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Identifying Chaotic FitzHugh–Nagumo Neurons Using Compressive Sensing

Ri-Qi Su, Ying-Cheng Lai, Xiao Wang
2014 Entropy  
The working and efficiency of the method are illustrated by using networks of non-identical FitzHugh-Nagumo neurons with randomly-distributed coupling weights.  ...  Our method is based on compressive sensing.  ...  One key virtue of compressive sensing, namely the low data requirement, enables us to accomplish the task of identifying chaos with short time series.  ... 
doi:10.3390/e16073889 fatcat:nozvx6hd5faefbemxiz6x24iwe

Revealing direction of coupling between neuronal oscillators from time series: Phase dynamics modeling versus partial directed coherence

Dmitry Smirnov, Bjoern Schelter, Matthias Winterhalder, Jens Timmer
2007 Chaos  
Here, we reveal coupling directions between neuronal oscillators by using a linear, partial directed coherence, and a nonlinear, phase dynamics modeling, time series analysis techniques for various spiking  ...  The problem of determining directional coupling between neuronal oscillators from their time series is addressed.  ...  Modified FitzHugh-Nagumo oscillator The second example is a modified FitzHugh-Nagumo ͑MFHN͒ oscillator where the limit cycle arises via "saddlenode off invariant curve" bifurcation. 40 The equations  ... 
doi:10.1063/1.2430639 pmid:17411247 fatcat:cpuog24tojfa3daimb3vr465ze

A practical method for estimating coupling functions in complex dynamical systems [article]

Isao T. Tokuda and Zoran Levnajic and Kazuyoshi Ishimura
2019 arXiv   pre-print
Second, it presents three new extensions: (i) algorithm for inference of the phase sensitivity function, (ii) coupling function to approximate interaction among phase-coherent chaotic oscillators, (iii  ...  The system of FitzHugh-Nagumo oscillators can be seen as a simple model for interacting neurons.  ...  Wang WX, Yang R, Lai YC, Kovanis V, Harrison MAF. 2011 Time-series-based prediction of complex oscillator networks via compressive sensing. EPL (Europhysics Letters) 94, 48006. 10.  ... 
arXiv:1904.11289v1 fatcat:fy3v7iyedrehtane7ekeyfdzka

Data based identification and prediction of nonlinear and complex dynamical systems

Wen-Xu Wang, Ying-Cheng Lai, Celso Grebogi
2016 Physics reports  
In this paper, we review the recent advances in this forefront and rapidly evolving field, aiming to cover topics such as compressive sensing (a novel optimization paradigm for sparse-signal reconstruction  ...  Example: identifying chaotic neurons in the FitzHugh-Nagumo (FHN) network The FHN model, a simplified version of the biophysically detailed Hodgkin-Huxley model [250] , is a mathematical paradigm for  ...  . . . . . . . . . . . . . . . 59 3.4.2 Example: identifying chaotic neurons in the FitzHugh-Nagumo (FHN) network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 3.5 Data based  ... 
doi:10.1016/j.physrep.2016.06.004 fatcat:6lrzh3dzdfb6ljnyvawpif35ve

ATTENTION-LOCKED COMPUTATION WITH CHAOTIC NEURAL NETS

CARLOS LOURENÇO
2004 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering  
In our approach, the periodic orbits are used as coding devices.  ...  The system is most of the time in an undetermined state characterized by a chaotic attractor.  ...  That is the case of the well-known FitzHugh-Nagumo model for excitable neurons [FitzHugh, 1961 [FitzHugh, , 1969 , which also features diffusive cou-pling.  ... 
doi:10.1142/s0218127404009442 fatcat:km36k5p6rrg3jecmibcl4yuute

Comparing the dynamics of periodically forced lasers and neurons

Jordi Tiana-Alsina, Carlos Alberto Quintero, Cristina Masoller
2019 New Journal of Physics  
with the stochastic FitzHugh-Nagumo model, with an applied periodic signal whose waveform is the same as that used to modulate the laser current.  ...  We also compare the laser and neuron dynamics using symbolic time series analysis.  ...  lidar [11] , compressive sensing [12] to name just a few.  ... 
doi:10.1088/1367-2630/ab4c86 fatcat:jajx7cpzjfgahlhzebbzbb3lsa

The Roadmap to Realize Memristive Three-Dimensional Neuromorphic Computing System [chapter]

Hongyu An, Kangjun Bai, Yang Yi
2018 Advances in Memristor Neural Networks - Modeling and Applications  
Hodgkin-Huxley (HH) and Fitzhugh-Nagumo (FN) neuron model Compared to the data that are extracted from the IF neuron, the HH neuron is found to be biologically meaningful and realistic [34] .  ...  Figure 6 . 6 Action potential of a biological neuron. Figure 7 . 7 Simplified neuron models of (a) integrate-and-fire, (b) Fitzhugh-Nagumo, (c) Hodgkin-Huxley, and (d) leaky integrate-and-fire.  ... 
doi:10.5772/intechopen.78986 fatcat:2sdrqk4x2fd4djcrywkonb5w6u

Editorial Comment on the Special Issue of "Information in Dynamical Systems and Complex Systems"

Erik Bollt, Jie Sun
2014 Entropy  
Interestingly, as reported in the paper "Identifying Chaotic FitzHugh-Nagumo Neurons Using Compressive Sensing" by by Su, Lai, and Wang (herein, Reference [15] ), another perspective of incorporating  ...  measurement matrix that arises after the nonlinear-to-linear transformation, Reference [15] still finds the 1 solution to be quite satisfactory, as illustrated for the synthetic network of nonlinear FitzHugh-Nagumo  ... 
doi:10.3390/e16095068 fatcat:sfxqeheru5ei7h2l3zb5wcrn3q

Chaotic Entanglement: Entropy and Geometry

Matthew A. Morena, Kevin M. Short
2021 Entropy  
In chaotic entanglement, pairs of interacting classically-chaotic systems are induced into a state of mutual stabilization that can be maintained without external controls and that exhibits several properties  ...  In this paper, we discuss the role that entropy plays in chaotic entanglement.  ...  In [16] , it is shown that persistent mutual stabilization could be achieved between a pair of Fitzhugh Nagumo neurons (mathematical neuron models where each individual model is two-dimensional, but the  ... 
doi:10.3390/e23101254 pmid:34681978 pmcid:PMC8534915 fatcat:cn3mgispdff5hfmnt2hok2wdvy

Teaching Computational Neuroscience [article]

Péter Érdi
2014 arXiv   pre-print
The two-dimensional approximation of the model (the FitzHugh-Nagumo model), at least its qualitative properties can be studied analytically, .  ...  Actually among the four parts of the book only the first two (1: Modeling Neurons, 2: Neural Networks) belong to computational neuroscience by using the term in a narrow sense, the other two parts (3.  ... 
arXiv:1412.5909v1 fatcat:rkbovwestbdelhecyjpoxwavtm

NEURAL EXCITABILITY, SPIKING AND BURSTING

EUGENE M. IZHIKEVICH
2000 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering  
Bifurcation mechanisms involved in the generation of action potentials (spikes) by neurons are reviewed here.  ...  We also describe the phenomenon of neural bursting, and we use geometric bifurcation theory to extend the existing classification of bursters, including many new types.  ...  One can easily modify existing models, such as the van der Pol or FitzHugh-Nagumo oscillators, to get such dynamics.  ... 
doi:10.1142/s0218127400000840 fatcat:ylin3n727nekxgor7e52lqydge

Sparse model selection via integral terms

Hayden Schaeffer, Scott G. McCalla
2017 Physical review. E  
Examples include nonlinear equations, population dynamics, chaotic systems, and fast-slow systems.  ...  The sparse regression model is constructed to fit the noisy data to the trajectory of the dynamical system while using the smallest number of active terms.  ...  This has lead to many application in compressive sensing and image processing.  ... 
doi:10.1103/physreve.96.023302 pmid:28950639 fatcat:6w2dhiwkgzgclj43wfipatm4ci

Control of chaos: methods and applications in mechanics

A. L. Fradkov, R. J. Evans, B. R. Andrievsky
2006 Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences  
A survey of the field related to control of chaotic systems is presented.  ...  Other areas of research such as control of distributed (spatio-temporal and delayed) systems, chaotic mixing are outlined. Applications to control of chaotic mechanical systems are discussed.  ...  These techniques are employed to stabilize some of the identified UPOs, confirming the possibility of using such approaches to control chaotic behaviour in mechanical systems using state space reconstruction  ... 
doi:10.1098/rsta.2006.1826 pmid:16893789 fatcat:rjfq6wnjdbhs3ikmkho4liw57u

Neuron models of the generic bifurcation type:network analysis and data modeling

Enno De Lange
2006
The FitzHugh-Nagumo model is only able to model pyramidal neurons and even then performs worse than simple threshold models; it should be used only when the advantages of the more realistic threshold mechanism  ...  By considering basic networks of FTM-coupled FitzHugh-Nagumo (spiking) or Hindmarsh-Rose (bursting) neurons, two main cooperative phenomena, synchronization and coincidence detections, are addressed.  ...  Models identified purely on sub-threshold data also predict qualitative features of super-threshold stimuli. The FitzHugh-Nagumo model was used as a paradigm for spiking behavior in neurons.  ... 
doi:10.5075/epfl-thesis-3617 fatcat:qcx5otp37vgvzejlddiqal7mbu

Machine Discovery of Partial Differential Equations from Spatiotemporal Data [article]

Ye Yuan, Junlin Li, Liang Li, Frank Jiang, Xiuchuan Tang, Fumin Zhang, Sheng Liu, Jorge Goncalves, Henning U.Voss, Xiuting Li, Jürgen Kurths, and Han Ding
2019 arXiv   pre-print
The method, called Sparse Spatiotemporal System Discovery (S^3d), decides which physical terms are necessary and which can be removed (because they are physically negligible in the sense that they do not  ...  The method is built on the recent development of Sparse Bayesian Learning; which enforces the sparsity in the to-be-identified PDEs, and therefore can balance the model complexity and fitting error with  ...  Paul Kolodner for useful discussion and allowing us to use the experimental data. All synthetic data and codes used in this manuscript are publicly available on GitHub https://github.com/HAIRLAB/S3d.  ... 
arXiv:1909.06730v1 fatcat:i2rorppvdvdp5cquq6hwfh56om
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