Nonlinear Behavior of Sinusoidally Forced Pyloric Pacemaker Neurons

2001 ◽  
Vol 85 (4) ◽  
pp. 1623-1638 ◽  
Author(s):  
Attila Szűcs ◽  
Robert C. Elson ◽  
Michail I. Rabinovich ◽  
Henry D. I. Abarbanel ◽  
Allen I. Selverston
Keyword(s):  
Complex Dynamics ◽  
Cooperative Behavior ◽  
Model Neuron ◽  
Nonlinear Behavior ◽  
Periodic Forcing ◽  
Pacemaker Neurons ◽  
Strongly Coupled ◽  
Electronic Model ◽  
Group 2 ◽  
Low Dimensional

Periodic current forcing was used to investigate the intrinsic dynamics of a small group of electrically coupled neurons in the pyloric central pattern generator (CPG) of the lobster. This group contains three neurons, namely the two pyloric dilator (PD) motoneurons and the anterior burster (AB) interneuron. Intracellular current injection, using sinusoidal waveforms of varying amplitude and frequency, was applied in three configurations of the pacemaker neurons: 1) the complete pacemaker group, 2) the two PDs without the AB, and 3) the AB neuron isolated from the PDs. Depending on the frequency and amplitude of the injected current, the intact pacemaker group exhibited a wide variety of nonlinear behaviors, including synchronization to the forcing, quasiperiodicity, and complex dynamics. In contrast, a single, broad 1:1 entrainment zone characterized the response of the PD neurons when isolated from the main pacemaker neuron AB. The isolated AB responded to periodic forcing in a manner similar to the complete pacemaker group, but with wider zones of synchronization. We have built an analog electronic circuit as an implementation of a modified Hindmarsh-Rose model for simulating the membrane potential activity of pyloric neurons. We subjected this electronic model neuron to the same periodic forcing as used in the biological experiments. This four-dimensional electronic model neuron reproduced the autonomous oscillatory firing patterns of biological pyloric pacemaker neurons, and it expressed the same stationary nonlinear responses to periodic forcing as its biological counterparts. This adds to our confidence in the model. These results strongly support the idea that the intact pyloric pacemaker group acts as a uniform low-dimensional deterministic nonlinear oscillator, and the regular pyloric oscillation is the outcome of cooperative behavior of strongly coupled neurons, having different dynamical and biophysical properties when isolated.

Response Characteristics of a Low-Dimensional Model Neuron

1996 ◽  
Vol 8 (8) ◽  
pp. 1643-1652 ◽  
Author(s):  
Bo Cartling
Keyword(s):  
Time Constant ◽  
Large Scale ◽  
Complex Dynamics ◽  
Model Neuron ◽  
Fast Response ◽  
Dimensional Model ◽  
Constant Input ◽  
Variable Model ◽  
Response Characteristics ◽  
Low Dimensional

It is shown that a low-dimensional model neuron with a response time constant smaller than the membrane time constant closely reproduces the activity and excitability behavior of a detailed conductance-based model of Hodgkin-Huxley type. The fast response of the activity variable also makes it possible to reduce the model to a one-dimensional model, in particular for typical conditions. As an example, the reduction to a single-variable model from a multivariable conductance-based model of a neocortical pyramidal cell with somatic input is demonstrated. The conditions for avoiding a spurious damped oscillatory response to a constant input are derived, and it is shown that a limit-cycle response cannot occur. The capability of the low-dimensional model to approximate higher-dimensional models accurately makes it useful for describing complex dynamics of nets of interconnected neurons. The simplicity of the model facilitates analytic studies, elucidation of neurocomputational mechanisms, and applications to large-scale systems.

A LOW-DIMENSIONAL, TIME-RESOLVED AND ADAPTING MODEL NEURON

1996 ◽  
Vol 07 (03) ◽  
pp. 237-246 ◽  
Author(s):  
BO CARTLING
Keyword(s):  
Firing Rate ◽  
Time Resolution ◽  
Neural Coding ◽  
Large Scale ◽  
Complex Dynamics ◽  
Model Neuron ◽  
Time Resolved ◽  
Practical Applications ◽  
Temporal Aspects ◽  
Low Dimensional

A low-dimensional, time-resolved and adapting model neuron is formulated and evaluated. The model is an extension of the integrate-and-fire type of model with respect to adaptation and of a recent adapting firing-rate model with respect to time-resolution. It is obtained from detailed conductance-based models by a separation of fast and slow ionic processes of action potential generation. The model explicitly includes firing-rate regulation via the slow afterhyperpolarization phase of action potentials, which is controlled by calcium-sensitive potassium channels. It is demonstrated that the model closely reproduces the firing pattern and excitability behaviour of a detailed multicompartment conductance-based model of a neocortical pyramidal cell. The inclusion of adaptation in a model neuron is important for its capability to generate complex dynamics of networks of interconnected neurons. The time-resolution is required for studies of systems in which the temporal aspects of neural coding are important. The simplicity of the model facilitates analytical studies, insight into neurocomputational mechanisms and simulations of large-scale systems. The capability to generate complex network computations may also make the model useful in practical applications of artificial neural networks.

scholarly journals A chiral switchable photovoltaic ferroelectric 1D perovskite

2020 ◽  
Vol 6 (9) ◽  
pp. eaay4213 ◽  
Author(s):  
Yang Hu ◽  
Fred Florio ◽  
Zhizhong Chen ◽  
W. Adam Phelan ◽  
Maxime A. Siegler ◽  
...  
Keyword(s):  
Electric Fields ◽  
Mirror Symmetry ◽  
Degrees Of Freedom ◽  
Electrical Measurements ◽  
Temperature Dependent ◽  
Paraelectric Phase Transition ◽  
Strongly Coupled ◽  
Yield Phenomena ◽  
Hybrid Perovskite ◽  
Low Dimensional

Spin and valley degrees of freedom in materials without inversion symmetry promise previously unknown device functionalities, such as spin-valleytronics. Control of material symmetry with electric fields (ferroelectricity), while breaking additional symmetries, including mirror symmetry, could yield phenomena where chirality, spin, valley, and crystal potential are strongly coupled. Here we report the synthesis of a halide perovskite semiconductor that is simultaneously photoferroelectricity switchable and chiral. Spectroscopic and structural analysis, and first-principles calculations, determine the material to be a previously unknown low-dimensional hybrid perovskite (R)-(−)-1-cyclohexylethylammonium/(S)-(+)-1 cyclohexylethylammonium) PbI3. Optical and electrical measurements characterize its semiconducting, ferroelectric, switchable pyroelectricity and switchable photoferroelectric properties. Temperature dependent structural, dielectric and transport measurements reveal a ferroelectric-paraelectric phase transition. Circular dichroism spectroscopy confirms its chirality. The development of a material with such a combination of these properties will facilitate the exploration of phenomena such as electric field and chiral enantiomer–dependent Rashba-Dresselhaus splitting and circular photogalvanic effects.

Nonlinear Dynamics of an Imperfect Microbeam Under an Axial Load and Electric Excitation

2011 ◽  
Author(s):  
Laura Ruzziconi ◽  
Mohammad I. Younis ◽  
Stefano Lenci
Keyword(s):  
Nonlinear Dynamics ◽  
Microelectromechanical Systems ◽  
Complex Dynamics ◽  
Nonlinear Behavior ◽  
Single Mode ◽  
Phase Portraits ◽  
Nonlinear Phenomena ◽  
Theoretical Point ◽  
Initial Shape ◽  
Electric Excitation

This study is motivated by the growing attention, both from a practical and a theoretical point of view, toward the nonlinear behavior of microelectromechanical systems (MEMS). We analyze the nonlinear dynamics of an imperfect microbeam under an axial force and electric excitation. The imperfection of the microbeam, typically due to microfabrication processes, is simulated assuming the microbeam to be of a shallow arched initial shape. The device has a bistable static behavior. The aim is that of illustrating the nonlinear phenomena, which arise due to the coupling of mechanical and electrical nonlinearities, and discussing their usefulness for the engineering design of the microstructure. We derive a single-mode-reduced-order model by combining the classical Galerkin technique and the Pade´ approximation. Despite its apparent simplicity, this model is able to capture the main features of the complex dynamics of the device. Extensive numerical simulations are performed using frequency response diagrams, attractor-basins phase portraits, and frequency-dynamic voltage behavior charts. We investigate the overall scenario, up to the inevitable escape, obtaining the theoretical boundaries of appearance and disappearance of the main attractors. The main features of the nonlinear dynamics are discussed, stressing their existence and their practical relevance. We focus on the coexistence of robust attractors, which leads to a considerable versatility of behavior. This is a very attractive feature in MEMS applications. The ranges of coexistence are analyzed in detail, remarkably at high values of the dynamic excitation, where the penetration of the escape (dynamic pull-in) inside the double well may prevent the safe jump between the attractors.

Memory and complex dynamics in cardiac Purkinje fibers

1997 ◽  
Vol 272 (4) ◽  
pp. H1826-H1832 ◽  
Author(s):  
R. F. Gilmour ◽  
N. F. Otani ◽  
M. A. Watanabe
Keyword(s):  
Cardiac Tissue ◽  
Complex Dynamics ◽  
Response Duration ◽  
Complex Behavior ◽  
Purkinje Fibers ◽  
Cardiac Purkinje Fibers ◽  
Diastolic Interval ◽  
Restitution Curve ◽  
Low Dimensional ◽  
The Relationship

The contribution of cumulative changes in action potential duration (memory) to complex cellular electrophysiological behavior was investigated in canine cardiac Purkinje fibers. Complex behavior induced during constant pacing was caused by reciprocal interactions between the time to full repolarization (TFR), where TFR = response duration + latency, and the diastolic interval (DI). The relationship between TFR and the preceding DI during complex behavior differed from that obtained using a standard restitution protocol. In particular, higher-order periodicities and chaos were produced in fibers in which the restitution curve lacked the prerequisites for such behavior. To investigate whether shifts in the restitution curve might be expected during rapid pacing, the relationship between TFR of a test response (TFR(n + 1)) and the immediately preceding response (TFR(n)) was determined. For any fixed DI(n), reduction of TFR(n) from 240 to 130 ms was accompanied by a corresponding reduction of TFR(n + 1), whereas as TFR(n) was reduced further to 120 ms, TFR(n + 1) increased. Because of the dependence of TFR(n + 1) on TFR(n) (memory) and on the preceding DI(n) (restitution), the slope of the low-dimensional relationship between TFR(n + 1) and DI(n) at a constant pacing cycle length depended on the slopes of the restitution and memory functions. These results suggest that rapid accumulation and dissipation of memory may contribute importantly to complex electrical behavior in cardiac tissue.

scholarly journals Characterization of Pathogen Airborne Inoculum Density by Information Theoretic Analysis of Spore Trap Time Series Data

Entropy ◽  
2020 ◽  
Vol 22 (12) ◽  
pp. 1343 ◽  
Author(s):  
Robin A. Choudhury ◽  
Neil McRoberts
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Complex Dynamics ◽  
Cost Effective ◽  
Series Data ◽  
Spore Trap ◽  
Abundance Data ◽  
Airborne Inoculum ◽  
Pathogen Dna ◽  
Low Dimensional

In a previous study, air sampling using vortex air samplers combined with species-specific amplification of pathogen DNA was carried out over two years in four or five locations in the Salinas Valley of California. The resulting time series data for the abundance of pathogen DNA trapped per day displayed complex dynamics with features of both deterministic (chaotic) and stochastic uncertainty. Methods of nonlinear time series analysis developed for the reconstruction of low dimensional attractors provided new insights into the complexity of pathogen abundance data. In particular, the analyses suggested that the length of time series data that it is practical or cost-effective to collect may limit the ability to definitively classify the uncertainty in the data. Over the two years of the study, five location/year combinations were classified as having stochastic linear dynamics and four were not. Calculation of entropy values for either the number of pathogen DNA copies or for a binary string indicating whether the pathogen abundance data were increasing revealed (1) some robust differences in the dynamics between seasons that were not obvious in the time series data themselves and (2) that the series were almost all at their theoretical maximum entropy value when considered from the simple perspective of whether instantaneous change along the sequence was positive.

scholarly journals Predictability and Information Theory. Part II: Imperfect Forecasts

2005 ◽  
Vol 62 (9) ◽  
pp. 3368-3381 ◽  
Author(s):  
Timothy DelSole
Keyword(s):  
Information Theory ◽  
Mutual Information ◽  
Dimensional Space ◽  
Nonlinear Behavior ◽  
Potential Predictability ◽  
Low Dimensional ◽  
Lower Dimensional Space ◽  
True System ◽  
Normally Distributed

Abstract This paper presents a framework for quantifying predictability based on the behavior of imperfect forecasts. The critical quantity in this framework is not the forecast distribution, as used in many other predictability studies, but the conditional distribution of the state given the forecasts, called the regression forecast distribution. The average predictability of the regression forecast distribution is given by a quantity called the mutual information. Standard inequalities in information theory show that this quantity is bounded above by the average predictability of the true system and by the average predictability of the forecast system. These bounds clarify the role of potential predictability, of which many incorrect statements can be found in the literature. Mutual information has further attractive properties: it is invariant with respect to nonlinear transformations of the data, cannot be improved by manipulating the forecast, and reduces to familiar measures of correlation skill when the forecast and verification are joint normally distributed. The concept of potential predictable components is shown to define a lower-dimensional space that captures the full predictability of the regression forecast without loss of generality. The predictability of stationary, Gaussian, Markov systems is examined in detail. Some simple numerical examples suggest that imperfect forecasts are not always useful for joint normally distributed systems since greater predictability often can be obtained directly from observations. Rather, the usefulness of imperfect forecasts appears to lie in the fact that they can identify potential predictable components and capture nonstationary and/or nonlinear behavior, which are difficult to capture by low-dimensional, empirical models estimated from short historical records.

scholarly journals Computation in a Single Neuron: Hodgkin and Huxley Revisited

2003 ◽  
Vol 15 (8) ◽  
pp. 1715-1749 ◽  
Author(s):  
Blaise Agüera y Arcas ◽  
Adrienne L. Fairhall ◽  
William Bialek
Keyword(s):  
Mutual Information ◽  
Feature Detection ◽  
Dimensional Space ◽  
Model Neuron ◽  
Realistic Model ◽  
High Time Resolution ◽  
Correlation Technique ◽  
Two Dimensional ◽  
Dimensional Approximation ◽  
Low Dimensional

A spiking neuron “computes” by transforming a complex dynamical input into a train of action potentials, or spikes. The computation performed by the neuron can be formulated as dimensional reduction, or feature detection, followed by a nonlinear decision function over the low-dimensional space. Generalizations of the reverse correlation technique with white noise input provide a numerical strategy for extracting the relevant low-dimensional features from experimental data, and information theory can be used to evaluate the quality of the low-dimensional approximation. We apply these methods to analyze the simplest biophysically realistic model neuron, the Hodgkin-Huxley (HH) model, using this system to illustrate the general methodological issues. We focus on the features in the stimulus that trigger a spike, explicitly eliminating the effects of interactions between spikes. One can approximate this triggering “feature space” as a two-dimensional linear subspace in the high-dimensional space of input histories, capturing in this way a substantial fraction of the mutual information between inputs and spike time. We find that an even better approximation, however, is to describe the relevant subspace as two dimensional but curved; in this way, we can capture 90% of the mutual information even at high time resolution. Our analysis provides a new understanding of the computational properties of the HH model. While it is common to approximate neural behavior as “integrate and fire,” the HH model is not an integrator nor is it well described by a single threshold.

scholarly journals Electrocorticography reveals thalamic control of cortical dynamics following traumatic brain injury

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Sima Mofakham ◽  
Adam Fry ◽  
Joseph Adachi ◽  
Patricia L. Stefancin ◽  
Tim Q. Duong ◽  
...  
Keyword(s):  
Traumatic Brain Injury ◽  
Brain Injury ◽  
Complex Dynamics ◽  
Low Complexity ◽  
Field Potentials ◽  
Cortical Dynamics ◽  
Thalamic Input ◽  
Electrophysiological Recordings ◽  
Efferent Projections ◽  
Low Dimensional

AbstractThe return of consciousness after traumatic brain injury (TBI) is associated with restoring complex cortical dynamics; however, it is unclear what interactions govern these complex dynamics. Here, we set out to uncover the mechanism underlying the return of consciousness by measuring local field potentials (LFP) using invasive electrophysiological recordings in patients recovering from TBI. We found that injury to the thalamus, and its efferent projections, on MRI were associated with repetitive and low complexity LFP signals from a highly structured phase space, resembling a low-dimensional ring attractor. But why do thalamic injuries in TBI patients result in a cortical attractor? We built a simplified thalamocortical model, which connotes that thalamic input facilitates the formation of cortical ensembles required for the return of cognitive function and the content of consciousness. These observations collectively support the view that thalamic input to the cortex enables rich cortical dynamics associated with consciousness.

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