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A Novel Measure Inspired by Lyapunov Exponents for the Characterization of Dynamics in State-Transition Networks

Bulcsú Sándor, Bence Schneider, Zsolt I. Lázár, Mária Ercsey-Ravasz
2021 Entropy  
By combining the considerations behind the Lyapunov exponent of dynamical systems and the average entropy of transition probabilities for Markov chains, we introduce a network measure for characterizing  ...  Motivated by providing proper use cases for studying the new measure, we also lay out a method for mapping time series to state transition networks by phase space coarse graining.  ...  The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.  ... 
doi:10.3390/e23010103 pmid:33445685 pmcid:PMC7828116 fatcat:72o4ad6o2bekfjqkfdsicuyqqm

The Value of Symbolic Computation

Whitney Tabor
2002 Ecological psychology  
In this regard, it is not in a position to characterize natural language systems in the lawful terms that ecological psychologists strive for.  ...  It is strong on providing a network of outposts that make scientific travel in the jungles of natural language feasible.  ...  ACKNOWLEDGMENTS This research was partly supported by University of Connecticut Research Foundation Grant FRS 444038. Thanks to Chaopeng Zhou for discussions and help with running the simulations.  ... 
doi:10.1207/s15326969eco1401&2double_3 fatcat:d52daz6rubd2rf5pgr5fhe65ya

The Value of Symbolic Computation

Whitney Tabor
2002 Ecological psychology  
In this regard, it is not in a position to characterize natural language systems in the lawful terms that ecological psychologists strive for.  ...  It is strong on providing a network of outposts that make scientific travel in the jungles of natural language feasible.  ...  ACKNOWLEDGMENTS This research was partly supported by University of Connecticut Research Foundation Grant FRS 444038. Thanks to Chaopeng Zhou for discussions and help with running the simulations.  ... 
doi:10.1080/10407413.2003.9652751 fatcat:gkv4mz3oszamjcru3cb7b6guna

Chaos in time delay systems, an educational review [article]

Hendrik Wernecke, Bulcsú Sándor, Claudius Gros
2019 arXiv   pre-print
Which are then the possible types of time delays, induced chaotic states, and methods suitable to characterize the resulting dynamics?  ...  This review presents an overview of the field that includes an in-depth discussion of the most important results, of the standard numerical approaches and of several novel tests for identifying chaos.  ...  W. thanks the organizers of the 675th Heraeus seminar on 'Delayed complex systems', Günter Radons, Andreas Otto, and Wolfram Just for an inspiring conference that facilitated the richness of topics in  ... 
arXiv:1901.04826v3 fatcat:fwfyma6tsfcjncnhsjjqgbvu3e

Geometric and dynamic perspectives on phase-coherent and noncoherent chaos

Yong Zou, Reik V. Donner, Jürgen Kurths
2012 Chaos  
In this work, we propose different measures based on recurrence properties of recorded trajectories, which characterize the underlying systems from both geometric and dynamic viewpoints.  ...  Our results demonstrate that especially geometric measures from recurrence network analysis are well suited for tracing transitions between spiral- and screw-type chaos, a common route from phase-coherent  ...  The authors thank Wei Zou for providing a code for estimating the largest Lyapunov exponent of the Mackey-Glass system, and Istvan Kiss for fruitful discussions.  ... 
doi:10.1063/1.3677367 pmid:22462991 fatcat:kzvd7i2d2vdstdgucaqet24r74

Connectivity, Dynamics, and Memory in Reservoir Computing with Binary and Analog Neurons

Lars Büsing, Benjamin Schrauwen, Robert Legenstein
2010 Neural Computation  
Our analyses are based on a novel estimation of the Lyapunov exponent of the network dynamics with the help of branching process theory, rank measures that estimate the kernel quality and generalization  ...  capabilities of recurrent networks, and a novel mean field predictor for computational performance.  ...  projects P17229-N04 and S9102-N13; and projects FP6-015879 (FACETS), FP7-216593 (SECO) of the European Union.  ... 
doi:10.1162/neco.2009.01-09-947 pmid:20028227 fatcat:7qlvzbmdgfckxbipai2oluvfi4

Thermalization dynamics of macroscopic weakly nonintegrable maps [article]

Merab Malishava, Sergej Flach
2022 arXiv   pre-print
We characterize the spatial properties of the tangent vector and arrive at a complete classification picture of weakly nonintegrable macroscopic thermalization dynamics.  ...  For weakly connected lattices the corresponding local observables are coupled into a short-range network.  ...  This work was supported by the Institute for Basic Science (Project number: IBS-R024-D1).  ... 
arXiv:2203.10461v1 fatcat:nkhrlfytafcvpa66npeo6yox6i

Theory of gating in recurrent neural networks [article]

Kamesh Krishnamurthy, Tankut Can, David J. Schwab
2021 arXiv   pre-print
The gate controlling timescales leads to a novel, marginally stable state, where the network functions as a flexible integrator.  ...  The rich dynamics are summarized in phase diagrams, thus providing a map for principled parameter initialization choices to ML practitioners.  ...  A NOVEL, DISCONTINUOUS TRANSITION TO CHAOS In this section, we describe in detail a novel state, characterized by a proliferation of unstable fixed-points, and the coexistence of a stable fixed-point with  ... 
arXiv:2007.14823v5 fatcat:3jlhewkijvhshpomv5i25dlmzm

Consistency in echo-state networks

Thomas Lymburn, Alexander Khor, Thomas Stemler, Débora C. Corrêa, Michael Small, Thomas Jüngling
2019 Chaos  
Through a replica test we measure the consistency levels of the high-dimensional response, yielding a comprehensive portrait of the echo-state property.  ...  We apply this concept to echo-state networks, which are an artificial-neural network version of reservoir computing.  ...  ACKNOWLEDGMENTS TL is supported by the Australian Government Research Training Program at The University of Western Australia. AK was supported by the Hackett Postgraduate Scholarship.  ... 
doi:10.1063/1.5079686 fatcat:674mp7iq3bbapnc6lbycntf6si

A Neurodynamic Account of Spontaneous Behaviour

Jun Namikawa, Ryunosuke Nishimoto, Jun Tani, Olaf Sporns
2011 PLoS Computational Biology  
Therefore, to reconstruct the phenomena, synthetic neuro-robotics experiments were conducted by using a neural network model, which is characterized by a generative model with intentional states and its  ...  in the slow dynamics part, provided that the timescale was adequately set for each part.  ...  Maximum Lyapunov Exponent The maximum Lyapunov exponent of a dynamic system is a quantity that characterizes the rate of exponential divergence from the perturbed initial conditions.  ... 
doi:10.1371/journal.pcbi.1002221 pmid:22028634 pmcid:PMC3197631 fatcat:pzsbvww5zvgzvelbnooj7suyoy

Phase Transition Adaptation [article]

Claudio Gallicchio, Alessio Micheli, Luca Silvestri
2021 arXiv   pre-print
In this paper, we propose an extension of the original approach, a local unsupervised learning mechanism we call Phase Transition Adaptation, designed to drive the system dynamics towards the 'edge of  ...  Here, the complex behavior exhibited by the system elicits an enhancement in its overall computational capacity.  ...  The edge of stability can be empirically detected by measuring Lyapunov exponents [42] , [38] , [39] .  ... 
arXiv:2104.10132v1 fatcat:y7meesc2tnh77dzakbkemyvzfi

Phase Transition Adaptation

Claudio Gallicchio, Alessio Micheli, Luca Silvestri
2021 Zenodo  
In this paper, we propose an extension of the original approach, a local unsupervised learning mechanism we call Phase Transition Adaptation, designed to drive the system dynamics towards the 'edge of  ...  Here, the complex behavior exhibited by the system elicits an enhancement in its overall computational capacity.  ...  The edge of stability can be empirically detected by measuring Lyapunov exponents [42] , [38] , [39] .  ... 
doi:10.5281/zenodo.5256887 fatcat:qamnqh4stzdh7dyv72fyzmg2bi

Chaotic memristive circuit: equivalent circuit realization and dynamical analysis

Bo-Cheng Bao, Jian-Ping Xu, Guo-Hua Zhou, Zheng-Hua Ma, Ling Zou
2011 Chinese Physics B  
The initial state-dependent and the circuit parameter-dependent dynamics of the chaotic memristive circuit are investigated via phase portraits, bifurcation diagrams and Lyapunov exponents.  ...  In this paper, a practical equivalent circuit of an active flux-controlled memristor characterized by smooth piecewise-quadratic nonlinearity is designed and an experimental chaotic memristive circuit  ...  Therefore, appreciable research interest have been inspired by the successful fabrication of memristors because of their potential applications in computers, neural networks, analog circuitries, and so  ... 
doi:10.1088/1674-1056/20/12/120502 fatcat:sqwauwsq5rhbriyve2a52oklmi

Toward prediction of physiological state signals in sleep apnea

J. Bock, D.A. Gough
1998 IEEE Transactions on Biomedical Engineering  
Joel Bock (M'98) received the B.A. degree in economics (1982) and the M.Sc. degree in aerospace engineering (1987), from San Diego State University, CA, and subsequently the M.Sc. in bioengineering (1996  ...  ) from the University of California, San Diego.  ...  ACKNOWLEDGMENT The authors gratefully acknowledge the comments and suggestions made J. Principe.  ... 
doi:10.1109/10.725330 pmid:9805832 fatcat:jqafswavtndahb65jvzwldx7ne

Designing spontaneous behavioral switching via chaotic itinerancy [article]

Katsuma Inoue, Kohei Nakajima, Yasuo Kuniyoshi
2020 arXiv   pre-print
Chaotic itinerancy is a frequently observed phenomenon in high-dimensional and nonlinear dynamical systems, and it is characterized by the random transitions among multiple quasi-attractors.  ...  In this study, we propose a novel way of implementing chaotic itinerancy reproducibly and at will in a generic high-dimensional chaotic system.  ...  Furthermore, we assessed the effect of innate training on the system's chaoticity by measuring the Lyapunov exponents of the system.  ... 
arXiv:2002.08332v1 fatcat:jv3z7vmb3nfvvndere2x7aluem
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