相关论文: Cluster Synchronization of Networks via a Canonica…
We present a general framework to study stability of the synchronous solution for a hypernetwork of coupled dynamical systems. We are able to reduce the dimensionality of the problem by using simultaneous block-diagonalization of matrices.…
We present a scalable approach for simplifying the stability analysis of cluster synchronization patterns on directed networks. When a network has directional couplings, decomposition of the coupling matrix into independent blocks (which in…
We discuss here the application of the simultaneous block diagonalization (SBD) of matrices to the study of the stability of both complete and cluster synchronization in random (generic) networks. For both problems, we define indices that…
It is well known that a set of non-defect matrices can be simultaneously diagonalized if and only if the matrices commute. In the case of non-commuting matrices, the best that can be achieved is simultaneous block diagonalization. Here we…
This article studies canonical forms derived from the finest simultaneous block diagonalization of a set of symmetric matrices via congruence. Our technique relies on Harrison's center theory, which is extended from a single higher degree…
We provide a solution to the problem of simultaneous $diagonalization$ $via$ $congruence$ of a given set of $m$ complex symmetric $n\times n$ matrices $\{A_{1},\ldots,A_{m}\}$, by showing that it can be reduced to a possibly…
In this paper, we study the network pinning control problem in the presence of two different types of coupling: (i) node-to-node coupling among the network nodes and (ii) input-to-node coupling from the source node to the `pinned nodes'.…
Symmetries are ubiquitous in network systems and have profound impacts on the observable dynamics. At the most fundamental level, many synchronization patterns are induced by underlying network symmetry, and a high degree of symmetry is…
We investigate the stability of synchronized states in delay-coupled networks where synchronization takes place in groups of different local dynamics or in cluster states in networks with identical local dynamics. Using a master stability…
In a recent paper, a new method was proposed to find the common invariant subspaces of a set of matrices. This paper invstigates the more general problem of putting a set of matrices into block triangular or block-diagonal form…
Synchronization is a widespread phenomenon observed across natural and artificial networked systems. It often manifests itself by clusters of units exhibiting coincident dynamics. These clusters are a direct consequence of the organization…
We respond briefly to a comment [1, arXiv:2110.15493] recently posted online on our paper [2, arXiv:2108.07893]. Complete and cluster synchronization of random networks is undoubtedly a topic of interest in the Physics, Engineering, and…
Consider a complete communication network of $n$ nodes, where the nodes receive a common clock pulse. We study the synchronous $c$-counting problem: given any starting state and up to $f$ faulty nodes with arbitrary behaviour, the task is…
Symmetry-based neural networks often constrain the architecture in order to achieve invariance or equivariance to a group of transformations. In this paper, we propose an alternative that avoids this architectural constraint by learning to…
This paper addresses the problem of synchronizing orthogonal matrices over directed graphs. For synchronized transformations (or matrices), composite transformations over loops equal the identity. We formulate the synchronization problem as…
The presence of synchronized clusters in neuron networks is a hallmark of information transmission and processing. The methods commonly used to study cluster synchronization in networks of coupled oscillators ground on simplifying…
Cluster synchronization is a phenomenon in which a network self-organizes into a pattern of synchronized sets. It has been shown that diverse patterns of stable cluster synchronization can be captured by symmetries of the network. Here we…
This paper proposes a control algorithm for stable implementation of asynchronous parallel quadratic programming (PQP) through dual decomposition technique. In general, distributed and parallel optimization requires synchronization of data…
Synchronous Counting is the task of reaching agreement on a common round counter in a synchronous system of $n$ nodes with up to $t$ Byzantine faults in a self-stabilizing manner. That is, after transient faults may have arbitrarily…
In this paper, stability analysis of time delay systems is considered based on decomposition of the systems to subsystems. The decomposition process needs matrices of these systems to be simultaneously block triangularize. We show that a…