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Replication of Continuous Chaos About Equilibria
Date
2016-01-01
Author
Akhmet, Marat
Fen, Mehmet Onur
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URI
https://hdl.handle.net/11511/99178
Journal
REPLICATION OF CHAOS IN NEURAL NETWORKS, ECONOMICS AND PHYSICS
DOI
https://doi.org/10.1007/978-3-662-47500-3_2
Collections
Department of Mathematics, Article
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We propose a rigorous method for replication of chaos from a prior one to systems with large dimensions. Extension of the formal properties and features of a complex motion can be observed such that ingredients of chaos united as known types of chaos, Devaney's, Li-Yorke and obtained through period-doubling cascade. This is true for other appearances of chaos: intermittency, structure of the chaotic attractor, its fractal dimension, form of the bifurcation diagram, the spectra of Lyapunov exponents, etc. Th...
Replication of Chaos in Neural Networks, Economics and Physics Introduction
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Replication of Chaos in Neural Networks, Economics and Physics Preface
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Replication of chaos in neural networks, economics and physics
Akhmet, Marat (Springer, London/Berlin , 2016-12-01)
This book presents detailed descriptions of chaos for continuous-time systems. It is the first-ever book to consider chaos as an input for differential and hybrid equations. Chaotic sets and chaotic functions are used as inputs for systems with attractors: equilibrium points, cycles and tori. The findings strongly suggest that chaos theory can proceed from the theory of differential equations to a higher level than previously thought. The approach selected is conducive to the in-depth analysis of different ...
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In online monitoring of critical systems, it is important to detect an abnormal behavior as early as possible. Signal temporal logic (STL) formulas are used to specify these undesired behaviors due to the expressivity and interpretability of the logic and the existence of efficient online monitoring algorithms. In this paper, we present a new method to synthesize formulas that belong to past time fragment of STL from a labeled dataset. In particular, we consider a dataset that includes signals and their lab...
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M. Akhmet and M. O. Fen, “Replication of Continuous Chaos About Equilibria,”
REPLICATION OF CHAOS IN NEURAL NETWORKS, ECONOMICS AND PHYSICS
, pp. 33–100, 2016, Accessed: 00, 2022. [Online]. Available: https://hdl.handle.net/11511/99178.