Abstract
Complex phenomena are observed in various situations. These complex phenomena are produced from deterministic dynamical systems or stochastic systems. Then, it is an important issue to clarify what is a source of the complex phenomena and to analyze what kind of response will emerge. Then, in this paper, we analyze deterministic chaos from a new aspect. The analysis method is based on the idea that attractors of nonlinear dynamical systems and networks are characterized by a two-dimensional matrix: a recurrence plot and an adjacent matrix. Then, we transformed the attractors to the networks, and evaluated the clustering coefficients and the characteristic path length to the networks. As a result, the networks constructed from the chaotic systems show a small world property.
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Shimada, Y., Kimura, T., Ikeguchi, T. (2008). Analysis of Chaotic Dynamics Using Measures of the Complex Network Theory. In: Kůrková, V., Neruda, R., Koutník, J. (eds) Artificial Neural Networks - ICANN 2008. ICANN 2008. Lecture Notes in Computer Science, vol 5163. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87536-9_7
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DOI: https://doi.org/10.1007/978-3-540-87536-9_7
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