scholarly journals Finite-Time Synchronization of Uncertain Complex Dynamic Networks with Nonlinear Coupling

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Yiping Luo ◽  
Yuejie Yao
Keyword(s):  
Finite Time ◽  
Time Synchronization ◽  
Dynamic Networks ◽  
Nonlinear Function ◽  
Time Instant ◽  
Control Input ◽  
Parameter Uncertainties ◽  
Complex Dynamic ◽  
Network Nodes ◽  
Analysis Techniques

The finite-time synchronization control is studied in this paper for a class of nonlinear uncertain complex dynamic networks. The uncertainties in the network are unknown but bounded and satisfy some matching conditions. The coupling relationship between network nodes is described by a nonlinear function satisfying the Lipchitz condition. By introducing a simple Lyapunov function, two main results regarding finite-time synchronization of a class of complex dynamic networks with parameter uncertainties are derived. By employing some analysis techniques like matrix inequalities, suitable controllers can be designed based on the obtained synchronization criteria. Moreover, with the obtained control input, the time instant required for the system to achieve finite-time synchronization can be estimated if a set of LMIs are feasible or an assumption on the eigenvalues of some matrices can be satisfied. Finally, the effectiveness of the proposed results is verified by numerical simulation.

scholarly journals Searching for Errors in Models of Complex Dynamic Systems

2021 ◽  
Vol 11 ◽  
Author(s):  
Dominik Kahl ◽  
Maik Kschischo
Keyword(s):  
Structural Model ◽  
Temporal Dynamics ◽  
Dynamic Networks ◽  
Model Errors ◽  
Complex Dynamic ◽  
Network Nodes ◽  
C Elegans ◽  
Daunting Task ◽  
Interacting Systems ◽  
And Control

Mathematical modeling is seen as a key step to understand, predict, and control the temporal dynamics of interacting systems in such diverse areas like physics, biology, medicine, and economics. However, for large and complex systems we usually have only partial knowledge about the network, the coupling functions, and the interactions with the environment governing the dynamic behavior. This incomplete knowledge induces structural model errors which can in turn be the cause of erroneous model predictions or misguided interpretations. Uncovering the location of such structural model errors in large networks can be a daunting task for a modeler. Here, we present a data driven method to search for structural model errors and to confine their position in large and complex dynamic networks. We introduce a coherence measure for pairs of network nodes, which indicates, how difficult it is to distinguish these nodes as sources of an error. By clustering network nodes into coherence groups and inferring the cluster inputs we can decide, which cluster is affected by an error. We demonstrate the utility of our method for the C. elegans neural network, for a signal transduction model for UV-B light induced morphogenesis and for synthetic examples.

Finite time synchronization diffusion of uncertain networks with the switching topology

2021 ◽  
pp. 2150165
Author(s):  
Chengye Zou ◽  
Xingyuan Wang ◽  
Haifeng Li
Keyword(s):  
Boundary Conditions ◽  
Numerical Simulations ◽  
Finite Time ◽  
Chaotic Systems ◽  
Time Synchronization ◽  
Diffusion Time ◽  
Switching Topology ◽  
Parameter Uncertainties ◽  
Uncertain Networks ◽  
The Impact

The finite time synchronization diffusion of uncertain networks with the switching topology is investigated in this paper. Spatiotemporal chaotic systems as nodes to construct the network, and the topology of network can jump from one construction to another to meet the actual demand. It is not like ordinary synchronization of network, our method can realize synchronization diffusion originated from boundary conditions, and the diffusion step can be determined by Taylor expand. The parameters are identified through proposed scheme against parameter uncertainties of system in practice. Numerical simulations are utilized to demonstrate the correctness and effectiveness of the finite time synchronization diffusion criteria. In the section of analysis and discussion, we have analyzed the impact of synchronization diffusion step and controller on the synchronization diffusion time.

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