EXCITATORY–INHIBITORY NETWORKS WITH DYNAMICAL THRESHOLDS

1990 ◽  
Vol 01 (03) ◽  
pp. 249-257 ◽  
Author(s):  
D. Horn ◽  
M. Usher
Keyword(s):  
Differential Equations ◽  
Numerical Simulations ◽  
Chaotic Motion ◽  
Inhibitory Neurons ◽  
Network Configuration ◽  
Dynamic Features ◽  
Mixed States ◽  
Dynamical Parameters ◽  
Feedback Networks ◽  
Inhibitory Networks

We investigate feedback networks containing excitatory and inhibitory neurons. The couplings between the neurons follow a Hebbian rule in which the memory patterns are encoded as cell assemblies of the excitatory neurons. Using disjoint patterns, we study the attractors of this model and point out the importance of mixed states. The latter become dominant at temperatures above 0.25. We use both numerical simulations and an analytic approach for our investigation. The latter is based on differential equations for the activity of the different memory patterns in the network configuration. Allowing the excitatory thresholds to develop dynamic features which correspond to fatigue of individual neurons, we obtain motion in pattern space, the space of all memories. The attractors turn into transients leading to chaotic motion for appropriate values of the dynamical parameters. The motion can be guided by overlaps between patterns, resembling a process of free associative thinking in the absence of any input.

Dynamics analysis of a gyrostat system with intermittent forcing

2021 ◽  
pp. 095965182110590
Author(s):  
Jianbin He ◽  
Jianping Cai
Keyword(s):  
Lyapunov Exponent ◽  
Numerical Simulations ◽  
Periodic Motion ◽  
Chaotic Motion ◽  
Dynamics Analysis ◽  
Bifurcation Diagrams ◽  
Stable Point ◽  
Dynamical Characteristics ◽  
Main Work ◽  
Selection Of

The dynamical characteristics of a gyrostat system with intermittent forcing are investigated, the main work and contributions are given as follows: (1) The gyrostat system with an intermittent forcing is studied, and its dynamical characteristics are investigated by the corresponding Lyapunov exponent spectrums and bifurcation diagrams with respect to the amplitude of intermittent forcing. The modified gyrostat system exists chaotic motion when the amplitude of intermittent forcing belongs to a certain interval, and it can be at a state of stable point or periodic motion by the design of amplitude. (2) The gyrostat system with multiple intermittent forcings is also investigated through the combination of Lyapunov exponent spectrums and bifurcation diagrams, and it behaves periodic motion or chaotic motion when the amplitude or forcing width is different. (3) By the selection of parameters in intermittent forcings, the modified gyrostat system is at a state of stable point, periodic motion or chaotic motion. Numerical simulations verify the feasibility and effectiveness of the modified gyrostat system.

Propagation of bursting oscillations

2009 ◽  
Vol 367 (1908) ◽  
pp. 4863-4875 ◽  
Author(s):  
Benjamin Ambrosio ◽  
Jean-Pierre Françoise
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Simulations ◽  
Time Evolution ◽  
Global Attractor ◽  
Reaction Diffusion ◽  
Functional Space ◽  
Excitable Cells ◽  
Diffusion Type ◽  
Bursting Oscillations

We investigate a system of partial differential equations of reaction–diffusion type which displays propagation of bursting oscillations. This system represents the time evolution of an assembly of cells constituted by a small nucleus of bursting cells near the origin immersed in the middle of excitable cells. We show that this system displays a global attractor in an appropriated functional space. Numerical simulations show the existence in this attractor of recurrent solutions which are waves propagating from the central source. The propagation seems possible if the excitability of the neighbouring cells is above some threshold.

scholarly journals Note on the Sensitivity of Simulated Solutions of the Nonlinear Singularly Perturbed Dynamical System on the Used Different Rewriting into a System of First Order Differential Equations

2016 ◽  
Vol 24 (39) ◽  
pp. 51-55
Author(s):  
Vladimír Liška ◽  
Zuzana Šútova ◽  
Dušan Pavliak
Keyword(s):  
Dynamical System ◽  
Numerical Methods ◽  
Differential Equations ◽  
Numerical Simulations ◽  
Numerical Scheme ◽  
Singularly Perturbed ◽  
First Order ◽  
First Order Differential Equations

Abstract In this paper we analyze the sensitivity of solutions to a nonlinear singularly perturbed dynamical system based on different rewriting into a System of the First Order Differential Equations to a numerical scheme. Numerical simulations of the solutions use numerical methods implemented in MATLAB.

Numerical vs. Experimental Predictions of Yaw Motion of Single Point Moored Vessel

2005 ◽  
Author(s):  
Mathieu Brotons ◽  
Philippe Jean
Keyword(s):  
Numerical Simulation ◽  
Differential Equations ◽  
Numerical Simulations ◽  
Time Domain ◽  
Model Tests ◽  
Linear Differential Equations ◽  
Integration Scheme ◽  
Engineering Model ◽  
Non Linear ◽  
Linear Differential

The accurate prediction of SPM vessel yaw motion is important to its mooring system design. Inconsistencies have been observed between the numerical and model test predictions of offloading responses. In some cases, the numerical simulation predicted unstable yaw behavior of the vessel (fishtailing) while the model tests did not show such instability. This discrepancy between experiment and theory casts doubt as to whether the numerical simulation predicts correctly the vessel yaw motion. The work presented in this paper investigates the following two hypotheses to possibly explain the non-expected fishtailing in the numerical simulations: The mooring software may not accurately integrate non-linear differential equations that describe the yaw motion of the SPM vessel. Some damping terms may be under-estimated in the software (user input issue). To validate the integration scheme of the system of non-linear differential equations as implemented in the mooring software, a stability analysis has been conducted on a shuttle tanker moored to a West Africa deep water buoy. Variations of parameters like the hawser length, its axial stiffness and the vessel’s drag coefficients have been studied to explore their impacts on the vessel yaw stability. The approach is to identify without performing any time domain simulations, the domains of stability by linearizing the differential equations of SPM vessel’s yaw motion around its equilibrium point. The validity of the developed approach is then confirmed by performing time domain simulations of the same case. The second conjecture which may explain the non-expected fishtailing in numerical simulations was that some damping terms may be under-estimated. A semi empirical formula for the drag moment can be derived from rotation tests and comparisons were performed with the engineering model implemented in the mooring analysis software. The results show that by calibrating this damping term with the one derived from the experiments, the numerical simulations would match the stable yaw motion behavior as predicted during model tests. Following the above findings, a tool has been developed to fit the yaw drag moment engineering model based on experimental measurements, for any case of mooring analysis.

scholarly journals 6.5. Hydrodynamical simulations as probes for the structure of the galactic center

1998 ◽  
Vol 184 ◽  
pp. 271-272
Author(s):  
K. Wada ◽  
T. Minezaki ◽  
K. Sakamoto ◽  
H. Fukuda
Keyword(s):  
Numerical Modeling ◽  
Numerical Simulations ◽  
Mass Distribution ◽  
Galactic Center ◽  
Dynamical Behavior ◽  
Interstellar Gas ◽  
Interstellar Gas In Galaxies ◽  
Dynamical Parameters ◽  
Pattern Speed ◽  
Hydrodynamical Simulations

Numerical modeling of the interstellar gas in galaxies is an effective approach to infer galactic gravitational structure. This is because the dynamical behavior of gas is very sensitive to the background gravitational potential. Since the dynamical resonances depend closely on the mass distribution and the pattern speed of the non-axisymmetric component, it is possible to determine these dynamical parameters by comparison of numerical simulations and gas observations.

scholarly journals Vibration Suppression Control of a Flexible Gantry Crane System with Varying Rope Length

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Tung Lam Nguyen ◽  
Trong Hieu Do ◽  
Hong Quang Nguyen
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Simulations ◽  
Vibration Suppression ◽  
Direct Method ◽  
Equations Of Motion ◽  
Gantry Crane ◽  
Partial Differential ◽  
Control Approach ◽  
Lyapunov’S Direct Method

The paper presents a control approach to a flexible gantry crane system. From Hamilton’s extended principle the equations of motion that characterized coupled transverse-transverse motions with varying rope length of the gantry is obtained. The equations of motion consist of a system of ordinary and partial differential equations. Lyapunov’s direct method is used to derive the control located at the trolley end that can precisely position the gantry payload and minimize vibrations. The designed control is verified through extensive numerical simulations.

scholarly journals Approximate ordinary differential equations for the optimal exercise boundaries of American put and call options

2013 ◽  
Vol 25 (1) ◽  
pp. 27-43 ◽  
Author(s):  
MARIANITO R. RODRIGO
Keyword(s):  
Differential Equations ◽  
Fluid Mechanics ◽  
Numerical Simulations ◽  
Ordinary Differential Equations ◽  
Boundary Layers ◽  
Mellin Transform ◽  
Call Option ◽  
Option Prices ◽  
Analytical Formulas ◽  
American Put

We revisit the American put and call option valuation problems. We derive analytical formulas for the option prices and approximate ordinary differential equations for the optimal exercise boundaries. Numerical simulations yield accurate option prices and comparable computational speeds when benchmarked against the binomial method for calculating option prices. Our approach is based on the Mellin transform and an adaptation of the Kármán–Pohlausen technique for boundary layers in fluid mechanics.

scholarly journals Behaviors and Numerical Simulations of Malaria Dynamic Models with Transgenic Mosquitoes

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Xiongwei Liu ◽  
Junjun Xu ◽  
Xiao Wang ◽  
Lizhi Cheng
Keyword(s):  
Theoretical Analysis ◽  
Differential Equations ◽  
Numerical Simulations ◽  
Basic Reproduction Number ◽  
Dynamic Models ◽  
Reproduction Number ◽  
Threshold Parameter ◽  
Endemic Disease ◽  
Target Field ◽  
Transgenic Mosquitoes

The release of transgenic mosquitoes to interact with wild ones is a promising method for controlling malaria. How to effectively release transgenic mosquitoes to prevent malaria is always a concern for researchers. This paper investigates two methods of releasing transgenic mosquitoes and proposes two epidemic models involving malaria patients, anopheles, wild mosquitoes, and transgenic mosquitoes based on system of continuous differential equations. A basic reproduction numberR0is defined for the models and it serves as a threshold parameter that predicts whether malaria will spread. By theoretical analysis of the dynamic behaviors of the models and numerical simulations, it is verified that malaria can be effectively controlled by the opportune release of transgenic mosquitoes; that is, whenR0≤1, malaria will disappear; whenR0>1, malaria will become an endemic disease in the target field.

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