scholarly journals Permanence and Extinction of a Stochastic Delay Logistic Model with Jumps

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Chun Lu ◽  
Xiaohua Ding
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Population Model ◽  
Logistic Model ◽  
Necessary Conditions ◽  
Biological Significance ◽  
Jump Process ◽  
Stochastic Permanence ◽  
Stochastic Delay ◽  
Sufficient And Necessary Conditions

This paper is concerned with a stochastic delay logistic model with jumps. Sufficient and necessary conditions for extinction are obtained as well as stochastic permanence. Numerical simulations are introduced to support the theoretical analysis results. The results show that the jump process can affect the properties of the population model significantly, which conforms to biological significance.

Sufficient and necessary conditions of stochastic permanence and extinction for stochastic logistic model with Markovian switching and Lévy noise

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5869-5883
Author(s):  
Sheng Wang ◽  
Linshan Wang ◽  
Tengda Wei
Keyword(s):  
Logistic Model ◽  
Necessary Conditions ◽  
Sample Path ◽  
Analytical Techniques ◽  
Markovian Switching ◽  
Matrix Analysis ◽  
Stationary Probability Distribution ◽  
Stochastic Permanence ◽  
Sufficient And Necessary Conditions ◽  
Stochastic Logistic Model

In this paper, stochastic permanence and extinction of a stochastic logistic model with Markovian switching and L?vy noise are investigated by combining stochastic analytical techniques with M-matrix analysis. Sufficient and necessary conditions of stochastic permanence and extinction are obtained. In the case of stochastic permanence, both the superior limit and the inferior limit of the average in time of the sample path of the solution are estimated by two constants related to the stationary probability distribution of the Markov chain and the parameters of the subsystems of the logistic model. Finally, our conclusions are illustrated through an example.

TWO PATCHES IMPULSIVE DIFFUSION PERIODIC SINGLE-SPECIES LOGISTIC MODEL

2010 ◽  
Vol 03 (01) ◽  
pp. 127-141 ◽  
Author(s):  
ZIJIAN LIU ◽  
ZHIDONG TENG ◽  
LONG ZHANG
Keyword(s):  
Periodic Solution ◽  
Iterative Method ◽  
Numerical Simulations ◽  
Logistic Model ◽  
Global Attractivity ◽  
Necessary Conditions ◽  
Positive Periodic Solution ◽  
Single Species ◽  
Impulsive Diffusion ◽  
Sufficient And Necessary Conditions

In this paper, we study a periodic single-species logistic system with impulsive diffusion in two patches. By using the iterative method, sufficient and necessary conditions on the existence, uniqueness and global attractivity of positive periodic solution and the extinction of species for this system are established. Two examples and numerical simulations are presented to illustrate the feasibility of our results.

Dynamics of an autonomous Gilpin–Ayala competition model with random perturbation

2021 ◽  
pp. 2050043
Author(s):  
Jing Fu ◽  
Qixing Han ◽  
Daqing Jiang ◽  
Yanyan Yang
Keyword(s):  
White Noise ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Necessary Conditions ◽  
Random Perturbation ◽  
Sufficient Conditions ◽  
Competition Model ◽  
Interacting Species ◽  
Sufficient And Necessary Conditions ◽  
Global Positive Solution

This paper discusses the dynamics of a Gilpin–Ayala competition model of two interacting species perturbed by white noise. We obtain the existence of a unique global positive solution of the system and the solution is bounded in [Formula: see text]th moment. Then, we establish sufficient and necessary conditions for persistence and the existence of an ergodic stationary distribution of the model. We also establish sufficient conditions for extinction of the model. Moreover, numerical simulations are carried out for further support of present research.

scholarly journals Dynamics Analysis of a Stochastic Delay Gilpin-Ayala Model with Markovian Switching

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Qiaoqin Gao ◽  
Zhijiang Luo ◽  
Guirong Liu
Keyword(s):  
Numerical Simulations ◽  
Existence And Uniqueness ◽  
Matrix Method ◽  
Lyapunov Method ◽  
Markovian Switching ◽  
Dynamics Analysis ◽  
Stochastic Permanence ◽  
Stochastic Delay ◽  
Global Positive Solution ◽  
Theoretical Results

This paper considers a stochastic delay Gilpin-Ayala model with Markovian switching. Using Lyapunov method, we show existence and uniqueness of global positive solution. Then, by using Chebyshev’s inequality, M-matrix method, and BDG’s inequality, stochastic permanence and asymptotic estimations of solutions are studied. Finally, numerical simulations illustrate the theoretical results. Our results generalize and improve the existing results.

Effects of aeroelasticity on coning motion of a spinning missile

2016 ◽  
Vol 230 (14) ◽  
pp. 2581-2595 ◽  
Author(s):  
Zhongjiao Shi ◽  
Liangyu Zhao
Keyword(s):  
Theoretical Analysis ◽  
Linear Equation ◽  
Vibration Mode ◽  
Necessary Conditions ◽  
Stable Region ◽  
Design Parameters ◽  
Governing Equations ◽  
First Order ◽  
Sufficient And Necessary Conditions ◽  
The Stability

The coning motion is a basic angular behavior of spinning missiles. Research on the stability of coning motion is always active. In this paper, the integrated nonlinear governing equations of rigid-elastic angular motion for a spinning missile with high fineness ratio are derived firstly following the Lagrangian approach. Secondly, a set of linear equation is obtained under some assumptions considering the first order vibration mode in the form of complex summation for theoretical analysis. Finally, the sufficient and necessary conditions of coning motion dynamic stability for spinning missile with and without an acceleration autopilot are analytically derived and verified by numerical simulations based on the linear equation. It is concluded that the aeroelasticity can shrink the stable region of the design parameters, even lead to a divergent coning motion.

scholarly journals Stochastic Delay Logistic Model under Regime Switching

2012 ◽  
Vol 2012 ◽  
pp. 1-26 ◽  
Author(s):  
Zheng Wu ◽  
Hao Huang ◽  
Lianglong Wang
Keyword(s):  
Regime Switching ◽  
Logistic Model ◽  
Sufficient Conditions ◽  
Function Technique ◽  
Stochastic Permanence ◽  
Stochastic Delay ◽  
Gronwall’S Inequality ◽  
Diffusion In Random Environment ◽  
Stochastically Ultimate Boundedness ◽  
Generalized Itô Formula

This paper is concerned with a delay logistical model under regime switching diffusion in random environment. By using generalized Itô formula, Gronwall's inequality, and Young's inequality, some sufficient conditions for existence of global positive solutions and stochastically ultimate boundedness are obtained, respectively. Also, the relationships between the stochastic permanence and extinction as well as asymptotic estimations of solutions are investigated by virtue ofV-function technique,M-matrix method, and Chebyshev's inequality. Finally, an example is given to illustrate the main results.

scholarly journals Dynamics of a General Stochastic Nonautonomous Lotka-Volterra Model with Delays and Impulsive Perturbations

2015 ◽  
Vol 2015 ◽  
pp. 1-17
Author(s):  
Qing Wang ◽  
Yongguang Yu ◽  
Shuo Zhang
Keyword(s):  
Theoretical Analysis ◽  
Stochastic Model ◽  
Numerical Simulations ◽  
Sufficient Conditions ◽  
Critical Value ◽  
Volterra Model ◽  
Stochastic Permanence ◽  
Stochastic Noises ◽  
The Mean ◽  
Impulsive Perturbations

A stochastic nonautonomous N-species Lotka-Volterra model with delays and impulsive perturbations is investigated. For this model, sufficient conditions for extinction, nonpersistence in the mean, weak persistence and stochastic permanence are given, respectively. The influences of the stochastic noises, and the impulsive perturbations on the properties of the stochastic model are also discussed. The critical value between weak persistence and extinction is obtained. Finally, numerical simulations are given to support the theoretical analysis results.

scholarly journals Theoretical Analysis and Design of an Innovative Coil Structure for Transcranial Magnetic Stimulation

2021 ◽  
Vol 11 (4) ◽  
pp. 1960
Author(s):  
Naming Zhang ◽  
Ziang Wang ◽  
Jinhua Shi ◽  
Shuya Ning ◽  
Yukuo Zhang ◽  
...  
Keyword(s):  
Electromagnetic Field ◽  
Transcranial Magnetic Stimulation ◽  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Magnetic Stimulation ◽  
Influential Factors ◽  
Intersection Angle ◽  
Electromagnetic Field Distribution ◽  
Analysis And Design ◽  
Coil Structure

Previous research showed that pulsed functional magnetic stimulation can activate brain tissue with optimum intensity and frequency. Conventional stimulation coils are always set as a figure-8 type or Helmholtz. However, the magnetic fields generated by these coils are uniform around the target, and their magnetic stimulation performance still needs improvement. In this paper, a novel type of stimulation coil is proposed to shrink the irritative zone and strengthen the stimulation intensity. Furthermore, the electromagnetic field distribution is calculated and measured. Based on numerical simulations, the proposed coil is compared to traditional coil types. Moreover, the influential factors, such as the diameter and the intersection angle, are also analyzed. It was demonstrated that the proposed coil has a better performance in comparison with the figure-8 coil. Thus, this work suggests a new way to design stimulation coils for transcranial magnetic stimulation.

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