Related Experiment Video
Updated: Feb 14, 2026

2D and 3D Matrices to Study Linear Invadosome Formation and Activity
Published on: June 2, 2017
Synchronization of heterogeneous linear networks with distinct inner coupling matrices
Quanyi Liang1, Lei Wang2, Qiqi Hao1
1SKLSDE, LMIB and School of Mathematics and Systems Science, Beihang University, Beijing, China.
Abstract:
In this paper, we study synchronization of heterogeneous linear networks with distinct inner coupling matrices. Firstly, for synchronous networks, we show that any synchronous trajectory will converge to a corresponding synchronous state. Then, we provide an invariant set, which can be exactly obtained by solving linear equations and then used for characterizing synchronous states. Afterwards, we use inner coupling matrices and node dynamics to successively decompose the original network into a new network, composed of the external part and the internal part. Moreover, this new network can be proved to synchronize to the above invariant set by constructing the corresponding desired Lyapunov-like functions for the internal part and the external part respectively. In particular, this result still holds if the coupling strength is disturbed slightly. Finally, examples with numerical simulations are given to illustrate the validity and applicability of our theoretical results.
Related Concept Videos
Protein Networks
These interactions can be represented through maps depicting protein-protein interaction networks, represented as nodes and edges. Nodes are circles that are representative of a protein,...
Network Covalent Solids
To break or to melt a covalent network solid, covalent bonds must be broken. Because covalent bonds are relatively strong, covalent network solids are typically...
Linear Equations
Linear Circuits
Linear Momentum
Linearization and Approximation

