology of complex networks is essential in various fields as engineering, biology, physics, and other scientific fields. We know in some general cases that there may be some unknown structure parameters in a complex network. In order to identify those unknown structure parameters, a topology identification method is proposed based on a chaotic ant swarm algorithm in this paper. The problem of topology identification is converted into that of parameter optimization which can be solved by a chaotic ant algorithm. The proposed method enables us to identify the topology of the synchronization network effectively. Numerical simulations are also provided to show the effectiveness and feasibility of the proposed method.

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Mathematical modeling and optimal control of corruption dynamics

Asian-European Journal of Mathematics ◽

10.1142/s1793557118500900 ◽

2018 ◽

Vol 11 (06) ◽

pp. 1850090 ◽

Cited By ~ 6

Author(s):

S. Athithan ◽

Mini Ghosh ◽

Xue-Zhi Li

Keyword(s):

Mathematical Modeling ◽

Optimal Control ◽

Developing Countries ◽

Numerical Simulations ◽

Equilibrium Point ◽

Present Model ◽

Control Model ◽

Asymptotically Stable ◽

Epidemiological Modeling ◽

Control Of Corruption

The problem of corruption is of serious concern in all the nations, more so in the developing countries. This paper presents the formulation of a corruption control model and its analysis using the theory of differential equations. We found the equilibria of the model and stability of these equilibria are discussed in detail. The threshold quantity [Formula: see text] which has a similar implication here as in the epidemiological modeling is obtained for the present model. The corruption free equilibrium is found to be stable when [Formula: see text] is less than [Formula: see text] and unstable for [Formula: see text]. The endemic equilibrium which signifies the presence of corrupted individuals in the society exists only when [Formula: see text]. This equilibrium point is locally asymptotically stable whenever it exists. We perform extensive numerical simulations to support the analytical findings. Furthermore, we extend the model to include optimal control and the optimal control profile is obtained to get the maximum control within a stipulated period of time. Our presented results show that the level of corruption in the society can be reduced if corruption control efforts through media/punishments etc. are increased and put in place.

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