scholarly journals Hamiltonian energy computation and complex behavior of a small heterogeneous network of three neurons: circuit implementation

2021 ◽  
Author(s):  
Zeric Tabekoueng Njitacke ◽  
Jan Awrejcewicz ◽  
Balamurali Ramakrishnan ◽  
Karthikeyan Rajagopal ◽  
Jacques Kengne
Keyword(s):  
Lyapunov Exponent ◽  
Integrated Circuits ◽  
Phase Portraits ◽  
Largest Lyapunov Exponent ◽  
Circuit Implementation ◽  
Brain Functions ◽  
Organizational Principle ◽  
Simultaneous Existence ◽  
Basin Of Attractions ◽  
Electrical Activities

AbstractBrain functions are sometimes emulated using some analog integrated circuits based on the organizational principle of natural neural networks. Neuromorphic engineering is the research branch devoted to the study and realization of such circuits with striking features. In this contribution, a novel small network of three neurons is introduced and investigated. The model is built from the coupling between two 2D Hindmarsh–Rose neurons through a 2D FitzHugh–Nagumo neuron. Thus, a heterogeneous coupled network is obtained. The biophysical energy released by the network during each electrical activity is evaluated. In addition, nonlinear analysis tools such as two-parameter Lyapunov exponent, bifurcation diagrams, the graph of the largest Lyapunov exponent, phase portraits, time series, as well as the basin of attractions are used to numerically investigate the network. It is found that the model can experience hysteresis justified by the simultaneous existence of three distinct electrical activities using the same set of parameters. Finally, the circuit implementation of the network is addressed in PSPICE to further support the obtained results.

scholarly journals Neurally Adjusted Ventilatory Assist Increases Respiratory Variability and Complexity in Acute Respiratory Failure

2010 ◽  
Vol 112 (3) ◽  
pp. 670-681 ◽  
Author(s):  
Matthieu Schmidt ◽  
Alexandre Demoule ◽  
Christophe Cracco ◽  
Alexandre Gharbi ◽  
Marie-Noëlle Fiamma ◽  
...  
Keyword(s):  
Lyapunov Exponent ◽  
Breathing Pattern ◽  
Ventilatory Support ◽  
Phase Portraits ◽  
Positive Pressure ◽  
Largest Lyapunov Exponent ◽  
Neurally Adjusted Ventilatory Assist ◽  
Dependent Manner ◽  
Ventilatory Assist ◽  
Respiratory Variability

Background Neurally adjusted ventilatory assist (NAVA) is a partial ventilatory support mode where positive pressure is provided in relation to diaphragmatic electrical activity (EAdi). Central inspiratory activity is normally not monotonous, but it demonstrates short-term variability and complexity. The authors reasoned that NAVA should produce a more "natural" or variable breathing pattern than other modes. This study compared respiratory variability and complexity during pressure support ventilation (PSV) and NAVA. Methods Flow and EAdi were recorded during routine PSV (tidal volume approximately 6-8 ml/kg) and four NAVA levels (1-4 cm H2O/microVEAdi) in 12 intubated patients. Breath-by-breath variability of flow and EAdi-related variables was quantified by the coefficient of variation (CV) and autocorrelation analysis. Complexity of flow and EAdi was described using noise titration, largest Lyapunov exponent, Kolmogorov-Sinai entropy, and three-dimensional phase portraits. Results Switching from PSV to NAVA increased the CV and decreased the autocorrelation for most flow-related variables in a dose-dependent manner (P < 0.05, partial eta for the CV of mean inspiratory flow 0.642). The changes were less marked for EAdi. A positive noise limit was consistently found for flow and EAdi. Largest Lyapunov exponent and Kolmogorov-Sinai entropy for flow were greater during NAVA than PSV and increased with NAVA level (P < 0.05, partial eta 0.334 and 0.312, respectively). Largest Lyapunov exponent and Kolmogorov-Sinai entropy for EAdi were not influenced by ventilator mode. Conclusions Compared with PSV, NAVA increases the breathing pattern variability and complexity of flow, whereas the complexity of EAdi is unchanged. Whether this improves clinical outcomes remains to be determined.

EFFECTS OF TREND AND PERIODICITY ON THE CORRELATION DIMENSION AND THE LYAPUNOV EXPONENTS

2008 ◽  
Vol 18 (12) ◽  
pp. 3679-3687 ◽  
Author(s):  
AYDIN A. CECEN ◽  
CAHIT ERKAL
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Correlation Dimension ◽  
Time Series Data ◽  
Logistic Map ◽  
Model Identification ◽  
Series Data ◽  
Largest Lyapunov Exponent ◽  
The Impact

We present a critical remark on the pitfalls of calculating the correlation dimension and the largest Lyapunov exponent from time series data when trend and periodicity exist. We consider a special case where a time series Zi can be expressed as the sum of two subsystems so that Zi = Xi + Yi and at least one of the subsystems is deterministic. We show that if the trend and periodicity are not properly removed, correlation dimension and Lyapunov exponent estimations yield misleading results, which can severely compromise the results of diagnostic tests and model identification. We also establish an analytic relationship between the largest Lyapunov exponents of the subsystems and that of the whole system. In addition, the impact of a periodic parameter perturbation on the Lyapunov exponent for the logistic map and the Lorenz system is discussed.

The Lyapunov Exponent Variance of an Electronic Manufacturing Enterprise’s Daily Qualified Rate Time Series by Improved Small Data Sets Approach

2012 ◽  
Vol 197 ◽  
pp. 271-277
Author(s):  
Zhu Ping Gong
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Chaotic Time Series ◽  
Quality System ◽  
Quality Level ◽  
Largest Lyapunov Exponent ◽  
Small Data ◽  
Data Set ◽  
Electronic Manufacturing ◽  
Small Data Set

Small data set approach is used for the estimation of Largest Lyapunov Exponent (LLE). Primarily, the mean period drawback of Small data set was corrected. On this base, the LLEs of daily qualified rate time series of HZ, an electronic manufacturing enterprise, were estimated and all positive LLEs were taken which indicate that this time series is a chaotic time series and the corresponding produce process is a chaotic process. The variance of the LLEs revealed the struggle between the divergence nature of quality system and quality control effort. LLEs showed sharp increase in getting worse quality level coincide with the company shutdown. HZ’s daily qualified rate, a chaotic time series, shows us the predictable nature of quality system in a short-run.

Study of Rehabilitation of Injured Knee Joint Applying Chaotic Theory in Human Body Motion

2007 ◽  
Vol 342-343 ◽  
pp. 581-584
Author(s):  
Byung Young Moon ◽  
Kwon Son ◽  
Jung Hong Park
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Angular Displacement ◽  
Three Dimensional ◽  
Gait Pattern ◽  
Body Motion ◽  
Largest Lyapunov Exponent ◽  
Chaos Analysis ◽  
Nonlinear Technique ◽  
Injured Knee

Gait analysis is essential to identify accurate cause and knee condition from patients who display abnormal walking. Traditional linear tools can, however, mask the true structure of motor variability, since biomechanical data from a few strides during the gait have limitation to understanding the system. Therefore, it is necessary to propose a more precise dynamic method. The chaos analysis, a nonlinear technique, focuses on understanding how variations in the gait pattern change over time. Healthy eight subjects walked on a treadmill for 100 seconds at 60 Hz. Three dimensional walking kinematic data were obtained using two cameras and KWON3D motion analyzer. The largest Lyapunov exponent from the measured knee angular displacement time series was calculated to quantify local stability. This study quantified the variability present in time series generated from gait parameter via chaos analysis. Gait pattern is found to be chaotic. The proposed Lyapunov exponent can be used in rehabilitation and diagnosis of recoverable patients.

A Very Simple Method to Calculate the (Positive) Largest Lyapunov Exponent Using Interval Extensions

2016 ◽  
Vol 26 (13) ◽  
pp. 1650226 ◽  
Author(s):  
Eduardo M. A. M. Mendes ◽  
Erivelton G. Nepomuceno
Keyword(s):  
Lyapunov Exponent ◽  
Lower Bound ◽  
Equations Of Motion ◽  
Original System ◽  
Glass System ◽  
Largest Lyapunov Exponent ◽  
Simple Method ◽  
Interval Extensions

In this letter, a very simple method to calculate the positive Largest Lyapunov Exponent (LLE) based on the concept of interval extensions and using the original equations of motion is presented. The exponent is estimated from the slope of the line derived from the lower bound error when considering two interval extensions of the original system. It is shown that the algorithm is robust, fast and easy to implement and can be considered as alternative to other algorithms available in the literature. The method has been successfully tested in five well-known systems: Logistic, Hénon, Lorenz and Rössler equations and the Mackey–Glass system.

scholarly journals Diagnostic of cardio-vascular disease with help of largest Lyapunov exponent of RR-sequences

2000 ◽  
Vol 11 (5) ◽  
pp. 807-814 ◽  
Author(s):  
Alexey N Pavlov ◽  
Natalia B Janson ◽  
Vadim S Anishchenko ◽  
Vladimir I Gridnev ◽  
Pavel Ya Dovgalevsky
Keyword(s):  
Lyapunov Exponent ◽  
Vascular Disease ◽  
Largest Lyapunov Exponent ◽  
Cardio Vascular Disease ◽  
Cardio Vascular

scholarly journals Estimating complexity of spike-wave discharges with largest Lyapunov exponent in computational models and experimental data

2020 ◽  
Vol 7 (2) ◽  
pp. 65-75
Author(s):  
T. M. Medvedeva ◽  
◽  
A. K. Lüttjohann ◽  
M. V. Sysoeva ◽  
G. van Luijtelaar ◽  
...  
Keyword(s):  
Experimental Data ◽  
Lyapunov Exponent ◽  
Computational Models ◽  
Largest Lyapunov Exponent ◽  
Spike Wave Discharges ◽  
Spike Wave

scholarly journals The futility of long-term predictions in bipolar disorder: mood fluctuations are the result of deterministic chaotic processes

2021 ◽  
Vol 9 (1) ◽  
Author(s):  
Abigail Ortiz ◽  
Kamil Bradler ◽  
Maxine Mowete ◽  
Stephane MacLean ◽  
Julie Garnham ◽  
...  
Keyword(s):  
Bipolar Disorder ◽  
Fractal Dimension ◽  
Lyapunov Exponent ◽  
Detrended Fluctuation Analysis ◽  
Largest Lyapunov Exponent ◽  
Fluctuation Analysis ◽  
Mood Regulation ◽  
The Largest Lyapunov Exponent ◽  
Depressive Episodes ◽  
Detrended Fluctuation

Abstract Background Understanding the underlying architecture of mood regulation in bipolar disorder (BD) is important, as we are starting to conceptualize BD as a more complex disorder than one of recurring manic or depressive episodes. Nonlinear techniques are employed to understand and model the behavior of complex systems. Our aim was to assess the underlying nonlinear properties that account for mood and energy fluctuations in patients with BD; and to compare whether these processes were different in healthy controls (HC) and unaffected first-degree relatives (FDR). We used three different nonlinear techniques: Lyapunov exponent, detrended fluctuation analysis and fractal dimension to assess the underlying behavior of mood and energy fluctuations in all groups; and subsequently to assess whether these arise from different processes in each of these groups. Results There was a positive, short-term autocorrelation for both mood and energy series in all three groups. In the mood series, the largest Lyapunov exponent was found in HC (1.84), compared to BD (1.63) and FDR (1.71) groups [F (2, 87) = 8.42, p < 0.005]. A post-hoc Tukey test showed that Lyapunov exponent in HC was significantly higher than both the BD (p = 0.003) and FDR groups (p = 0.03). Similarly, in the energy series, the largest Lyapunov exponent was found in HC (1.85), compared to BD (1.76) and FDR (1.67) [F (2, 87) = 11.02; p < 0.005]. There were no significant differences between groups for the detrended fluctuation analysis or fractal dimension. Conclusions The underlying nature of mood variability is in keeping with that of a chaotic system, which means that fluctuations are generated by deterministic nonlinear process(es) in HC, BD, and FDR. The value of this complex modeling lies in analyzing the nature of the processes involved in mood regulation. It also suggests that the window for episode prediction in BD will be inevitably short.

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