Application of Coupled Dynamical Systems for Communities Detection in Complex Networks

2013 ◽  
pp. 139-159
Author(s):  
Nikolai Nefedov
Keyword(s):  
Dynamical Systems ◽  
Complex Networks

Invariant Multiparameter Sensitivity to Characterize Dynamical Systems on Complex Networks

2015 ◽  
Vol 84 (2) ◽  
pp. 024002
Author(s):  
Kenzaburo Fujiwara ◽  
Takuma Tanaka ◽  
Kiyohiko Nakamura
Keyword(s):  
Dynamical Systems ◽  
Complex Networks

Distributed adaptive consensus and synchronization in complex networks of dynamical systems

Automatica ◽  
2018 ◽  
Vol 91 ◽  
pp. 233-243 ◽  
Author(s):  
Miloje S. Radenković ◽  
Miroslav Krstić
Keyword(s):  
Dynamical Systems ◽  
Complex Networks

Preservation of relevant properties of interconnected dynamical systems over complex networks

2013 ◽  
Vol 350 (10) ◽  
pp. 2849-2852
Author(s):  
Guillermo Fernández-Anaya ◽  
Eric Campos-Cantón ◽  
Sergej Čelikovský ◽  
Antonio Loria
Keyword(s):  
Dynamical Systems ◽  
Complex Networks ◽  
Interconnected Dynamical Systems

scholarly journals Mapping dynamical systems onto complex networks

2007 ◽  
Vol 58 (4) ◽  
pp. 469-474 ◽  
Author(s):  
E. P. Borges ◽  
D. O. Cajueiro ◽  
R. F.S. Andrade
Keyword(s):  
Dynamical Systems ◽  
Complex Networks

RECURRING HARMONIC WALKS AND NETWORK MOTIFS IN WESTERN MUSIC

2006 ◽  
Vol 09 (01n02) ◽  
pp. 121-132 ◽  
Author(s):  
SHALEV ITZKOVITZ ◽  
RON MILO ◽  
NADAV KASHTAN ◽  
REUVEN LEVITT ◽  
AMIR LAHAV ◽  
...  
Keyword(s):  
Dynamical Systems ◽  
Complex Networks ◽  
Popular Music ◽  
Music Theory ◽  
Western Music ◽  
Compact Representation ◽  
Network Motifs ◽  
Basic Principles ◽  
Musical Harmony ◽  
Dynamical Patterns

Western harmony is comprised of sequences of chords, which obey grammatical rules. It is of interest to develop a compact representation of the harmonic movement of chord sequences. Here, we apply an approach from analysis of complex networks, known as "network motifs" to define repeating dynamical patterns in musical harmony. We describe each piece as a graph, where the nodes are chords and the directed edges connect chords which occur consecutively in the piece. We detect several patterns, each of which is a walk on this graph, which recur in diverse musical pieces from the Baroque to modern-day popular music. These patterns include cycles of three or four nodes, with up to two mutual edges (edges that point in both directions). Cliques and patterns with more than two mutual edges are rare. Some of these universal patterns of harmony are well known and correspond to basic principles of music theory such as hierarchy and directionality. This approach can be extended to search for recurring patterns in other musical components and to study other dynamical systems that can be represented as walks on graphs.

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