SYNCHRONIZATION TRANSITION INDUCED BY SYNAPTIC DELAY IN COUPLED FAST-SPIKING NEURONS

2008 ◽  
Vol 18 (04) ◽  
pp. 1189-1198 ◽  
Author(s):  
QINGYUN WANG ◽  
QISHAO LU ◽  
GUANRONG CHEN
Keyword(s):  
Spiking Neurons ◽  
Synaptic Delay ◽  
Largest Lyapunov Exponent ◽  
Bifurcation Diagrams ◽  
Chaotic Motions ◽  
Collective Behaviors ◽  
Phase Errors ◽  
Different Types ◽  
Fast Spiking ◽  
Chemical Synapses

Synchronization of coupled fast-spiking neurons with chemical synapses is studied in this paper. It is shown that by varying some key parameters such as the coupling strength and the decay rate of synapses, two coupled fast-spiking neurons can exhibit various firing synchronizations including periodic and chaotic motions. Different types of firing synchronizations are diagnosed by means of bifurcation diagrams and the largest Lyapunov exponent of the error dynamical system. However, with the synaptic delay considered, two coupled neurons can show different types of transitions of in-phase and anti-phase synchronizations and these transitions can be identified from the bifurcation diagrams and the variations of the phase errors of the coupled neurons. The revealed complicated synchronization modes effectively provide important guidelines to understanding collective behaviors of coupled neurons.

scholarly journals Stability Analysis and Chaos Control of Electronic Throttle Dynamical System

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Shun-Chang Chang
Keyword(s):  
Control Strategy ◽  
Chaos Control ◽  
Period Doubling ◽  
Largest Lyapunov Exponent ◽  
Bifurcation Diagrams ◽  
Chaotic Motions ◽  
Electronic Throttle ◽  
Controlling Chaos ◽  
Analysis Techniques ◽  
Continuous Feedback

This study addresses bifurcation analysis and controlling chaos in a vehicular electronic throttle. Using analysis techniques from nonlinear dynamics of an electronic throttle system based on bifurcation diagrams, we establish the existence of period-doubling and intermittency routes to chaos. The largest Lyapunov exponent is estimated from the synchronization to identify periodic and chaotic motions. Finally, the proposed continuous feedback control is employed to control chaos. To verify the effectiveness of the raised control strategy, we present a number of numerical simulations.

scholarly journals Theoretical and Experimental Investigation of Two-to-One Internal Resonance in MEMS Arch Resonators

2018 ◽  
Vol 14 (1) ◽  
Author(s):  
Feras K. Alfosail ◽  
Amal Z. Hajjaj ◽  
Mohammad I. Younis
Keyword(s):  
Internal Resonance ◽  
Nonlinear Response ◽  
Multiple Scales ◽  
Hopf Bifurcations ◽  
Chaotic Motions ◽  
Different Types ◽  
Quadratic Nonlinearities ◽  
Multiple Scales Perturbation Method ◽  
Good Agreement ◽  
Perturbation Solutions

We investigate theoretically and experimentally the two-to-one internal resonance in micromachined arch beams, which are electrothermally tuned and electrostatically driven. By applying an electrothermal voltage across the arch, the ratio between its first two symmetric modes is tuned to two. We model the nonlinear response of the arch beam during the two-to-one internal resonance using the multiple scales perturbation method. The perturbation solution is expanded up to three orders considering the influence of the quadratic nonlinearities, cubic nonlinearities, and the two simultaneous excitations at higher AC voltages. The perturbation solutions are compared to those obtained from a multimode Galerkin procedure and to experimental data based on deliberately fabricated Silicon arch beam. Good agreement is found among the results. Results indicate that the system exhibits different types of bifurcations, such as saddle node and Hopf bifurcations, which can lead to quasi-periodic and potentially chaotic motions.

SIMULATING VERTICAL AND HORIZONTAL INHIBITION WITH SHORT-TERM DYNAMICS IN A MULTI-COLUMN MULTI-LAYER MODEL OF NEOCORTEX

2014 ◽  
Vol 24 (05) ◽  
pp. 1440002 ◽  
Author(s):  
BEATA STRACK ◽  
KIMBERLE M. JACOBS ◽  
KRZYSZTOF J. CIOS
Keyword(s):  
Epileptiform Activity ◽  
Inhibitory Neuron ◽  
Normal Function ◽  
Spiking Neurons ◽  
Layer Model ◽  
Neuronal Connectivity ◽  
Short Term ◽  
Short Term Plasticity ◽  
Low Threshold ◽  
Fast Spiking

The paper introduces a multi-layer multi-column model of the cortex that uses four different neuron types and short-term plasticity dynamics. It was designed with details of neuronal connectivity available in the literature and meets these conditions: (1) biologically accurate laminar and columnar flows of activity, (2) normal function of low-threshold spiking and fast spiking neurons, and (3) ability to generate different stages of epileptiform activity. With these characteristics the model allows for modeling lesioned or malformed cortex, i.e. examine properties of developmentally malformed cortex in which the balance between inhibitory neuron subtypes is disturbed.

Neuregulin 1 regulates excitability of fast-spiking neurons through Kv1.1 and acts in epilepsy

2011 ◽  
Vol 15 (2) ◽  
pp. 267-273 ◽  
Author(s):  
Ke-Xin Li ◽  
Ying-Mei Lu ◽  
Zheng-Hao Xu ◽  
Jing Zhang ◽  
Jun-Ming Zhu ◽  
...  
Keyword(s):  
Spiking Neurons ◽  
Neuregulin 1 ◽  
Fast Spiking

scholarly journals Synchronisation phenomenon in three blades rotor driven by regular or chaotic oscillations

2018 ◽  
Vol 148 ◽  
pp. 06002
Author(s):  
Zofia Szmit ◽  
Jerzy Warmiński
Keyword(s):  
Time Series ◽  
Numerical Calculation ◽  
Duffing Oscillator ◽  
Equations Of Motion ◽  
Composite Beams ◽  
Chaotic Oscillations ◽  
Rotating System ◽  
Chaotic Motions ◽  
Structural Differences ◽  
Different Types

The goal of the paper is to analysed the influence of the different types of excitation on the synchronisation phenomenon in case of the rotating system composed of a rigid hub and three flexible composite beams. In the model is assumed that two blades, due to structural differences, are de-tuned. Numerical calculation are divided on two parts, firstly the rotating system is exited by a torque given by regular harmonic function, than in the second part the torque is produced by chaotic Duffing oscillator. The synchronisation phenomenon between the beams is analysed both either for regular or chaotic motions. Partial differential equations of motion are solved numerically and resonance curves, time series and Poincaré maps are presented for selected excitation torques.

Chaotic Motion of a Parametrically Excited Dielectric Elastomer

2020 ◽  
Vol 12 (03) ◽  
pp. 2050033
Author(s):  
Hamidreza Heidari ◽  
Amin Alibakhshi ◽  
Habib Ramezannejad Azarboni
Keyword(s):  
Time Integration ◽  
Nonlinear Behavior ◽  
Strain Energy Function ◽  
Nonlinear Ordinary Differential Equation ◽  
Dielectric Elastomer ◽  
Dissipation Function ◽  
Bifurcation Diagrams ◽  
Chaotic Motions ◽  
Poincaré Sections ◽  
Poincare Sections

In this paper, an effort is made to study the chaotic motions of a dielectric elastomer (DE). The DE is activated by a time-dependent voltage (AC voltage), which is superimposed on a DC voltage. The Gent strain energy function is employed to model the nonlinear behavior of the elastomeric matter. The nonlinear ordinary differential equation (ODE) in terms of the stretch of the elastomer governing the motion of the system is deduced using the Euler–Lagrange method and the Rayleigh dissipation function. This ODE is solved via the use of a time integration-based solver. The bifurcation diagrams of Poincaré sections are generated to identify the chaotic domains. The largest Lyapunov exponents (LLEs) are illustrated for validation of the results obtained by the bifurcation diagrams. Various types of motion for the system are precisely discussed through the depiction of stretch-time responses, phase-plane diagrams, Poincaré sections and power spectral density (PSD) diagrams. The results reveal that the damping coefficient plays an influential role in suppressing the chaos phenomenon. Besides, the initial stretch of the elastomer could affect the chaotic interval of system parameters.

scholarly journals Dynamical Analysis of a New Chaotic Fractional Discrete-Time System and Its Control

Entropy ◽  
2020 ◽  
Vol 22 (12) ◽  
pp. 1344
Author(s):  
A. Othman Almatroud ◽  
Amina-Aicha Khennaoui ◽  
Adel Ouannas ◽  
Giuseppe Grassi ◽  
M. Mossa Al-sawalha ◽  
...  
Keyword(s):  
Discrete Time ◽  
Software Package ◽  
Control Method ◽  
Approximate Entropy ◽  
Dynamical Analysis ◽  
Largest Lyapunov Exponent ◽  
Bifurcation Diagrams ◽  
Discrete Time System ◽  
Time System ◽  
Quadratic Nonlinearities

This article proposes a new fractional-order discrete-time chaotic system, without equilibria, included two quadratic nonlinearities terms. The dynamics of this system were experimentally investigated via bifurcation diagrams and largest Lyapunov exponent. Besides, some chaotic tests such as the 0–1 test and approximate entropy (ApEn) were included to detect the performance of our numerical results. Furthermore, a valid control method of stabilization is introduced to regulate the proposed system in such a way as to force all its states to adaptively tend toward the equilibrium point at zero. All theoretical findings in this work have been verified numerically using MATLAB software package.

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