The Nonlinear Dynamics of the Crayfish Mechanoreceptor System

2003 ◽  
Vol 13 (08) ◽  
pp. 2013-2034 ◽  
Author(s):  
Sonya Bahar ◽  
Frank Moss
Keyword(s):  
Nonlinear Dynamics ◽  
Second Harmonic ◽  
Random Processes ◽  
Neural System ◽  
Nonlinear Dynamical ◽  
Caudal Photoreceptor ◽  
Dynamical Properties ◽  
Low Dimensional ◽  
Photoreceptor Neurons ◽  
Sensory Root

We review here the nonlinear dynamical properties of the crayfish mechanoreceptor system from the hydrodynamically sensitive hairs on the tailfan through the caudal photoreceptor neurons embedded in the 6th ganglion. Emphasis is on the extraction of low dimensional behavior from the random processes (noise) that dominate this neural system. We begin with stochastic resonance in the sensory root afferents and continue with a discussion of the photoreceptor oscillator and its instabilities. Stochastic synchronization, rectification and the generation of second harmonic responses in the photoreceptors are finally discussed.

Cardiac Alternans Suppression Under T ± 𝜖 Feedback Control: Nonlinear Dynamics Analysis

2019 ◽  
Vol 29 (13) ◽  
pp. 1930036
Author(s):  
Shiuan-Ni Liang ◽  
Duy-Manh Le ◽  
Pik-Yin Lai
Keyword(s):  
Nonlinear Dynamics ◽  
Feedback Control ◽  
Chaotic Dynamics ◽  
Critical Threshold ◽  
Dynamics Analysis ◽  
Ionic Model ◽  
Nonlinear Dynamical ◽  
Cardiac Alternans ◽  
Dynamical Properties ◽  
Cardiac Restitution

The nonlinear dynamical properties of the recently proposed [Formula: see text] feedback control for suppressing cardiac alternans is investigated in detail for the discrete cardiac restitution map model and the continuous Luo–Rudy I ionic model. It is shown that cardiac alternans, induced by fast pacing, can be dramatically reduced by small changes of fixed magnitude ([Formula: see text]) under feedback control when [Formula: see text] exceeds a critical threshold. Remarkably, the suppression is achieved by utilizing the induced chaotic dynamics. Detailed information on the nature and mechanism of the control, and properties of the attractors are analyzed and discussed in the light of nonlinear dynamics.

scholarly journals Data-driven spectral analysis for coordinative structures in periodic systems with unknown and redundant dynamics

2019 ◽  
Author(s):  
Keisuke Fujii ◽  
Naoya Takeishi ◽  
Benio Kibushi ◽  
Motoki Kouzaki ◽  
Yoshinobu Kawahara
Keyword(s):  
Spectral Analysis ◽  
Nonlinear Dynamical Systems ◽  
Data Driven ◽  
Periodic Systems ◽  
Limit Cycle Oscillation ◽  
Control Mechanisms ◽  
Nonlinear Dynamical ◽  
Reduction Methods ◽  
Dynamical Properties ◽  
Low Dimensional

AbstractLiving organisms dynamically and flexibly operate a great number of components. As one of such redundant control mechanisms, low-dimensional coordinative structures among multiple components have been investigated. However, structures extracted from the conventional statistical dimensionality reduction methods do not reflect dynamical properties in principle. Here we regard coordinative structures in biological periodic systems with unknown and redundant dynamics as a nonlinear limit-cycle oscillation, and apply a data-driven operator-theoretic spectral analysis, which obtains dynamical properties of coordinative structures such as frequency and phase from the estimated eigenvalues and eigenfunctions of a composition operator. First, from intersegmental angles during human walking, we extracted the speed-independent harmonics of gait frequency. Second, we discovered the speed-dependent time-evolving behaviors of the phase on the conventional low-dimensional structures by estimating the eigenfunctions. Our approach contributes to the understanding of biological periodic phenomena with unknown and redundant dynamics from the perspective of nonlinear dynamical systems.

DETECTING LOW DIMENSIONAL DYNAMICS IN BIOLOGICAL EXPERIMENTS

1996 ◽  
Vol 07 (04) ◽  
pp. 429-435 ◽  
Author(s):  
XING PEI ◽  
FRANK MOSS
Keyword(s):  
Action Potentials ◽  
Sensory System ◽  
Random Processes ◽  
High Dimensional ◽  
Time Intervals ◽  
Dynamical Behaviors ◽  
Caudal Photoreceptor ◽  
The Times ◽  
Low Dimensional ◽  
Low Dimensional Dynamics

We discuss the well-known problems associated with efforts to detect and characterize chaos and other low dimensional dynamics in biological settings. We propose a new method which shows promise for addressing these problems, and we demonstrate its effectiveness in an experiment with the crayfish sensory system. Recordings of action potentials in this system are the data. We begin with a pair of assumptions: that the times of firings of neural action potentials are largely determined by high dimensional random processes or “noise”; and that most biological files are non stationary, so that only relatively short files can be obtained under approximately constant conditions. The method is thus statistical in nature. It is designed to recognize individual “events” in the form of particular sequences of time intervals between action potentials which are the signatures of certain well defined dynamical behaviors. We show that chaos can be distinguished from limit cycles, even when the dynamics is heavily contaminated with noise. Extracellular recordings from the crayfish caudal photoreceptor, obtained while hydrodynamically stimulating the array of hair receptors on the tailfan, are used to illustrate the method.

Nonlinear Dynamics of Trajectories Generated by Fully-Stretching Piecewise Linear Maps

2014 ◽  
Vol 24 (05) ◽  
pp. 1450071 ◽  
Author(s):  
T. Papamarkou ◽  
A. J. Lawrance
Keyword(s):  
Nonlinear Dynamics ◽  
Lyapunov Exponent ◽  
Piecewise Linear ◽  
Nonlinear Dynamical ◽  
Chaotic Orbits ◽  
Linear Maps ◽  
Piecewise Linear Maps ◽  
The Mean ◽  
Dynamical Properties ◽  
Analytical Expressions

This paper focuses on the nonlinear dynamical properties of chaotic orbits iteratively generated by maps composed of linear branches which expand across the whole map range. The nonlinear dynamics of such orbits involve both their statistical and chaotic properties. More specifically, analytical expressions are provided for the mean-adjusted quadratic autocorrelation function (ACF) and for the Lyapunov exponent of trajectories produced by the considered collection of piecewise linear maps.

scholarly journals Non-intrusive nonlinear model reduction via machine learning approximations to low-dimensional operators

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Zhe Bai ◽  
Liqian Peng
Keyword(s):  
Machine Learning ◽  
Nonlinear Dynamical Systems ◽  
Reduced Order Models ◽  
Simulation Code ◽  
Nonlinear Dynamical ◽  
Reduced Order ◽  
Nonlinear Model Reduction ◽  
Regression Techniques ◽  
Low Dimensional ◽  
Modern Machine

AbstractAlthough projection-based reduced-order models (ROMs) for parameterized nonlinear dynamical systems have demonstrated exciting results across a range of applications, their broad adoption has been limited by their intrusivity: implementing such a reduced-order model typically requires significant modifications to the underlying simulation code. To address this, we propose a method that enables traditionally intrusive reduced-order models to be accurately approximated in a non-intrusive manner. Specifically, the approach approximates the low-dimensional operators associated with projection-based reduced-order models (ROMs) using modern machine-learning regression techniques. The only requirement of the simulation code is the ability to export the velocity given the state and parameters; this functionality is used to train the approximated low-dimensional operators. In addition to enabling nonintrusivity, we demonstrate that the approach also leads to very low computational complexity, achieving up to $$10^3{\times }$$ 10 3 × in run time. We demonstrate the effectiveness of the proposed technique on two types of PDEs. The domain of applications include both parabolic and hyperbolic PDEs, regardless of the dimension of full-order models (FOMs).

Generating Fully Bounded Chaotic Attractors

2013 ◽  
pp. 148-153
Author(s):  
Zeraoulia Elhadj
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Dynamical Behavior ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Nonlinear Dynamical ◽  
Dynamical Properties ◽  
The Given

Generating chaotic attractors from nonlinear dynamical systems is quite important because of their applicability in sciences and engineering. This paper considers a class of 2-D mappings displaying fully bounded chaotic attractors for all bifurcation parameters. It describes in detail the dynamical behavior of this map, along with some other dynamical phenomena. Also presented are some phase portraits and some dynamical properties of the given simple family of 2-D discrete mappings.

Bistability and its regulation by serotonin in the endogenously bursting neuron R15 in Aplysia

1996 ◽  
Vol 75 (2) ◽  
pp. 957-962 ◽  
Author(s):  
H. A. Lechner ◽  
D. A. Baxter ◽  
J. W. Clark ◽  
J. H. Byrne
Keyword(s):  
Electrical Activity ◽  
Dynamic Properties ◽  
Computational Studies ◽  
Nonlinear Dynamical ◽  
Bursting Neuron ◽  
Current Pulses ◽  
Low Concentrations ◽  
Dynamical Properties ◽  
Mode Transitions ◽  
Model Support

1. Previous computational studies of models of neuron R15 in Aplysia have indicated that several distinct modes of electrical activity may coexist at a given set of parameters, that this multistability can be modulated by transmitters such as serotonin (5-HT) and that brief perturbations of the membrane potential can induce persistent changes in the mode of electrical activity. To test these predictions, the responses of R15 neurons to injections of brief (1.5 s) current pulses were recorded intracellularly in the absence and presence of 5-HT. 2. In the absence of 5-HT, brief perturbations induced abrupt transitions in the electrical activity from bursting to beating. Such transitions were observed in approximately 20% of the cases. The duration of beating activity varied from several seconds to tens of minutes. In the presence of low concentrations (1 microM) of 5-HT, both the probability of mode transitions and the duration of induced beating activity increased significantly. 3. These results indicate that at least two stable modes of electrical activity can coexist in R15 neurons and that this bistability can be regulated by 5-HT. In general, these conclusions agree with the results from analyses of mathematical models of R15. Although the function of these dynamic properties in R15 is speculative, our results, interpreted on the background of the model, support the notion that nonlinear dynamical properties of individual neurons can endow them with richer forms of information processing than has generally been appreciated.

scholarly journals The evolution of nonlinear dynamics in political science and public administration: Methods, modeling and momentum

2000 ◽  
Vol 5 (4) ◽  
pp. 265-279 ◽  
Author(s):  
L. Douglas Kiel
Keyword(s):  
Nonlinear Dynamics ◽  
Political Science ◽  
Public Administration ◽  
20Th Century ◽  
Continuous Time ◽  
The Political ◽  
Nonlinear Dynamical ◽  
Current State ◽  
Administration Methods

This paper examines the evolution of the application of nonlinear dynamics and related methods to the study of political science and public administration throughout the 20th century. Some analysts understood the importance of nonlinearity to political and administrative studies in the early part of the century. More recently, a growing number of scholars understand that the political and administrative worlds are ripe with nonlinearity and thus amenable to nonlinear dynamical techniques and models. The current state of the application of both discrete and continuous time models in political science and public administration are presented. There is growing momentum in political and public administration studies that may serve to enhance the realism and applicability of these sciences to a nonlinear world.

scholarly journals Deterministic Chaos in the Microstructure of Radio Pulses of PSR 0809+74

1992 ◽  
Vol 128 ◽  
pp. 329-331
Author(s):  
V. I. Zhuravlev ◽  
M. V. Popov
Keyword(s):  
Radio Emission ◽  
Random Sequence ◽  
Nonlinear Dynamical System ◽  
Deterministic Chaos ◽  
Relativistic Plasma ◽  
Emission Region ◽  
Polar Cap ◽  
Nonlinear Dynamical ◽  
Developed Turbulence ◽  
Low Dimensional

Abstract480 single pulses from PSR 0809+74, recorded at 102.5 MHz with a time resolution of 10μs, have been analyzed by the time delay technique in order to look for the parameters of deterministic chaos in the microstructure of radio pulses. The correlation dimension n was shown to be less than 5 in more than 20% of the analyzed pulses. This means that on such occasions the microstructure of pulsar radio emission with the time scales 10 to 100μs may be determined by the behavior of a nonlinear dynamical system with comparatively small numbers of independent parameters. For example, the observed low dimensional chaos may result from a turbulence process associated with the outflow of plasma—as in versions of the polar cap model where microstructure can be interpreted as reflecting the spatial structure of relativistic plasma outflow in the radio emission region.However, the correlation-time distribution demonstrates the tendency for microstructure to consist of a random sequence of unresolved micropulses in the majority of cases, which means in the framework of polar cap models the presence of well developed turbulence in the relativistic plasma outflow.

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