scholarly journals Dynamics of a delayed population model with feedback control

2000 ◽  
Vol 41 (4) ◽  
pp. 451-457 ◽  
Author(s):  
Wang Wendi ◽  
Tang Chunlei
Keyword(s):  
Feedback Control ◽  
Population Growth ◽  
Population Model ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Positive Equilibrium ◽  
Delayed Population Model

This paper studies a system proposed by K. Gopalsamy and P. X. Weng to model a population growth with feedback control and time delays. Sufficient conditions are established under which the positive equilibrium of the system is globally attracting. The conjecture proposed by Gopalsamy and Weng is here confirmed and improved.

scholarly journals Dynamic Analysis of Stochastic Lotka–Volterra Predator-Prey Model with Discrete Delays and Feedback Control

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Jinlei Liu ◽  
Wencai Zhao
Keyword(s):  
Feedback Control ◽  
Deterministic Model ◽  
Sufficient Conditions ◽  
Positive Equilibrium ◽  
Theoretical Derivation ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Discrete Delays ◽  
Positive Equilibrium Point

In this paper, a stochastic Lotka–Volterra predator-prey model with discrete delays and feedback control is studied. Firstly, the existence and uniqueness of global positive solution are proved. Further, we investigate the asymptotic property of stochastic system at the positive equilibrium point of the corresponding deterministic model and establish sufficient conditions for the persistence and extinction of the model. Finally, the correctness of the theoretical derivation is verified by numerical simulations.

GLOBAL STABILITY OF A NONLINEAR DISCRETE POPULATION MODEL WITH TIME DELAYS

2007 ◽  
Vol 10 (03) ◽  
pp. 315-333
Author(s):  
NA FANG ◽  
XIAOXING CHEN
Keyword(s):  
Global Stability ◽  
Positive Solution ◽  
Positive Solutions ◽  
Population Model ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Volterra Type ◽  
Discrete Population ◽  
Liapunov Functionals ◽  
Discrete Population Model

The global stability of a nonlinear discrete population model of Volterra type is studied. The model incorporates time delays. By linearization of the model at positive solutions and construction of Liapunov functionals, sufficient conditions are obtained to ensure that a positive solution of the model is stable and attracts all positive solutions. An example shows the feasibility of our main results.

Spatial dynamics of a lattice population model with two age classes and maturation delay

2014 ◽  
Vol 26 (1) ◽  
pp. 61-91 ◽  
Author(s):  
SHI-LIANG WU ◽  
PEIXUAN WENG ◽  
SHIGUI RUAN
Keyword(s):  
Population Model ◽  
Global Attractivity ◽  
Spatial Dynamics ◽  
Sufficient Conditions ◽  
Growth Function ◽  
Spreading Speed ◽  
Positive Equilibrium ◽  
Structured Population Model ◽  
Minimal Wave Speed ◽  
Age Structured

This paper is concerned with the spatial dynamics of a monostable delayed age-structured population model in a 2D lattice strip. When there exists no positive equilibrium, we prove the global attractivity of the zero equilibrium. Otherwise, we give some sufficient conditions to guarantee the global attractivity of the unique positive equilibrium by establishing a series of comparison arguments. Furthermore, when those conditions do not hold, we show that the system is uniformly persistent. Finally, the spreading speed, including the upward convergence, is established for the model without the monotonicity of the growth function. The linear determinacy of the spreading speed and its coincidence with the minimal wave speed are also proved.

scholarly journals Stability and Global Hopf Bifurcation Analysis on a Ratio-Dependent Predator-Prey Model with Two Time Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-15
Author(s):  
Huitao Zhao ◽  
Yiping Lin ◽  
Yunxian Dai
Keyword(s):  
Hopf Bifurcation ◽  
Time Delays ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Positive Equilibrium ◽  
Global Hopf Bifurcation ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Ratio Dependent

A ratio-dependent predator-prey model with two time delays is studied. By means of an iteration technique, sufficient conditions are obtained for the global attractiveness of the positive equilibrium. By comparison arguments, the global stability of the semitrivial equilibrium is addressed. By using the theory of functional equation and Hopf bifurcation, the conditions on which positive equilibrium exists and the quality of Hopf bifurcation are given. Using a global Hopf bifurcation result of Wu (1998) for functional differential equations, the global existence of the periodic solutions is obtained. Finally, an example for numerical simulations is also included.

scholarly journals Stability Analysis of a Population Model with Maturation Delay and Ricker Birth Function

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Chongwu Zheng ◽  
Fengqin Zhang ◽  
Jianquan Li
Keyword(s):  
Population Model ◽  
Sufficient Conditions ◽  
Single Species ◽  
Positive Equilibrium ◽  
Stability Switch ◽  
Birth Function ◽  
Maturation Delay ◽  
Trivial Equilibrium ◽  
Species Population ◽  
Single Species Population

A single species population model is investigated, where the discrete maturation delay and the Ricker birth function are incorporated. The threshold determining the global stability of the trivial equilibrium and the existence of the positive equilibrium is obtained. The necessary and sufficient conditions ensuring the local asymptotical stability of the positive equilibrium are given by applying the Pontryagin's method. The effect of all the parameter values on the local stability of the positive equilibrium is analyzed. The obtained results show the existence of stability switch and provide a method of computing maturation times at which the stability switch occurs. Numerical simulations illustrate that chaos may occur for the model, and the associated parameter bifurcation diagrams are given for certain values of the parameters.

On the uniform stability for a ‘food-limited’ population model with time delay

1995 ◽  
Vol 125 (5) ◽  
pp. 991-1002 ◽  
Author(s):  
Joseph W.-H. So ◽  
J. S. Yu
Keyword(s):  
Time Delay ◽  
Asymptotic Stability ◽  
Population Model ◽  
Sufficient Conditions ◽  
Uniform Stability ◽  
Positive Equilibrium

In this paper, we provide sufficient conditions which guarantee the uniform stability as well as asymptotic stability of the positive equilibrium for a food limited population model with time delay.

QUALITATIVE ANALYSIS OF A NEURAL NETWORK MODEL WITH MULTIPLE TIME DELAYS

1999 ◽  
Vol 09 (08) ◽  
pp. 1585-1595 ◽  
Author(s):  
SUE ANN CAMPBELL ◽  
SHIGUI RUAN ◽  
JUNJIE WEI
Keyword(s):  
Neural Network ◽  
Network Model ◽  
Neural Network Model ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Positive Equilibrium ◽  
Multiple Time ◽  
Local Stability Analysis ◽  
Multiple Time Delays ◽  
Transcendental Functions

We consider a simplified neural network model for a ring of four neurons where each neuron receives two time delayed inputs: One from itself and another from the previous neuron. Local stability analysis of the positive equilibrium leads to a characteristic equation containing products of four transcendental functions. By analyzing the equivalent system of four scalar transcendental equations, we obtain sufficient conditions for the linear stability of the positive equilibrium. Furthermore, we show that a Hopf bifurcation can occur when the positive equilibrium loses stability.

scholarly journals Delay-Dependent Robust Stabilization for Nonlinear Large Systems via Decentralized Fuzzy Control

2011 ◽  
Vol 2011 ◽  
pp. 1-20 ◽  
Author(s):  
Chun-xia Dou ◽  
Zhi-sheng Duan ◽  
Xing-bei Jia ◽  
Xiao-gang Li ◽  
Jin-zhao Yang ◽  
...  
Keyword(s):  
Time Delay ◽  
Fuzzy Control ◽  
Upper Bound ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Large System ◽  
Disturbance Attenuation ◽  
Robust Controller ◽  
Large Systems ◽  
Delay Dependent

A delay-dependent robust fuzzy control approach is developed for a class of nonlinear uncertain interconnected time delay large systems in this paper. First, an equivalent T–S fuzzy model is extended in order to accurately represent nonlinear dynamics of the large system. Then, a decentralized state feedback robust controller is proposed to guarantee system stabilization with a prescribedH∞disturbance attenuation level. Furthermore, taking into account the time delays in large system, based on a less conservative delay-dependent Lyapunov function approach combining with linear matrix inequalities (LMI) technique, some sufficient conditions for the existence ofH∞robust controller are presented in terms of LMI dependent on the upper bound of time delays. The upper bound of time-delay and minimizedH∞performance index can be obtained by using convex optimization such that the system can be stabilized and for all time delays whose sizes are not larger than the bound. Finally, the effectiveness of the proposed controller is demonstrated through simulation example.

scholarly journals On a predator-prey system interaction under fluctuating water level with nonselective harvesting

2020 ◽  
Vol 18 (1) ◽  
pp. 458-475
Author(s):  
Na Zhang ◽  
Yonggui Kao ◽  
Fengde Chen ◽  
Binfeng Xie ◽  
Shiyu Li
Keyword(s):  
Water Level ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Optimal Harvesting ◽  
Positive Equilibrium ◽  
Predator Population ◽  
Model Interaction ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Fluctuating Water Level

Abstract A predator-prey model interaction under fluctuating water level with non-selective harvesting is proposed and studied in this paper. Sufficient conditions for the permanence of two populations and the extinction of predator population are provided. The non-negative equilibrium points are given, and their stability is studied by using the Jacobian matrix. By constructing a suitable Lyapunov function, sufficient conditions that ensure the global stability of the positive equilibrium are obtained. The bionomic equilibrium and the optimal harvesting policy are also presented. Numerical simulations are carried out to show the feasibility of the main results.

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