scholarly journals Dynamics Analysis of Neuron Bursting under the Modulation of Periodic Stimulation

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Ying Ji ◽  
Wenbo Tang ◽  
Tingting Hua ◽  
Zhiduo Xin ◽  
Zhiya Chen ◽  
...  
Keyword(s):  
Vector Field ◽  
Bifurcation Analysis ◽  
Cortical Neurons ◽  
Neuron Model ◽  
Dynamics Analysis ◽  
Periodic Excitation ◽  
External Excitation ◽  
Periodic Stimulation ◽  
Nonsmooth Bifurcation

A nonsmooth neuron model with periodic excitation which can reproduce spiking and bursting behavior of cortical neurons is investigated in this paper. Based on nonsmooth bifurcation analysis, the mechanism of the bursting behavior induced by slow-changing periodical stimulation as well as the associated evolution with the variation of the stimulation is explored. The modulating character of the external excitation and the effect of the bifurcation occurring at the switching boundary of the vector field are presented.

scholarly journals Нелинейная динамика паттернов импульсной активности ноцицептивных нейронов при коррекции повреждающего болевого воздействия

2019 ◽  
Vol 89 (3) ◽  
pp. 465
Author(s):  
О.Е. Дик
Keyword(s):  
Bifurcation Analysis ◽  
Active Ingredient ◽  
Activity Pattern ◽  
Neuron Model ◽  
Nociceptive Neuron ◽  
Firing Activity ◽  
Comenic Acid ◽  
Pain Stimulation ◽  
Activation Gating ◽  
Nonopioid Analgesic

AbstractA bifurcation analysis of a nociceptive neuron model was performed to study how the firing activity pattern changes when an antinociceptive response to damaging pain stimulation arises in rat dorsal ganglia. Ectopic train activity was found to arise in the model. Suppression of train activity was demonstrated to proceed solely through modification of the activation gating structure of the Na _ V 1.8 slow sodium channel in response to comenic acid, which exerts an analgesic effect and is an active ingredient of the new nonopioid analgesic Anoceptin.

Order Reduction of Nonlinear Systems Subjected to an External Periodic Excitation

2005 ◽  
Author(s):  
Sangram Redkar ◽  
S. C. Sinha
Keyword(s):  
Nonlinear Systems ◽  
State Space ◽  
Invariant Manifold ◽  
Large Scale ◽  
Order Reduction ◽  
Reduced Order Models ◽  
Periodic Excitation ◽  
External Excitation ◽  
Reduced Order ◽  
Linear Approach

In this work, the basic problem of order reduction nonlinear systems subjected to an external periodic excitation is considered. This problem deserves attention because the modes that interact (linearly or nonlinearly) with the external excitation dominate the response. A linear approach like the Guyan reduction does not always guarantee accurate results, particularly when nonlinear interactions are strong. In order to overcome limitations of the linear approach, a nonlinear order reduction methodology through a generalization of the invariant manifold technique is proposed. Traditionally, the invariant manifold techniques for unforced problems are extended to the forced problems by ‘augmenting’ the state space, i.e., forcing is treated as an additional degree of freedom and an invariant manifold is constructed. However, in the approach suggested here a nonlinear time-dependent relationship between the dominant and the non-dominant states is assumed and the dimension of the state space remains the same. This methodology not only yields accurate reduced order models but also explains the consequences of various ‘primary’ and ‘secondary resonances’ present in the system. Following this approach, various ‘reducibility conditions’ are obtained that show interactions among the eigenvalues, the nonlinearities and the external excitation. One can also recover all ‘resonance conditions’ commonly obtained via perturbation or averaging techniques. These methodologies are applied to some typical problems and results for large-scale and reduced order models are compared. It is anticipated that these techniques will provide a useful tool in the analysis and control of large-scale externally excited nonlinear systems.

Bifurcation analysis and circuit implementation for a tabu learning neuron model

2020 ◽  
Vol 121 ◽  
pp. 153235 ◽  
Author(s):  
Bocheng Bao ◽  
Liping Hou ◽  
Yongxin Zhu ◽  
Huagan Wu ◽  
Mo Chen
Keyword(s):  
Bifurcation Analysis ◽  
Neuron Model ◽  
Circuit Implementation

Analytical Predication of Complex Motion of a Ball in a Periodically Shaken Horizontal Impact Pair

2011 ◽  
Vol 7 (2) ◽  
Author(s):  
Yu Guo ◽  
Albert C. J. Luo
Keyword(s):  
Dynamical System ◽  
Bifurcation Analysis ◽  
Periodic Motion ◽  
Analytical Prediction ◽  
Periodic Excitation ◽  
Complex Motion ◽  
Chaotic Motions ◽  
Discontinuous Dynamical System ◽  
Mapping Structures ◽  
Stability And Bifurcation Analysis

In this paper, complex motions of a ball in the horizontal impact pair with a periodic excitation are studied analytically using the theory of discontinuous dynamical system. Analytical conditions for motion switching caused by impacts are developed, and generic mapping structures are introduced to describe different periodic and chaotic motions. Analytical prediction of complex periodic motion of the ball in the periodically shaken impact pair is completed, and the corresponding stability and bifurcation analysis are also carried out. Numerical illustrations of periodic and chaotic motions are given.

scholarly journals Bifurcation of an Orbit Homoclinic to a Hyperbolic Saddle of a Vector Field inR4

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Tiansi Zhang ◽  
Dianli Zhao
Keyword(s):  
Vector Field ◽  
Bifurcation Analysis ◽  
Transverse Section ◽  
Bifurcation Diagrams ◽  
Saddle Node Bifurcation ◽  
Saddle Node ◽  
Hyperbolic Saddle

We perform a bifurcation analysis of an orbit homoclinic to a hyperbolic saddle of a vector field inR4. We give an expression of the gap between returning points in a transverse section by renormalizing system, through which we find the existence of homoclinic-doubling bifurcation in the case1+α>β>ν. Meanwhile, after reparametrizing the parameter, a periodic-doubling bifurcation appears and may be close to a saddle-node bifurcation, if the parameter is varied. These scenarios correspond to the occurrence of chaos. Based on our analysis, bifurcation diagrams of these bifurcations are depicted.

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