scholarly journals Permanence and Global Attractivity of a Discrete Logistic Model with Impulses

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Chunyu Gao ◽  
Qingxi Guo
Keyword(s):  
Dynamic System ◽  
Numerical Simulations ◽  
Positive Solutions ◽  
Continuous Time ◽  
Logistic Model ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Euler Method ◽  
Logistic Equation ◽  
Time Dynamic

By piecewise Euler method, we construct a discrete logistic equation with impulses. The constructed model is more easily implemented at computer and is a better analogue of the continuous-time dynamic system. The dynamic behaviors of the constructed model are investigated. Sufficient conditions which guarantee the permanence and the global attractivity of positive solutions of the model are obtained. Numerical simulations show the feasibility of the main results.

scholarly journals Global Stability and Oscillation of a Discrete Annual Plants Model

2010 ◽  
Vol 2010 ◽  
pp. 1-18
Author(s):  
S. H. Saker
Keyword(s):  
Fixed Point ◽  
Global Stability ◽  
Numerical Simulations ◽  
Positive Solutions ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Annual Plants ◽  
Discrete Delay ◽  
The Stability ◽  
Positive Fixed Point

The objective of this paper is to systematically study the stability and oscillation of the discrete delay annual plants model. In particular, we establish some sufficient conditions for global stability of the unique positive fixed point and establish an explicit sufficient condition for oscillation of the positive solutions about the fixed point. Some illustrative examples and numerical simulations are included to demonstrate the validity and applicability of the results.

scholarly journals On limit periodicity of discrete time stochastic processes

2014 ◽  
Vol 14 (04) ◽  
pp. 1450011 ◽  
Author(s):  
Alexandra Rodkina ◽  
Nikolai Dokuchaev ◽  
John Appleby
Keyword(s):  
Difference Equation ◽  
Dynamic System ◽  
Stochastic Processes ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Stochastic Noise ◽  
Mean Square ◽  
Periodic Process ◽  
Time Dynamic ◽  
Sufficient Conditions For Convergence

We consider a discrete time dynamic system described by a difference equation with periodic coefficients and with additive stochastic noise. We investigate the possibility of the periodicity of the solution. In particular, we established sufficient conditions for convergence of the solution in mean square or almost surely to some stochastic periodic process.

scholarly journals GLOBAL ATTRACTIVITY IN A NONAUTONOMOUS DELAY-LOGISTIC EQUATION

1995 ◽  
Vol 26 (2) ◽  
pp. 159-164
Author(s):  
JIANHUA SHEN ◽  
ZHICHENG WANG
Keyword(s):  
Steady State ◽  
Global Attractor ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Logistic Equation ◽  
Positive Steady State ◽  
Delay Logistic Equation

Consider the nonautonomous delay-Logistic equation \[x'(t)=r(t)x(t)[1-b_1x(t-\tau_1)-b_2x(t-\tau_2)], \quad t\ge 0.\] We obtain sufficient conditions for the positive steady state $x^* =1/(b_1+b_2)$ to be a global attractor. An application of our result also solves a conjecture of Gopalsamy.

scholarly journals On the Dynamics of a Nonautonomous Predator-Prey Model with Hassell-Varley Type Functional Response

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Yan Zhang ◽  
Shujing Gao ◽  
Kuangang Fan
Keyword(s):  
Lyapunov Function ◽  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Incidence Rate ◽  
Functional Response ◽  
Global Attractivity ◽  
Migratory Birds ◽  
Sufficient Conditions ◽  
Predator Prey ◽  
Predator Prey Model

The dynamic behaviors of a nonautonomous system for migratory birds with Hassell-Varley type functional response and the saturation incidence rate are studied. Under quite weak assumptions, some sufficient conditions are obtained for the permanence and extinction of the disease. Moreover, the global attractivity of the model is discussed by constructing a Lyapunov function. Numerical simulations which support our theoretical analysis are also given.

DYNAMICAL PROPERTIES OF A STOCHASTIC TWO-SPECIES SCHOENER'S COMPETITIVE MODEL

2012 ◽  
Vol 05 (05) ◽  
pp. 1250035 ◽  
Author(s):  
JINGLIANG LV ◽  
KE WANG ◽  
MENG LIU
Keyword(s):  
Growth Rate ◽  
Positive Solutions ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Uniform Continuity ◽  
Stochastic Permanence ◽  
Sample Paths ◽  
Competitive Model ◽  
Dynamical Properties

A stochastic two-species Schoener's competitive model is proposed and investigated. Sufficient conditions for the existence of global positive solutions, boundedness, uniform continuity, global attractivity, stochastic permanence and extinction are obtained. Moreover, the upper-growth rate and the average in time of the sample paths of solutions are also estimated. Finally, some figures are introduced to illustrate the main results.

scholarly journals Continuous-time dynamic system identification with multisine random excitation revisited

2010 ◽  
Vol 20 (2) ◽  
pp. 133-149 ◽  
Author(s):  
Jarosław Figwer
Keyword(s):  
System Identification ◽  
Dynamic System ◽  
Data Acquisition ◽  
Continuous Time ◽  
Output Signal ◽  
Random Excitation ◽  
Single Input Single Output ◽  
Time Dynamic ◽  
Data Acquisition Systems ◽  
Input And Output

Continuous-time dynamic system identification with multisine random excitation revisitedThe paper presents a new, revisited and unified approach to a linear continuous-time dynamic single-input single-output system identification using input and output signal samples acquired with a deterministic constant or random sampling interval. The approach is based on a specially designed identification experiment with excitation of the form of a continuous-time multisine random excitation and digital processing of the corresponding signal samples obtained without analogue antialiasing filtration in the case of disturbances satisfying or not satisfying the Shannon's sampling theorem. Properties of the proposed approach are discussed taking into account nonlinearity of the excitation generation and data acquisition systems with a focus on model identification in the case of input and output signal levels comparable with data acquisition system accuracy. Methods reducing influence of the disturbances (including aliasing) as well as nonlinearities of the excitation generation and data acquisition systems on identification results are proposed, too.

scholarly journals Asymptotic Behaviors of a Delayed Nonautonomous Predator-Prey System Governed by Difference Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Lili Liu ◽  
Zhijun Liu
Keyword(s):  
Numerical Simulations ◽  
Positive Solutions ◽  
Differential System ◽  
Difference Equations ◽  
Global Attractivity ◽  
Asymptotic Behaviors ◽  
Predator Prey ◽  
Prey System ◽  
Discretization Technique ◽  
Theoretical Results

Based on a predator-prey differential system with continuously distributed delays, we derive a corresponding difference version by using the method of a discretization technique. A good understanding of permanence of system and global attractivity of positive solutions of system is gained. An example and its numerical simulations are presented to substantiate our theoretical results.

A Markov-switching predator–prey model with Allee effect for preys

2020 ◽  
Vol 13 (03) ◽  
pp. 2050018
Author(s):  
Xiaoxia Guo ◽  
Zhiming Guo
Keyword(s):  
Numerical Simulations ◽  
Allee Effect ◽  
Global Attractivity ◽  
Markov Switching ◽  
Sufficient Conditions ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Theoretical Results ◽  
Prey Populations

This paper concerns with a Markov-switching predator–prey model with Allee effect for preys. The conditions under which extinction of predator and prey populations occur have been established. Sufficient conditions are also given for persistence and global attractivity in mean. In addition, stability in the distribution of the system under consideration is derived under some assumptions. Finally, numerical simulations are carried out to illustrate theoretical results.

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