scholarly journals Behavior of the Solutions for Predator-Prey Dynamic Systems with Beddington-DeAngelis Type Functional Response on Periodic Time Scales in Shifts

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Neslihan Nesliye Pelen ◽  
Ayşe Feza Güvenilir ◽  
Billur Kaymakçalan
Keyword(s):  
Periodic Solution ◽  
Functional Response ◽  
Time Scales ◽  
Dynamic Systems ◽  
Two Dimensional ◽  
Predator Prey ◽  
Prey System ◽  
Special Case

We consider two-dimensional predator-prey system with Beddington-DeAngelis type functional response on periodic time scales in shifts. For this special case we try to find under which conditions the system hasδ±-periodic solution.

scholarly journals Permanence and Periodic Solution of Predator-Prey System with Holling Type Functional Response and Impulses

2007 ◽  
Vol 2007 ◽  
pp. 1-15 ◽  
Author(s):  
Weibing Wang ◽  
Jianhua Shen ◽  
Juan J. Nieto
Keyword(s):  
Periodic Solution ◽  
Functional Response ◽  
Impulsive Effect ◽  
Two Dimensional ◽  
Stable Periodic Solution ◽  
Predator Prey ◽  
Prey System ◽  
Stable Periodic ◽  
Holling Type Functional Response

We considered a nonautonomous two dimensional predator-prey system with impulsive effect. Conditions for the permanence of the system and for the existence of a unique stable periodic solution are obtained.

EXISTENCE FOR PERIODIC SOLUTIONS OF A RATIO-DEPENDENT PREDATOR-PREY SYSTEM WITH TIME-VARYING DELAYS ON TIME SCALES

2010 ◽  
Vol 08 (03) ◽  
pp. 227-233
Author(s):  
HUIJUAN LI ◽  
ANPING LIU ◽  
ZUTAO HAO
Keyword(s):  
Periodic Solution ◽  
Periodic Solutions ◽  
Functional Response ◽  
Time Scales ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Time Varying ◽  
Predator Prey ◽  
Prey System ◽  
Ratio Dependent

In this paper, by using the continuation theorem of coincidence degree theory we study the existence of periodic solution for a two-species ratio-dependent predator-prey system with time-varying delays and Machaelis–Menten type functional response on time scales. Some new results are obtained.

scholarly journals Investigation on dynamics of an impulsive predator–prey system with generalized Holling type IV functional response and anti-predator behavior

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sekson Sirisubtawee ◽  
Nattawut Khansai ◽  
Akapak Charoenloedmongkhon
Keyword(s):  
Periodic Solution ◽  
Functional Response ◽  
Impulsive Control ◽  
Positive Periodic Solution ◽  
Existence Condition ◽  
Predator Prey ◽  
Type Iv ◽  
Prey System ◽  
Existence And Stability ◽  
Predator Behavior

AbstractIn the present article, we propose and analyze a new mathematical model for a predator–prey system including the following terms: a Monod–Haldane functional response (a generalized Holling type IV), a term describing the anti-predator behavior of prey populations and one for an impulsive control strategy. In particular, we establish the existence condition under which the system has a locally asymptotically stable prey-eradication periodic solution. Violating such a condition, the system turns out to be permanent. Employing bifurcation theory, some conditions, under which the existence and stability of a positive periodic solution of the system occur but its prey-eradication periodic solution becomes unstable, are provided. Furthermore, numerical simulations for the proposed model are given to confirm the obtained theoretical results.

scholarly journals Oscillation of Two-Dimensional Neutral Delay Dynamic Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Xinli Zhang ◽  
Shanliang Zhu
Keyword(s):  
Time Scales ◽  
Dynamic Systems ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Real Sequence ◽  
Two Dimensional ◽  
Positive Real ◽  
Neutral Delay ◽  
All Solutions ◽  
Special Case

We consider a class of nonlinear two-dimensional dynamic systems of the neutral type(x(t)-a(t)x(τ1(t)))Δ=p(t)f1(y(t)),yΔ(t)=-q(t)f2(x(τ2(t))).We obtain sufficient conditions for all solutions of the system to be oscillatory. Our oscillation results whena(t)=0improve the oscillation results for dynamic systems on time scales that have been established by Fu and Lin (2010), since our results do not restrict to the case wheref(u)=u. Also, as a special case when𝕋=ℝ, our results do not requireanto be a positive real sequence. Some examples are given to illustrate the main results.

scholarly journals Existence and Uniqueness of Globally Attractive Positive Almost Periodic Solution in a Predator-Prey Dynamic System with Beddington-DeAngelis Functional Response

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Wenquan Wu
Keyword(s):  
Periodic Solution ◽  
Functional Response ◽  
Time Scales ◽  
Fixed Point Theory ◽  
Continuous System ◽  
Point Theory ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Predator Prey ◽  
Positive Almost Periodic Solution

This paper is concerned with a predator-prey system with Beddington-DeAngelis functional response on time scales. By using the theory of exponential dichotomy on time scales and fixed point theory based on monotone operator, some simple conditions are obtained for the existence of at least one positive (almost) periodic solution of the above system. Further, by means of Lyapunov functional, the global attractivity of the almost periodic solution for the above continuous system is also investigated. The main results in this paper extend, complement, and improve the previously known result. And some examples are given to illustrate the feasibility and effectiveness of the main results.

scholarly journals Almost Periodic Sequence Solutions of a Discrete Predator-Prey System with Beddington-DeAngelis Functional Response

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Zengji Du ◽  
Wenbin Li
Keyword(s):  
Periodic Solution ◽  
Lyapunov Function ◽  
Functional Response ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Periodic Sequence ◽  
Asymptotically Stable ◽  
Almost Periodic ◽  
Predator Prey ◽  
Prey System

This paper considers a discrete predator-prey system with Beddington-DeAngelis functional response. Sufficient conditions are obtained for the existence of the almost periodic solution which is uniformly asymptotically stable by constructing a Lyapunov function.

scholarly journals Existence of Unique and Global Asymptotically Stable Almost Periodic Solution of a Discrete Predator-Prey System with Beddington-DeAngelis Functional Response and Density Dependent

2018 ◽  
Vol 52 (1) ◽  
pp. 87-105
Author(s):  
Cosme Duque
Keyword(s):  
Periodic Solution ◽  
Functional Response ◽  
Almost Periodic Solution ◽  
Asymptotically Stable ◽  
Almost Periodic ◽  
Predator Prey ◽  
Density Dependent ◽  
Prey System ◽  
El Sistema

El objetivo principal de este artículo es el de estudiar la dinámica de un sistema depredador-presa discreto con respuesta funcional Beddington-DeAngelis y densamente dependiente del depredador, asumiendo que los coeficientes involucrados en el sistema son casi periódicos. De forma más concreta, bajo ciertas condiciones, probaremos la existencia de una única solución casi periódica la cual es globalmente atractiva. Exhibimos algunos ejemplos numéricos de los resultados.

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