Self-adaptive complex network synchronization method based on hybrid coupling

Abstract

The invention discloses a hybrid coupling-based adaptive complex network synchronization method, which belongs to the technical field of networked control, and is characterized by comprising the following steps of: for a complex dynamic network, when more than one variable exists in a dynamic function of a single node in the network; on a randomly selected variable, each node is mutually coupled with all neighbor nodes of the node, only one neighbor node of the node is randomly selected on residual variables of the node for interaction, and the coupling strength between the nodes is adjusted through a self-adaptive strategy, so that a complex network stably achieves synchronization. According to the method, the communication burden of a complex network and the coupling strength between nodes can be reduced, and the method is more convenient to use in an actual network.

Description

Technical Field

[0001] The invention belongs to the technical field of networked control systems, and in particular relates to an adaptive complex network synchronization method based on hybrid coupling. Background Art

[0002] As the scale of networks continues to increase and the network topology becomes more and more complex, the current control problem of achieving synchronization in a connected complex network is to ensure that the coupling strength of all nodes on all variables is greater than a threshold. However, when the state variable of a single node is greater than 1, this will bring a heavy communication burden; at the same time, the appropriate coupling strength threshold between nodes required for network synchronization is not easy to obtain in advance. Summary of the invention

[0003] In order to solve the deficiencies in the prior art, the present invention provides a hybrid coupled adaptive complex network synchronization method, which can not only synchronize the complex network, but also reduce the communication burden between nodes and avoid system congestion. At the same time, the coupling strength between nodes required for the network to achieve synchronization can be adaptively obtained, which is more convenient to use in actual networks.

[0004] To achieve the above purpose, the technical solution adopted by the present invention is an adaptive complex network synchronization method based on hybrid coupling. For a complex dynamic network, when the dynamic function of a single node in the network has more than one variable, each node is mutually coupled with all its neighboring nodes on a randomly selected variable, and only one of its neighboring nodes is randomly selected for interaction on the remaining variables of the node, and the coupling strength between nodes is adjusted through an adaptive strategy so that the complex network can be stably synchronized.

[0005] Furthermore, a complex multidimensional dynamic network has N linearly coupled nodes, each of which is an n-dimensional autonomous dynamic system, and its equation is: where x i (t) = [x i1 (t),…,x in (t)] T ∈R n The state of node i at time t; function f(·) is the dynamic function of a single node; c(t)=[c1(t),…,c n (t)] T ∈R n is the coupling strength between nodes; time t is a positive real number, A=(a ij (t)) N×N is the adjacency matrix. When there is an edge between node i and node j, then a ij (t) = a ji(t)=1(i≠j), otherwise a ij (t) = a ji (t) = 0 (i≠j), the diagonal elements of the matrix A are taken as

[0006] Furthermore, when the dynamics function of a single node in the network has more than one variable, formula (1) can be written as two parts: global coupling and partial coupling. The global coupling part only includes the first variable of each node, without loss of generality, it can be written as: The partially coupled part includes the remaining variables for each node: Here i = 1, 2, ..., N, k = 2, ..., n. j1 is a node randomly selected from the neighbors of node i.

[0007] Furthermore, the choice j in formula (3) i is the node with the most neighbors among the neighbors of node i. If there is more than one such node with the most neighbors, one is randomly selected from them.

[0008] Furthermore, here i = 1, 2, ..., N, k = 2, ..., n. j1 is a node randomly selected from the neighbors of node i.

[0009] Furthermore, the coupling strength adaptation strategy in formula (2) and formula (3) is: Here β is the adaptive gain.

[0010] Furthermore, the dynamic function of node i is the Rossler oscillator, and its formula is: BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 An adaptive complex network synchronization method based on hybrid coupling is provided in an embodiment of the present invention. The node state of a BA scale-free network of 15 nodes is provided. The BA scale-free network of the 15-node network used is provided. The network generation method is as follows: starting from the initial two connected nodes, two edges are added each time according to the priority growth strategy.

[0012] Figure 2 An adaptive complex network synchronization method based on hybrid coupling is provided in an embodiment of the present invention, and the coupling strength c between nodes changes with time. DETAILED DESCRIPTION

[0013] The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and cannot be used to limit the protection scope of the present invention.

[0014] The present invention discloses an adaptive complex network synchronization method based on hybrid coupling. For a complex dynamic network, when the dynamic function of a single node in the network has more than one variable. On a randomly selected variable, each node is mutually coupled with all its neighbor nodes, and only one neighbor node is randomly selected for interaction on the remaining variables of the node. The coupling strength between nodes is adjusted through an adaptive strategy so that the complex network can be stably synchronized, which can reduce the communication burden of the complex network and the coupling strength between nodes, and is more convenient to use in actual networks.

[0015] Consider a BA scale-free network with 15 nodes. The network generation method is: starting from the initial two connected nodes, two edges are added each time according to the priority growth strategy until the network size reaches 15. The dynamic function of a single node is formula (5), then each independent node has 3 variables and n = 3. At this time, the dynamic function of node i in the complex network is: where x i (t) = [x i1 (t),…,x i3 (t)] T ∈R 3 The state of node i at time t; function f(·) is the dynamic function of a single node; c(t)=[c1(t),…,c n (t)] T ∈R 3 is the coupling strength between nodes; time t is a positive real number, A=(a ij (t)) N×N is the adjacency matrix. When there is an edge between node i and node j, then a ij (t) = a ji (t)=1(i≠j), otherwise a ij (t) = a ji (t) = 0 (i≠j), the diagonal elements of the matrix A are taken as

[0016] When the dynamic dimension n of a single node is 3, formula (5) can be written as two parts: global coupling and partial coupling. The global coupling part only includes one random dimension per node. Without loss of generality, it can be written as:

[0017] The partially coupled part includes the remaining variables for each node:

[0018] Here i = 1, 2, ..., N, k = 2, ..., n. j1 is a node randomly selected from the neighbors of node i.

[0019] In formula (7), j i is the node with the most neighbors among the neighbors of node i. If there is more than one such node with the most neighbors, one is randomly selected from them.

[0020] The coupling strength adaptation strategy in formula (6) and formula (7) is: Here β=0.002 is the adaptive gain.

[0021] The initial states of the nodes are randomly distributed in the interval [-1010]. Figure 1 It can be seen that the network reaches synchronization time on three variables: 0.5s, 0.4s and 0.7s. This means that the entire network can reach synchronization at time 0.7s, greatly reducing the number of communications between nodes and reducing communication network congestion.

[0022] from Figure 2 It can be seen that the coupling strength between nodes is 0.199, 0.173 and 0.191 respectively at t>0.5s, t>0.4s and t>0.7s on the three variables, which is consistent with Figure 1 If we do not use adaptive control separately, the coupling strength on each variable must be greater than 0.199, which will result in excess coupling strength on the second and third variables, resulting in waste.

[0023] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. An adaptive complex network synchronization method based on hybrid coupling, characterized in that: For a complex dynamic network, when the dynamic function of a single node in the network has more than one variable, each node is mutually coupled with all its neighbor nodes on a randomly selected variable, and only one of its neighbor nodes is randomly selected to interact on the remaining variables of the node. The coupling strength between nodes is adjusted through adaptive strategies so that the complex network can achieve stable synchronization.

2. The method for adaptive complex network synchronization based on hybrid coupling according to claim 1, characterized in that: A complex multidimensional dynamic network has N linearly coupled nodes, each of which is an n-dimensional autonomous dynamic system, and its equation is: where x i (t) = [x i1 (t),…,x in (t)] T ∈R n The state of node i at time t; function f(·) is the dynamic function of a single node; c(t)=[c1(t),…,c n (t)] T ∈R n is the coupling strength between nodes; time t is a positive real number, A=(a ij (t)) N×N is the adjacency matrix. When there is an edge between node i and node j, then a ij (t) = a ji (t)=1(i≠j), otherwise a ij (t) = a ji (t) = 0 (i≠j), the diagonal elements of the matrix A are taken as 3. The method for adaptive complex network synchronization based on hybrid coupling according to claim 1, characterized in that: When the dynamics function of a single node in the network has more than one variable, formula (1) can be written as two parts: global coupling and partial coupling. The global coupling part only includes the first variable of each node. Without loss of generality, it can be written as: The partially coupled part includes the remaining variables for each node: Here i=1,2,…,N, k=2,…,n, and j1 is a node randomly selected from the neighbors of node i.

4. The method for adaptive complex network synchronization based on hybrid coupling according to claim 3, characterized in that: The choice j in formula (3) i is the node with the most neighbors among the neighbors of node i. If there is more than one such node with the most neighbors, one is randomly selected from them.

5. The method for adaptive complex network synchronization based on hybrid coupling according to claim 3, characterized in that: The coupling strength adaptation strategy in formula (2) and formula (3) is: Here β is the adaptive gain.

6. The method for adaptive complex network synchronization based on hybrid coupling according to claim 1, characterized in that: The dynamic function of node i is Rossler oscillator, and its formula is:

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