scholarly journals Extinction in a Nonautonomous Discrete Lotka-Volterra Competitive System with Time Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Meng Hu ◽  
Jingyuan Wei
Keyword(s):  
Time Delay ◽  
Positive Solution ◽  
Analytical Techniques ◽  
Logistic Equation ◽  
The Other ◽  
Competitive System ◽  
Globally Attractive ◽  
System With Time Delay

This paper is concerned with a nonautonomous discrete Lotka-Volterra competitive system with time delay. By using some analytical techniques, we prove that, under certain conditions, one of the species will be driven to extinction while the other one will be globally attractive with any positive solution of a discrete logistic equation.

scholarly journals Extinction in Two-Species Nonlinear Discrete Competitive System

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Liqiong Pu ◽  
Xiangdong Xie ◽  
Fengde Chen ◽  
Zhanshuai Miao
Keyword(s):  
Numerical Simulations ◽  
Positive Solution ◽  
Discrete System ◽  
Sufficient Conditions ◽  
The Other ◽  
Discrete Equation ◽  
Toxic Substances ◽  
Competitive System ◽  
Globally Attractive ◽  
Nonlinear Discrete System

We propose a nonlinear discrete system of two species with the effect of toxic substances. By constructing a suitable Lyapunov-type function, we obtain the sufficient conditions which guarantee that one of the components will be driven to extinction while the other will be globally attractive with any positive solution of a discrete equation. Two examples together with their numerical simulations illustrate the feasibility of our main results. The results not only improve but also complement some known results.

Dynamical behavior of simplified FitzHugh–Nagumo neural system with time delay driven by Lévy noise

2021 ◽  
pp. 2150240
Author(s):  
Weida Qiu ◽  
Yongfeng Guo ◽  
Xiuxian Yu
Keyword(s):  
Time Delay ◽  
First Passage Time ◽  
Dynamical Behavior ◽  
Passage Time ◽  
Neural System ◽  
The Other ◽  
Lévy Noise ◽  
First Passage ◽  
Levy Noise ◽  
System With Time Delay

In this paper, the dynamical behavior of the FitzHugh–Nagumo (FHN) neural system with time delay driven by Lévy noise is studied from two aspects: the mean first-passage time (MFPT) and the probability density function (PDF) of the first-passage time (FPT). Using the Janicki–Weron algorithm to generate the Lévy noise, and through the order-4 Runge–Kutta algorithm to simulate the FHN system response, the time that the system needs from one stable state to the other one is tracked in the process. Using the MATLAB software to simulate the process above 20,000 times and recording the PFTs, the PDF of the FPT and the MFPT is obtained. Finally, the effects of the Lévy noise and time-delay on the FPT are discussed. It is found that the increase of both time-delay feedback intensity and Lévy noise intensity can promote the transition of the particle from the resting state to the excited state. However, the two parameters produce the opposite effects in the other direction.

A very rapid in situ Kikuchi technique to determine relative crystal misorientation

1988 ◽  
Vol 46 ◽  
pp. 830-831
Author(s):  
J. I. Bennetch
Keyword(s):  
Electron Beam ◽  
Analytical Techniques ◽  
Superplastic Forming ◽  
The Other ◽  
Kikuchi Pattern ◽  
Kikuchi Line ◽  
Line Analysis

In a recent study of the superplastic forming (SPF) behavior of certain Al-Li-X alloys, the relative misorientation between adjacent (sub)grains proved to be an important parameter. It is well established that the most accurate way to determine misorientation across boundaries is by Kikuchi line analysis. However, the SPF study required the characterization of a large number of (sub)grains in each sample to be statistically meaningful, a very time-consuming task even for comparatively rapid Kikuchi analytical techniques.In order to circumvent this problem, an alternate, even more rapid in-situ Kikuchi technique was devised, eliminating the need for the developing of negatives and any subsequent measurements on photographic plates. All that is required is a double tilt low backlash goniometer capable of tilting ± 45° in one axis and ± 30° in the other axis. The procedure is as follows. While viewing the microscope screen, one merely tilts the specimen until a standard recognizable reference Kikuchi pattern is centered, making sure, at the same time, that the focused electron beam remains on the (sub)grain in question.

Design of Master's Position Controller for Bilateral Control System with Time Delay

2015 ◽  
Vol 135 (3) ◽  
pp. 268-275 ◽  
Author(s):  
Daisuke Yashiro ◽  
Tadashi Hieno ◽  
Kazuhiro Yubai ◽  
Satoshi Komada
Keyword(s):  
Control System ◽  
Time Delay ◽  
Bilateral Control ◽  
Position Controller ◽  
System With Time Delay

scholarly journals A time delay dynamical model for outbreak of 2019-nCoV and the parameter identification

2020 ◽  
Vol 28 (2) ◽  
pp. 243-250 ◽  
Author(s):  
Yu Chen ◽  
Jin Cheng ◽  
Yu Jiang ◽  
Keji Liu
Keyword(s):  
Dynamical System ◽  
Time Delay ◽  
Parameter Identification ◽  
Typical Feature ◽  
The Novel ◽  
Isolation Rate ◽  
High Isolation ◽  
The Government ◽  
System With Time Delay ◽  
Official Data

AbstractIn this paper, we propose a novel dynamical system with time delay to describe the outbreak of 2019-nCoV in China. One typical feature of this epidemic is that it can spread in the latent period, which can therefore be described by time delay process in the differential equations. The accumulated numbers of classified populations are employed as variables, which is consistent with the official data and facilitates the parameter identification. The numerical methods for the prediction of the outbreak of 2019-nCoV and parameter identification are provided, and the numerical results show that the novel dynamic system can well predict the outbreak trend so far. Based on the numerical simulations, we suggest that the transmission of individuals should be greatly controlled with high isolation rate by the government.

scholarly journals Nonlinear vibrations and time delay control of an extensible slowly rotating beam

2020 ◽  
Author(s):  
Jerzy Warminski ◽  
Lukasz Kloda ◽  
Jaroslaw Latalski ◽  
Andrzej Mitura ◽  
Marcin Kowalczuk
Keyword(s):  
Time Delay ◽  
Control Strategies ◽  
Vibration Reduction ◽  
Least Action ◽  
Active Elements ◽  
Principle Of Least Action ◽  
Second Mode ◽  
Delay Control ◽  
Speed Range ◽  
System With Time Delay

AbstractNonlinear dynamics of a rotating flexible slender beam with embedded active elements is studied in the paper. Mathematical model of the structure considers possible moderate oscillations thus the motion is governed by the extended Euler–Bernoulli model that incorporates a nonlinear curvature and coupled transversal–longitudinal deformations. The Hamilton’s principle of least action is applied to derive a system of nonlinear coupled partial differential equations (PDEs) of motion. The embedded active elements are used to control or reduce beam oscillations for various dynamical conditions and rotational speed range. The control inputs generated by active elements are represented in boundary conditions as non-homogenous terms. Classical linear proportional (P) control and nonlinear cubic (C) control as well as mixed ($$P-C$$ P - C ) control strategies with time delay are analyzed for vibration reduction. Dynamics of the complete system with time delay is determined analytically solving directly the PDEs by the multiple timescale method. Natural and forced vibrations around the first and the second mode resonances demonstrating hardening and softening phenomena are studied. An impact of time delay linear and nonlinear control methods on vibration reduction for different angular speeds is presented.

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