Abstract
A complex system is an entity composed of interconnected parts, such that the collective behavior of those parts is more than the sum of the individual components. Those collective behaviors that appear as the interaction of the interconnected parts are usually called emergent.
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Notes
- 1.
Solution: The total number of combinations is \(2.8462596809 \times 10^{35659}\).
- 2.
Another frequent notation is the \(\Omega \) notation, that provides a lower bound in the function growth rate.
- 3.
In dynamical systems, a bifurcation diagram shows the possible long-term values (equilibria/fixed points or periodic orbits) of a system as a function of a bifurcation parameter.
- 4.
The function was \(f(x) = \sum _{n=1}^{\infty } b^n.cos(x \pi a^n)\), with \(a \in \mathbb {Z}^+\) and \(0< b < 1\).
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Acknowledgements
This work was supported by grant No. GACR P103/15/06700S of the Grant Agency of Czech Republic, and the European Regional Development Fund (ERDF) together with the Galician Regional Government under agreement for funding the Atlantic Research Center for Information and Communication Technologies (AtlantTIC).
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Zelinka, I., Burguillo, J.C. (2018). Complex Systems. In: Self-organizing Coalitions for Managing Complexity. Emergence, Complexity and Computation, vol 29. Springer, Cham. https://doi.org/10.1007/978-3-319-69898-4_2
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