scholarly journals Bifurcation Scenarios of Neural Firing Patterns across Two Separated Chaotic Regions as Indicated by Theoretical and Biological Experimental Models

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Huaguang Gu ◽  
Baobao Pan ◽  
Jian Xu
Keyword(s):  
Period Doubling ◽  
Prediction Method ◽  
Experimental Models ◽  
Nonlinear Prediction ◽  
Neural Firing ◽  
Firing Patterns ◽  
Chaotic Bursting ◽  
Chaotic Region ◽  
Period 2 ◽  
Experimental Findings

Nonlinear dynamics can be used to identify relationships between different firing patterns, which play important roles in the information processing. The present study provides novel biological experimental findings regarding complex bifurcation scenarios from period-1 bursting to period-1 spiking with chaotic firing patterns. These bifurcations were found to be similar to those simulated using the Hindmarsh-Rose model across two separated chaotic regions. One chaotic region lay between period-1 and period-2 burstings. This region has not attracted much attention. The other region is a well-known comb-shaped chaotic region, and it appears after period-2 bursting. After period-2 bursting, the chaotic firings lay in a period-adding bifurcation scenario or in a period-doubling bifurcation cascade. The deterministic dynamics of the chaotic firing patterns were identified using a nonlinear prediction method. These results provided details regarding the processes and dynamics of bifurcation containing the chaotic bursting between period-1 and period-2 burstings and other chaotic firing patterns within the comb-shaped chaotic region. They also provided details regarding the relationships between different firing patterns in parameter space.

DIFFERENT BIFURCATION SCENARIOS OF NEURAL FIRING PATTERNS OBSERVED IN THE BIOLOGICAL EXPERIMENT ON IDENTICAL PACEMAKERS

2013 ◽  
Vol 23 (12) ◽  
pp. 1350195 ◽  
Author(s):  
HUAGUANG GU
Keyword(s):  
Parameter Space ◽  
Period Doubling ◽  
Two Dimensional ◽  
Neural Firing ◽  
Biological Experiment ◽  
Dimensional Parameter ◽  
Simple Process ◽  
Firing Patterns ◽  
Complex Process ◽  
Different Levels

Two different bifurcation scenarios of spontaneous neural firing patterns with decreasing extracellular calcium concentrations were observed in the biological experiment on identical pacemakers when potassium concentrations were fixed at two different levels. Six typical experimental scenarios manifesting dynamics closely matching those previously simulated using the Hindmarsh–Rose model and Chay model are provided as representative examples. Bifurcation scenarios from period-1 bursting to period-1 spiking via a complex process and via a simple process, period-doubling bifurcation to chaos, period-adding bifurcation with chaos, and period-adding bifurcation with stochastic burstings were identified. The results not only reveal that an experimental neural pacemaker is capable of generating different bifurcation scenarios but also provide a basic framework for bifurcations in neural firing patterns in a two-dimensional parameter space.

THE BIFURCATION STRUCTURE OF FIRING PATTERN TRANSITIONS IN THE CHAY NEURONAL PACEMAKER MODEL

2008 ◽  
Vol 16 (01) ◽  
pp. 33-49 ◽  
Author(s):  
ZHUOQIN YANG ◽  
QISHAO LU
Keyword(s):  
Bifurcation Analysis ◽  
Calcium Concentration ◽  
Period Doubling ◽  
Nerve Fibers ◽  
Neuronal Firing ◽  
Dynamical Parameter ◽  
True Nature ◽  
Firing Patterns ◽  
Chaotic Bursting ◽  
Period Doubling Bifurcations

Different transitions of neuronal firing patterns are explored by the combination of experimental results, numerical simulation and bifurcation analysis. Three types of firing sequences with respect to extracellular calcium concentration ([ Ca 2+] o ) were observed in experiments on neural pacemakers. In accordance with them, the corresponding transitions of neuronal firing patterns are surveyed by standard bifurcation analysis of the Chay model, where λn corresponds to different nerve fibers and VC is the dynamical parameter. The results are listed in this paper. Firstly, it is obtained that the transitions of periodic firing patterns from period-1 bursting to period-1 spiking without any bifurcation, from period-1 to -2 to -1 through a pair of period-doubling bifurcations and from period-1 to -2 to -1 through two pairs of period-doubling bifurcations. Secondly, one supercritical and two subcritical period-doubling bursting sequences with different appearances lead to chaos, respectively. Then the former transits directly to an inverse supercritical period-doubling spiking sequence via chaos, and the latter transit to it through the period-adding bursting sequences from period-1 to -3 and from -1 to -5 with chaotic bursting, respectively. Thirdly, we reveal the true nature of period-adding bursting sequence without chaotic bursting. Every periodic bursting is closely related to two period-doubling bifurcations of the corresponding periodic spiking, except for period-1 bursting appearing via Hopf bifurcation and disappearing via period-doubling bifurcation. As a consequence, the period-adding bursting sequence without chaotic bursting has a compound structure of elementary bifurcations with transitions from spiking to bursting. Thus period-adding bifurcation without chaos cannot be regarded as a new elementary bifurcation.

Difference Between Intermittent Chaotic Bursting and Spiking of Neural Firing Patterns

2014 ◽  
Vol 24 (06) ◽  
pp. 1450082 ◽  
Author(s):  
Huaguang Gu ◽  
Weiwei Xiao
Keyword(s):  
Deep Understanding ◽  
Slow Variable ◽  
Type I ◽  
Neural Firing ◽  
Firing Patterns ◽  
Return Map ◽  
Smooth Structures ◽  
Chaotic Bursting ◽  
Type V ◽  
Intermittent Chaos

The chaotic spiking and intermittent chaotic bursting were observed from biological experiment on a neural pacemaker. The intermittent chaotic bursting manifested alternation between a phase of nearly period-3 bursting and another phase of irregular bursting, and exhibited a nonsmooth-like structure in the first return map of interspike interval (ISI) series. The chaotic spiking manifested a smooth structure. The intermittent chaotic bursting and spiking simulated in the Chay model were identified by the dissection of the fast-slow variables. The intermittent chaotic bursting manifested nonsmooth-like structures in the first return map of both ISI and slow variable, while spiking exhibited smooth structures. The intermittent chaotic bursting and spiking manifested different scale laws of the averaged length of periodic phase with respect to the changes of parameter value. The scale law of bursting was similar to those of both type V intermittent chaos generated in a nonsmooth map and type I in a smooth system, while that of spiking resembled type I more than type V. The results revealed the dynamics of intermittent chaotic firing patterns, the differences between the intermittent chaotic bursting and spiking patterns and the relationships to the smooth and nonsmooth-like characteristics, provided a deep understanding of intermittent chaotic firing patterns, and indicated different mechanisms of the adjustment of variables from slow to fast between bursting and spiking patterns.

scholarly journals Zero Average Surface Controlled Boost-Flyback Converter

Energies ◽  
2020 ◽  
Vol 14 (1) ◽  
pp. 57
Author(s):  
Juan-Guillermo Muñoz ◽  
Fabiola Angulo ◽  
David Angulo-Garcia
Keyword(s):  
Duty Cycle ◽  
Period Doubling ◽  
Power Converter ◽  
Control Technique ◽  
Average Surface ◽  
Flyback Converter ◽  
Stable Period ◽  
Period 2 ◽  
Wide Range ◽  
The Right

The boost-flyback converter is a DC-DC step-up power converter with a wide range of technological applications. In this paper, we analyze the boost-flyback dynamics when controlled via a modified Zero-Average-Dynamics control technique, hereby named Zero-Average-Surface (ZAS). While using the ZAS strategy, it is possible to calculate the duty cycle at each PWM cycle that guarantees a desired stable period-1 solution, by forcing the system to evolve in such way that a function that is constructed with strategical combination of the states over the PWM period has a zero average. We show, by means of bifurcation diagrams, that the period-1 orbit coexists with a stable period-2 orbit with a saturated duty cycle. While using linear stability analysis, we demonstrate that the period-1 orbit is stable over a wide range of parameters and it loses stability at high gains and low loads via a period doubling bifurcation. Finally, we show that, under the right choice of parameters, the period-1 orbit controller with ZAS strategy satisfactorily rejects a wide range of disturbances.

Color Reproduction Accuracy Promotion of 3D-Printed Surfaces Based on Microscopic Image Analysis

2019 ◽  
Vol 34 (01) ◽  
pp. 2054004 ◽  
Author(s):  
Xiaochun Wang ◽  
Chen Chen ◽  
Jiangping Yuan ◽  
Guangxue Chen
Keyword(s):  
Surface Roughness ◽  
Image Analysis ◽  
Three Dimensional ◽  
Prediction Method ◽  
Chromatic Aberration ◽  
Optimization Methods ◽  
Experimental Models ◽  
Microscopic Image ◽  
Color Reproduction ◽  
Microscopic Image Analysis

Full-color three-dimensional (3D) printing technology is a powerful process to manufacture intelligent customized colorful objects with improved surface qualities; however, poor surface color optimization methods are the main impeding factors for its commercialization. As such, the paper explored the correlation between microstructure and color reproduction, then an assessment and prediction method of color optimization based on microscopic image analysis was proposed. The experimental models were divided into 24-color plates and 4-color cubes printed by ProJet 860 3D printer, then impregnated according to preset parameters, at last measured by a spectrophotometer and observed using both a digital microscope and a scanning electron microscope. The results revealed that the samples manifested higher saturation and smaller chromatic aberration ([Formula: see text]) after postprocessing. Moreover, the brightness of the same color surface increased with the increasing soaked surface roughness. Further, reduction in surface roughness, impregnation into surface pores, and enhancement of coating transparency effectively improved the accuracy of color reproduction, which could be verified by the measured values. Finally, the chromatic aberration caused by positioning errors on different faces of the samples was optimized, and the value of [Formula: see text] for a black cube was reduced from 8.12 to 0.82, which is undetectable to human eyes.

IDENTIFYING DISTINCT STOCHASTIC DYNAMICS FROM CHAOS: A STUDY ON MULTIMODAL NEURAL FIRING PATTERNS

2009 ◽  
Vol 19 (02) ◽  
pp. 453-485 ◽  
Author(s):  
MINGHAO YANG ◽  
ZHIQIANG LIU ◽  
LI LI ◽  
YULIN XU ◽  
HONGJV LIU ◽  
...  
Keyword(s):  
Time Series ◽  
Limit Cycle ◽  
Stochastic Dynamics ◽  
Nonlinear Time Series ◽  
Special Importance ◽  
Neuronal System ◽  
Neural Firing ◽  
Firing Patterns ◽  
Theoretical Simulation ◽  
Definition Of

Some chaotic and a series of stochastic neural firings are multimodal. Stochastic multimodal firing patterns are of special importance because they indicate a possible utility of noise. A number of previous studies confused the dynamics of chaotic and stochastic multimodal firing patterns. The confusion resulted partly from inappropriate interpretations of estimations of nonlinear time series measures. With deliberately chosen examples the present paper introduces strategies and methods of identification of stochastic firing patterns from chaotic ones. Aided by theoretical simulation we show that the stochastic multimodal firing patterns result from the effects of noise on neuronal systems near to a bifurcation between two simpler attractors, such as a point attractor and a limit cycle attractor or two limit cycle attractors. In contrast, the multimodal chaotic firing trains are generated by the dynamics of a specific strange attractor. Three systems were carefully chosen to elucidate these two mechanisms. An experimental neural pacemaker model and the Chay mathematical model were used to show the stochastic dynamics, while the deterministic Wang model was used to show the deterministic dynamics. The usage and interpretation of nonlinear time series measures were systematically tested by applying them to firing trains generated by the three systems. We successfully identified the distinct differences between stochastic and chaotic multimodal firing patterns and showed the dynamics underlying two categories of stochastic firing patterns. The first category results from the effects of noise on the neuronal system near a Hopf bifurcation. The second category results from the effects of noise on the period-adding bifurcation between two limit cycles. Although direct application of nonlinear measures to interspike interval series of these firing trains misleadingly implies chaotic properties, definition of eigen events based on more appropriate judgments of the underlying dynamics leads to accurate identifications of the stochastic properties.

Nonstationary Response of a Two-Degrees-of-Freedom Nonlinear Ship Model Under Modulated Excitation

1995 ◽  
Author(s):  
Ruigui Pan ◽  
Huw G. Davies
Keyword(s):  
Degrees Of Freedom ◽  
Stability Boundary ◽  
Period Doubling ◽  
Approximate Solutions ◽  
Loss Of Stability ◽  
Two Degrees Of Freedom ◽  
Ship Model ◽  
Nonstationary Response ◽  
Period 2 ◽  
The Stability

Abstract Nonstationary response of a two-degrees-of-freedom system with quadratic coupling under a time varying modulated amplitude sinusoidal excitation is studied. The nonlinearly coupled pitch and roll ship model is based on Nayfeh, Mook and Marshall’s work for the case of stationary excitation. The ship model has a 2:1 internal resonance and is excited near the resonance of the pitch mode. The modulated excitation (F0 + F1 cos ωt) cosQt is used to model a narrow band sea-wave excitation. The response demonstrates a variety of bifurcations, loss of stability, and chaos phenomena that are not present in the stationary case. We consider here the periodically modulated response. Chaotic response of the system is discussed in a separate paper. Several approximate solutions, under both small and large modulating amplitudes F1, are obtained and compared with the exact one. The stability of an exact solution with one mode having zero amplitude is studied. Loss of stability in this case involves either a rapid transition from one of two stable (in the stationary sense) branches to another, or a period doubling bifurcation. From Floquet theory, various stability boundary diagrams are obtained in F1 and F0 parameter space which can be used to predict the various transition phenomena and the period-2 bifurcations. The study shows that both the modulation parameters F1 and ω (the modulating frequency) have great effect on the stability boundaries. Because of the modulation, the stable area is greatly expanded, and the stationary bifurcation point can be exceeded without loss of stability. Decreasing ω can make the stability boundary very complicated. For very small ω the response can make periodic transitions between the two (pseudo) stable solutions.

Degrees of Freedom

2006 ◽  
Author(s):  
Huug van den Dool
Keyword(s):  
Phase Space ◽  
Degrees Of Freedom ◽  
Prediction Method ◽  
Data Sets ◽  
Nonlinear Prediction ◽  
Orthogonal Direction ◽  
Empirical Prediction ◽  
Long Run ◽  
Dimensional Phase Space ◽  
Natural Analogues

How many degrees of freedom are evident in a physical process represented by f(s, t)? In some form questions about “degrees of freedom” (d.o.f.) are common in mathematics, physics, statistics, and geophysics. This would mean, for instance, in how many independent directions a weight suspended from the ceiling could move. Dofs are important for three reasons that will become apparent in the remaining chapters. First, dofs are critically important in understanding why natural analogues can (or cannot) be applied as a forecast method in a particular problem (Chapter 7). Secondly, understanding dofs leads to ideas about truncating data sets efficiently, which is very important for just about any empirical prediction method (Chapters 7 and 8). Lastly, the number of dofs retained is one aspect that has a bearing on how nonlinear prediction methods can be (Chapter 10). In view of Chapter 5 one might think that the total number of orthogonal directions required to reproduce a data set is the dof. However, this is impractical as the dimension would increase (to infinity) with ever denser and slightly imperfect observations. Rather we need a measure that takes into account the amount of variance represented by each orthogonal direction, because some directions are more important than others. This allows truncation in EOF space without lowering the “effective” dof very much. We here think schematically of the total atmospheric or oceanic variance about the mean state as being made up by N equal additive variance processes. N can be thought of as the dimension of a phase space in which the atmospheric state at one moment in time is a point. This point moves around over time in the N-dimensional phase space. The climatology is the origin of the phase space. The trajectory of a sequence of atmospheric states is thus a complicated Lissajous figure in N dimensions, where, importantly, the range of the excursions in each of the N dimensions is the same in the long run. The phase space is a hypersphere with an equal probability radius in all N directions.

Wavelet decomposition and nonlinear prediction of nonstationary vibration signals

2020 ◽  
Vol 51 (3) ◽  
pp. 52-59 ◽  
Author(s):  
Xiao-bin Fan ◽  
Bin Zhao ◽  
Bing-xu Fan
Keyword(s):  
Wavelet Decomposition ◽  
Wavelet Packet ◽  
Prediction Method ◽  
Vibration Signal ◽  
Signal Denoising ◽  
Maximum Lyapunov Exponent ◽  
Nonlinear Prediction ◽  
Local Method ◽  
Time Frequency ◽  
Nonstationary Vibration

In order to overcome the shortcomings (such as the time–frequency localization and the nonstationary signal analysis ability) of the Fourier transform, time–frequency analysis has been carried out by wavelet packet decomposition and reconstruction according to the actual nonstationary vibration signal from a large equipment located in a large Steel Corporation in this article. The effect of wavelet decomposition on signal denoising and the selection of high-frequency weight coefficients for each layer on signal denoising were analyzed. The nonlinear prediction of the chaotic time series was made by global method, local method, weighted first-order local method, and maximum Lyapunov exponent prediction method correspondingly. It was found the multi-step prediction method is better than other prediction methods.

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