Inner synchronization of controlled multi-valued logical networks
Yunyun Deng, Xiaolong Qi, Yi Liang, Yun Shang, Yun Shang, Yun Shang
TL;DR
This paper explores how to synchronize the states of multi-valued logical networks using a driving node and provides theoretical conditions for achieving synchronization.
Contribution
The paper introduces a novel synchronization model and derives necessary and sufficient conditions for inner synchronization using the semi-tensor product.
Findings
A necessary and sufficient condition for synchronization is derived when all nodes match the driving node's state.
A more general synchronization model is proposed where nodes synchronize among themselves, not necessarily with the driving node.
Simulation examples confirm the validity of the synchronization criteria.
Abstract
This paper studies the inner synchronization problem of multi-valued logical networks by introducing an external single node, which is also called the driving node. Firstly, for the case where the synchronized state of all network nodes equals the state of the driving node, the inner synchronization model of the controlled multi-valued logical network is established, and a necessary and sufficient condition is obtained using the semi-tensor product. Secondly, based on the above synchronization model, a more general model of inner synchronization is discussed, where all nodes of the multi-valued logical network synchronize with each other, but not necessarily to the same as state of the driving node; inner synchronization criteria are established through theoretical proof. Finally, two simulation examples are given to verify the validity of the conclusions.
Click any figure to enlarge with its caption.
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Figure 13
Figure 14
Figure 15
Figure 16
Figure 17
Figure 18
Figure 19
Figure 20
Figure 21
Figure 22
Figure 23
Figure 24
Figure 25
Figure 26
Figure 27
Figure 28
Figure 29
Figure 30
Figure 31
Figure 32
Figure 33
Figure 34
Figure 35
Figure 36
Figure 37
Figure 38
Figure 39
Figure 40
Figure 41
Figure 42
Figure 43
Figure 44
Figure 45
Figure 46
Figure 47
Figure 48
Figure 49
Figure 50Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsNeural Networks Stability and Synchronization · Gene Regulatory Network Analysis · DNA and Biological Computing