Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userThe Effects of Structural Perturbations on the Synchronizability of Diffusive Networks
103
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We investigate the effects of structural perturbations of both, undirected and directed diffusive networks on their ability to synchronize. We establish a classification of directed links according to their impact on synchronizability. We focus on adding directed links in weakly connected networks having a strongly connected component acting as driver. When the connectivity of the driver is not stronger than the connectivity of the slave component, we can always make the network strongly connected while hindering synchronization. On the other hand, we prove the existence of a perturbation which makes the network strongly connected while increasing the synchronizability. Under additional conditions, there is a node in the driving component such that adding a single link starting at an arbitrary node of the driven component and ending at this node increases the synchronizability.
rate research
Read More
In this paper, we investigate the collective synchronization of system of coupled oscillators on Barab{a}si-Albert scale-free network. We propose an approach of structural perturbations aiming at those nodes with maximal betweenness. This method can markedly enhance the network synchronizability, and is easy to be realized. The simulation results show that the eigenratio will sharply decrease to its half when only 0.6% of those hub nodes are under 3-division processes when network size N=2000. In addition, the present study also provides a theoretical evidence that the maximal betweenness plays a main role in network synchronization.
In this paper, we work on the notion of k-synchronizability: a system is k-synchronizable if any of its executions, up to reordering causally independent actions, can be divided into a succession of k-bounded interaction phases. We show two results (both for mailbox and peer-to-peer automata): first, the reachability problem is decidable for k-synchronizable systems; second, the membership problem (whether a given system is k-synchronizable) is decidable as well. Our proofs fix several important issues in previous attempts to prove these two results for mailbox automata.
Determining the effect of structural perturbations on the eigenvalue spectra of networks is an important problem because the spectra characterize not only their topological structures, but also their dynamical behavior, such as synchronization and cascading processes on networks. Here we develop a theory for estimating the change of the largest eigenvalue of the adjacency matrix or the extreme eigenvalues of the graph Laplacian when small but arbitrary set of links are added or removed from the network. We demonstrate the effectiveness of our approximation schemes using both real and artificial networks, showing in particular that we can accurately obtain the spectral ranking of small subgraphs. We also propose a local iterative scheme which computes the relative ranking of a subgraph using only the connectivity information of its neighbors within a few links. Our results may not only contribute to our theoretical understanding of dynamical processes on networks, but also lead to practical applications in ranking subgraphs of real complex networks.
We consider large networks of theta neurons and use the Ott/Antonsen ansatz to derive degree-based mean field equations governing the expected dynamics of the networks. Assuming random connectivity we investigate the effects of varying the widths of the in- and out-degree distributions on the dynamics of excitatory or inhibitory synaptically coupled networks, and gap junction coupled networks. For synaptically coupled networks, the dynamics are independent of the out-degree distribution. Broadening the in-degree distribution destroys oscillations in inhibitory networks and decreases the range of bistability in excitatory networks. For gap junction coupled neurons, broadening the degree distribution varies the values of parameters at which there is an onset of collective oscillations. Many of the results are shown to also occur in networks of more realistic neurons.
In this paper, we study the bifurcate of limit cycles for Bogdanov-Takens system($dot{x}=y$, $dot{y}=-x+x^{2}$) under perturbations of piecewise smooth polynomials of degree $2$ and $n$ respectively. We bound the number of zeros of first order Melnikov function which controls the number of limit cycles bifurcating from the center. It is proved that the upper bounds of the number of limit cycles with switching curve $x=y^{2m}$($m$ is a positive integral) are $(39m+36)n+77m+21(mgeq 2)$ and $50n+52(m=1)$ (taking into account the multiplicity). The upper bounds number of limit cycles with switching lines $x=0$ and $y=0$ are 11 (taking into account the multiplicity) and it can be reached.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
