Collective chaos induced by structures of complex networks

Abstract

Mapping a complex network of N coupled identical oscillators to a quantum system, the nearest neighbor level spacing (NNLS) distribution is used to identify collective chaos in the corresponding classical dynamics on the complex network. The classical dynamics on an Erdos-Renyi network with the wiring probability p ER ≤ 1 N is in the state of collective order, while that on an Erdos-Renyi network with p ER > 1 N in the state of collective chaos. The dynamics on a WS Small-world complex network evolves from collective order to collective chaos rapidly in the region of the rewiring probability p r ∈ [0.0, 0.1], and then keeps chaotic up to p r = 1.0. The dynamics on a Growing Random Network (GRN) is in a special state deviates from order significantly in a way opposite to that on WS small-world networks. Each network can be measured by a couple values of two parameters (β, η).

Synchronization, non-linear dynamics and low-frequency fluctuations: Analogy between spontaneous brain activity and networked single-transistor chaotic oscillators

“…[72][73][74][75][76][77] In particular, insertion of long-distance shortcuts according to small-world topology leads to chaos even in networks that cannot otherwise be chaotic. [78][79][80][81] At the same time, in-vitro recordings of neuronal cultures on substrate-integrated multi-electrode arrays, indexing mesoscale activity in networks of %10 4 -10 5 neurons, demonstrate the emergence of self-organized small-world functional connectivity during culture maturation. It has separately been shown that the prevalence of chaotic activity in these cultures gradually increases as the number of active sites grows, in turn suggesting that the gradual formation of a dense and complex network promotes the emergence of chaos.…”

Collaborative Production Structure of Knowledge Sharing Behavior in Internet Communities

“…Networks with all identical nodes are called homogeneous networks. Yang et al used a similar mapping model to map homogeneous networks into quantum systems [28][29][30]. However, the nodes in current network model cannot all be identical.…”

“…Thus the spectrum of adjacency matrix can be used to analyze the nearest neighbor level spacing distribution directly. The process of determining the NNLS distribution from the spectrum of adjacency matrix was briefly reviewed as follows [28]. Given the spectrum of adjacency matrix, denoted with { | = 1, 2, .…”

“…As in the method used by Yang et al when determining the values of parameters with formula (11), the present work also focused on whether the NNLS distribution follows a Brody distribution from the main linear trend region [28]. The fitting results were checked by comparing the theoretical results to the actual ones in main linear trend regions.…”

Network-based identification of reliable bio-markers for cancers

“…To cite examples, τ X is selected to be the special value at which behavior of degree distribution function transitions from Poisson to power-law, or behavior of nearest neighbor level spacing distribution changes from $ s Á expðÀs 2 Þ to $ expðÀsÞ (Luo et al, 2006;Yang et al, 2006;Sun et al, 2007). Here, s denotes nearest neighbor level spacing for ranked spectrum of adjacency matrix.…”