1887
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Self-organized topology of recurrence-based complex networks
Rent:
Rent this article for
USD
10.1063/1.4829877
/content/aip/journal/chaos/23/4/10.1063/1.4829877
http://aip.metastore.ingenta.com/content/aip/journal/chaos/23/4/10.1063/1.4829877

Figures

Image of FIG. 1.
FIG. 1.

Graphical illustration of the state space (a) and its recurrence plot (b). The recurrence plot characterizes the proximity of state vectors, i.e., whether or not the state-space distance between two “state” and is below a certain recurrence threshold . It is mathematically defined as , where Θ is the Heaviside function and is a distance measure.

Image of FIG. 2.
FIG. 2.

The example of an adjacency matrix in a complex recurrence network.

Image of FIG. 3.
FIG. 3.

Illustrations of the self-organizing process of complex network based on the nodes and edges in the recurrence matrix. (a)–(f) Iterative self-organization of 292 nodes in a network at 300, 600, 900, 1200, 1800, and 1900 iterations. The optimal two-wing layout is achieved at 1900 iterations with a minimal energy and a steady topological structure.

Image of FIG. 4.
FIG. 4.

Cause and effect diagram for performance evaluation of self-organizing network algorithms.

Image of FIG. 5.
FIG. 5.

(a) Lorenz attractor (i.e., unequally spaced) generated from the equations: with the step , (b)equally spaced Lorenz attractor, (c) original Rossler attractor (i.e., unequally spaced) generated from the equations: with the step , and (d) equally spaced Rossler attractor.

Image of FIG. 6.
FIG. 6.

The adjacency matrices of original Lorenz attractor that are derived with the use of (a) recurrence network (i.e., a fixed size of the neighborhood) and (b) k-nearest neighbors network (i.e., a fixed number of neighbors).

Image of FIG. 7.
FIG. 7.

The self-organizing process of complex network based on the nodes and edges in the recurrence-based adjacency matrix of Lorenz system. (a)-(h) Iterative self-organization for the random layout, 1000, 2000, 3000, 4000, 5000, 6000, and 7000 iterations.

Image of FIG. 8.
FIG. 8.

The self-organizing process of complex network based on the nodes and edges in the KNN-based adjacency matrix of Lorenz system. (a)-(h) Iterative self-organization for the random layout, 1000, 2000, 3000, 4000, 5000, 6000, and 7000 iterations.

Image of FIG. 9.
FIG. 9.

The iterative variations of the system energy for the self-organizing process in the complex network using the (a) recurrence-based adjacency matrix and (b) KNN-based adjacency matrix.

Image of FIG. 10.
FIG. 10.

The adjacency matrices of original Rossler attractor that are derived with the use of (a) recurrence network (i.e., a fixed size of the neighborhood) and (b) k-nearest neighbors network (i.e., a fixed number of neighbors).

Image of FIG. 11.
FIG. 11.

The self-organizing process of complex networks based on the nodes and edges in the recurrence-based adjacency matrix of Rossler system. (a)-(h) Iterative self-organization for the random layout, 1000, 2000, 3000, 4000, 5000, 6000, and 7000 iterations.

Image of FIG. 12.
FIG. 12.

The self-organizing process of complex networks based on the nodes and edges in the KNN-based adjacency matrix of Rossler system. (a)-(h) Iterative self-organization for the random layout, 1000, 2000, 3000, 4000, 5000, 6000, and 7000 iterations.

Image of FIG. 13.
FIG. 13.

The self-organizing process of recurrence-based complex network of Lorenz system with the force-model parameter equal to 2. (a-h): Iterative self-organization for the random layout, 1000, 2000, 3000, 4000, 5000, 6000, and 7000 iterations.

Image of FIG. 14.
FIG. 14.

The self-organizing process of recurrence-based complex network of Lorenz system with the force-model parameter equal to 3. (a)-(h) Iterative self-organization for the random layout, 1000, 2000, 3000, 4000, 5000, 6000, and 7000 iterations.

Image of FIG. 15.
FIG. 15.

The self-organizing process of recurrence-based complex network of Rossler system with the force-model parameter equal to 2. (a)-(h) Iterative self-organization for the random layout, 1000, 2000, 3000, 4000, 5000, 6000, and 7000 iterations.

Image of FIG. 16.
FIG. 16.

The self-organizing process of recurrence-based complex network of Rossler system with the force-model parameter equal to 3. (a)-(h) Iterative self-organization for the random layout, 1000, 2000, 3000, 4000, 5000, 6000, and 7000 iterations.

Image of FIG. 17.
FIG. 17.

The recurrence-based adjacency matrices of equally spaced (a) Lorenz attractor and (b) Rossler attractor.

Image of FIG. 18.
FIG. 18.

The self-organizing process of recurrence-based complex network for the equally spaced Lorenz attractor with the force-model parameter equal to 2. (a)-(h) The random layout, 1000, 2000, 3000, 4000, 5000, 6000, and 7000 iterations.

Image of FIG. 19.
FIG. 19.

The self-organizing process of recurrence-based complex network for the equally spaced Rossler attractor with the force-model parameter equal to 2. (a)-(h) The random layout, 1000, 2000, 3000, 4000, 5000, 6000, and 7000 iterations.

Image of FIG. 20.
FIG. 20.

The flow chart of both geometrical and statistical investigations of recurrence networks.

Tables

Generic image for table
Table I.

Design of experiments to evaluate the geometry of self-organizing network.

Loading

Article metrics loading...

/content/aip/journal/chaos/23/4/10.1063/1.4829877
2013-11-08
2014-04-21
Loading

Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Self-organized topology of recurrence-based complex networks
http://aip.metastore.ingenta.com/content/aip/journal/chaos/23/4/10.1063/1.4829877
10.1063/1.4829877
SEARCH_EXPAND_ITEM