scholarly journals Delay Partial Synchronization of Mutual Delay Coupled Boolean Networks

2020 ◽  
Vol 53 (5-6) ◽  
pp. 870-875 ◽  
Author(s):  
Qiang Wei ◽  
Cheng-jun Xie ◽  
Xu-ri Kou ◽  
Wei Shen
Keyword(s):  
Theoretical Analysis ◽  
Network Model ◽  
Upper Bound ◽  
Boolean Network ◽  
Sufficient Conditions ◽  
Boolean Networks ◽  
Partial Synchronization ◽  
Synchronization Time ◽  
Boolean Network Model ◽  
Necessary And Sufficient

This paper studies the delay partial synchronization for mutual delay-coupled Boolean networks. First, the mutual delay-coupled Boolean network model is presented. Second, some necessary and sufficient conditions are derived to ensure the delay partial synchronization of the mutual delay-coupled Boolean networks. The upper bound of synchronization time is obtained. Finally, an example is provided to illustrate the efficiency of the theoretical analysis.

scholarly journals Synchronization of mutual time-varying delay-coupled temporal Boolean networks

2020 ◽  
Vol 53 (7-8) ◽  
pp. 1504-1511
Author(s):  
Qiang Wei ◽  
Cheng-jun Xie
Keyword(s):  
Theoretical Analysis ◽  
Upper Bound ◽  
Boolean Network ◽  
Sufficient Conditions ◽  
Boolean Networks ◽  
Time Varying ◽  
Time Varying Delay ◽  
Boolean Network Model ◽  
Necessary And Sufficient ◽  
Varying Delay

This paper presents mutual time-varying delay-coupled temporal Boolean network model and investigates synchronization issue for mutual time-varying delay-coupled temporal Boolean networks. The necessary and sufficient conditions for the synchronization are given, and the check criterion of the upper bound is presented. An example is given to illustrate the correctness of the theoretical analysis.

scholarly journals A Note on the Observability of Temporal Boolean Control Network

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Wenping Shi ◽  
Bo Wu ◽  
Jing Han
Keyword(s):  
Boolean Network ◽  
Sufficient Conditions ◽  
Boolean Networks ◽  
Control Networks ◽  
Linear Dynamic Systems ◽  
Regulatory Interactions ◽  
Boolean Control Network ◽  
Boolean Network Model ◽  
Necessary And Sufficient ◽  
Product Of Matrices

Temporal Boolean network is a generalization of the Boolean network model that takes into account the time series nature of the data and tries to incorporate into the model the possible existence of delayed regulatory interactions among genes. This paper investigates the observability problem of temporal Boolean control networks. Using the semi tensor product of matrices, the temporal Boolean networks can be converted into discrete time linear dynamic systems with time delays. Then, necessary and sufficient conditions on the observability via two kinds of inputs are obtained. An example is given to illustrate the effectiveness of the obtained results.

Estimation of delays in generalized asynchronous Boolean networks

2016 ◽  
Vol 12 (10) ◽  
pp. 3098-3110 ◽  
Author(s):  
Haimabati Das ◽  
Ritwik Kumar Layek
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Network Model ◽  
Boolean Network ◽  
Equation Model ◽  
Boolean Networks ◽  
Temporal Behavior ◽  
Ordinary Differential Equation Model ◽  
Differential Equation Model ◽  
Boolean Network Model

The generalized asynchronous Boolean network model proposed in this paper can reliably mimic the temporal behavior of the Ordinary Differential Equation model without compromising the flexibility of the Boolean network model.

ASYNCHRONOUS RANDOM BOOLEAN NETWORK MODEL WITH VARIABLE NUMBER OF PARENTS BASED ON ELEMENTARY CELLULAR AUTOMATA RULE 126

2006 ◽  
Vol 20 (08) ◽  
pp. 897-923 ◽  
Author(s):  
MIHAELA T. MATACHE
Keyword(s):  
Cellular Automata ◽  
Network Model ◽  
Boolean Network ◽  
Random Variable ◽  
Variable Number ◽  
Boolean Networks ◽  
Random Boolean Networks ◽  
Elementary Cellular Automata ◽  
Boolean Network Model ◽  
Point Analysis

A Boolean network with N nodes, each node's state at time t being determined by a certain number of parent nodes, which can vary from one node to another, is considered. This is a generalization of previous results obtained for a constant number of parent nodes, by Matache and Heidel in "Asynchronous Random Boolean Network Model Based on Elementary Cellular Automata Rule 126", Phys. Rev. E71, 026 232, 2005. The nodes, with randomly assigned neighborhoods, are updated based on various asynchronous schemes. The Boolean rule is a generalization of rule 126 of elementary cellular automata, and is assumed to be the same for all the nodes. We provide a model for the probability of finding a node in state 1 at a time t for the class of generalized asynchronous random Boolean networks (GARBN) in which a random number of nodes can be updated at each time point. We generate consecutive states of the network for both the real system and the models under the various schemes, and use simulation algorithms to show that the results match well. We use the model to study the dynamics of the system through sensitivity of the orbits to initial values, bifurcation diagrams, and fixed point analysis. We show that the GARBN's dynamics range from order to chaos, depending on the type of random variable generating the asynchrony and the parameter combinations.

Synchronization in mutual-coupled temporal Boolean networks

2017 ◽  
Vol 40 (7) ◽  
pp. 2211-2216 ◽  
Author(s):  
Qiang Wei ◽  
Cheng-jun Xie
Keyword(s):  
Theoretical Analysis ◽  
Tensor Product ◽  
Sufficient Conditions ◽  
Boolean Networks ◽  
Necessary And Sufficient Conditions ◽  
Complete Synchronization ◽  
Logical Relationship ◽  
Algebraic Form ◽  
Algebraic Forms ◽  
Necessary And Sufficient

In this paper, we first propose a mutual-coupled temporal Boolean networks model and then investigate complete synchronization in mutual-coupled temporal Boolean networks. The mutual-coupled temporal Boolean networks model with logical relationship is converted into an algebraic form based on a semi-tensor product. Necessary and sufficient conditions are derived to realize synchronization based on the algebraic forms. An example illustrates the effectiveness of the theoretical analysis.

scholarly journals A strict upper bound for size multipartite Ramsey numbers of paths versus stars

2017 ◽  
Vol 1 (2) ◽  
pp. 9
Author(s):  
Chula Jayawardene
Keyword(s):  
Natural Number ◽  
Complete Graph ◽  
Upper Bound ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Infinite Class ◽  
Ramsey Numbers ◽  
Necessary And Sufficient

<p>Let $P_n$ represent the path of size $n$. Let $K_{1,m-1}$ represent a star of size $m$ and be denoted by $S_{m}$. Given a two coloring of the edges of a complete graph $K_{j \times s}$ we say that $K_{j \times s}\rightarrow (P_n,S_{m+1})$ if there is a copy of $P_n$ in the first color or a copy of $S_{m+1}$ in the second color. The size Ramsey multipartite number $m_j(P_n, S_{m+1})$ is the smallest natural number $s$ such that $K_{j \times s}\rightarrow (P_n,S_{m+1})$. Given $j,n,m$ if $s=\left\lceil \dfrac{n+m-1-k}{j-1} \right\rceil$, in this paper, we show that the size Ramsey numbers $m_j(P_n,S_{m+1})$ is bounded above by $s$ for $k=\left\lceil \dfrac{n-1}{j} \right\rceil$. Given $j\ge 3$ and $s$, we will obtain an infinite class $(n,m)$ that achieves this upper bound $s$. In the later part of the paper, will also investigate necessary and sufficient conditions needed for the upper bound to hold.</p>

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