scholarly journals Multiple Periodic Solutions of Generalized Gause-Type Predator-Prey Systems with Nonmonotonic Numerical Responses and Impulse

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Zhenguo Luo ◽  
Liping Luo ◽  
Yunhui Zeng
Keyword(s):  
Periodic Solutions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Continuation Theorem ◽  
Coincidence Degree Theory ◽  
Sufficient Condition ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Multiple Periodic Solutions

We consider an impulsive periodic generalized Gause-type predator-prey model with nonmonotonic numerical responses. Using the continuation theorem of coincidence degree theory, we present an easily verifiable sufficient condition on the existence of multiple periodic solutions. As corollaries, some applications are listed. In particular, our results extend and improve some known criteria.

scholarly journals Multiple Periodic Solutions of an Impulsive Population System with Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Wenbo Zhao ◽  
Caochuan Ma ◽  
Lijun Chen
Keyword(s):  
Periodic Solutions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Continuation Theorem ◽  
Coincidence Degree Theory ◽  
Sufficient Condition ◽  
Population System ◽  
Multiple Periodic Solutions

A nonautonomous plant-hare model with impulse is considered. By using the continuation theorem of coincidence degree theory, we present an easily verifiable sufficient condition on the existence of multiple periodic solutions. Though Gao et al. (2014) considered the periodic solutions of plant-hare model, such model with impulses and delay has not been studied in previous paper.

scholarly journals Multiple Positive Periodic Solutions for a Gilpin-Ayala Competition Predator-Prey System with Harvesting Terms

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Yongzhi Liao ◽  
Yongkun Li ◽  
Xiaoyan Dou
Keyword(s):  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Continuation Theorem ◽  
Coincidence Degree Theory ◽  
Positive Periodic Solutions ◽  
Mawhin’S Continuation Theorem ◽  
Predator Prey ◽  
Prey System

By applying Mawhin’s continuation theorem of coincidence degree theory, we study the existence of multiple positive periodic solutions for a Gilpin-Ayala competition predator-prey system with harvesting terms and obtain some sufficient conditions for the existence of multiple positive periodic solutions for the system under consideration. The result of this paper is completely new. An example is employed to illustrate our result.

scholarly journals Existence and Uniqueness of Positive Periodic Solutions for a Delayed Predator-Prey Model with Dispersion and Impulses

2014 ◽  
Vol 2014 ◽  
pp. 1-21
Author(s):  
Zhenguo Luo ◽  
Liping Luo ◽  
Liu Yang ◽  
Zhenghui Gao ◽  
Yunhui Zeng
Keyword(s):  
Periodic Solutions ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Predator Population ◽  
Positive Periodic Solutions ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

An impulsive Lotka-Volterra type predator-prey model with prey dispersal in two-patch environments and time delays is investigated, where we assume the model of patches with a barrier only as far as the prey population is concerned, whereas the predator population has no barriers between patches. By applying the continuation theorem of coincidence degree theory and by means of a suitable Lyapunov functional, a set of easily verifiable sufficient conditions are obtained to guarantee the existence, uniqueness, and global stability of positive periodic solutions of the system. Some known results subject to the underlying systems without impulses are improved and generalized. As an application, we also give two examples to illustrate the feasibility of our main results.

COMPLEXITY OF A DELAYED PREDATOR–PREY MODEL WITH IMPULSIVE HARVEST AND HOLLING TYPE II FUNCTIONAL RESPONSE

2008 ◽  
Vol 11 (01) ◽  
pp. 77-97 ◽  
Author(s):  
GUANGZHAO ZENG ◽  
FENGYAN WANG ◽  
JUAN J. NIETO
Keyword(s):  
Periodic Solutions ◽  
Functional Response ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Type Ii ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Delay Differential ◽  
Type Ii Functional Response

We study an impulsive delay differential predator–prey model with Holling type II functional response. The stability of the trivial equilibrium is analyzed by means of impulsive Floquet theory providing a sufficient condition for extinction. Using coincidence degree theory we show the existence of positive periodic solutions. The system is then analyzed numerically, revealing that the presence of delays and impulses may lead to chaotic solutions, quasi-periodic solutions, or multiple periodic solutions. Several simulations and examples are presented.

scholarly journals Multiple Periodic Solutions to a Kind of Lotka-Volterra Food-Chain System with Delays and Impulses on Time Scales

2012 ◽  
Vol 2012 ◽  
pp. 1-29
Author(s):  
Kaihong Zhao ◽  
Liang Ding ◽  
Fengzao Yang
Keyword(s):  
Periodic Solutions ◽  
Time Scales ◽  
Food Chain ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Continuation Theorem ◽  
Coincidence Degree Theory ◽  
Mawhin’S Continuation Theorem ◽  
Chain System ◽  
Multiple Periodic Solutions

By using Mawhin’s continuation theorem of coincidence degree theory and some skills of inequalities, we establish the existence of at least 2n periodic solutions for a kind of n-species Lotka-Volterra food-chain system with delays and impulses on time scales. One example is given to illustrate the effectiveness of our results.

scholarly journals Periodic Solutions for Gause-Type Ratio-Dependent Predator-Prey Systems with Delays on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Xiaoquan Ding ◽  
Hongyuan Liu ◽  
Fengye Wang
Keyword(s):  
Periodic Solutions ◽  
Time Scales ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Continuation Theorem ◽  
Coincidence Degree Theory ◽  
Predator Prey ◽  
Existence Of Periodic Solutions ◽  
Ratio Dependent

This paper is devoted to periodic Gause-type ratio-dependent predator-prey systems with monotonic or nonmonotonic numerical responses on time scales. By using a continuation theorem based on coincidence degree theory, we establish easily verifiable criteria for the existence of periodic solutions. In particular, our results improve and generalize some known ones.

scholarly journals Positive Periodic Solutions for Neutral Delay Ratio-Dependent Predator-Prey Model with Holling-Tanner Functional Response

2011 ◽  
Vol 2011 ◽  
pp. 1-14
Author(s):  
Guirong Liu ◽  
Sanhu Wang ◽  
Jurang Yan
Keyword(s):  
Periodic Solutions ◽  
Functional Response ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Positive Periodic Solutions ◽  
Neutral Delay ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Ratio Dependent

By using a continuation theorem based on coincidence degree theory, we establish some easily verifiable criteria for the existence of positive periodic solutions for neutral delay ratio-dependent predator-prey model with Holling-Tanner functional responsex'(t)=x(t)[r(t)-a(t)x(t-σ(t))-b(t)x'(t-σ(t))]-c(t)x(t)y(t)/h(t)y(t)+x(t),y'(t)=y(t)d(t)-f(t)y(t-τ(t))/x(t-τ(t)).

scholarly journals Multiple Periodic Solutions of a Nonautonomous Plant-Hare Model

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Yongfei Gao ◽  
P. J. Y. Wong ◽  
Y. H. Xia ◽  
Xiaoqing Yuan
Keyword(s):  
Periodic Solutions ◽  
Functional Response ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Coincidence Degree Theory ◽  
New Technique ◽  
Positive Periodic Solutions ◽  
Multiple Periodic Solutions

Based on Mawhin's coincidence degree theory, sufficient conditions are obtained for the existence of at leasttwopositive periodic solutions for a plant-hare model with toxin-determined functional response (nonmonotone). Some new technique is used in this paper, because standard arguments in the literature are not applicable.

scholarly journals 2 N POSITIVE PERIODIC SOLUTIONS TO N SPECIES NON‐AUTONOMOUS LOTKA‐VOLTERRA UNIDIRECTIONAL FOOD CHAINS WITH HARVESTING TERMS

2010 ◽  
Vol 15 (3) ◽  
pp. 313-326 ◽  
Author(s):  
Yongkun Li ◽  
Kaihong Zhao
Keyword(s):  
Periodic Solutions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Continuation Theorem ◽  
Coincidence Degree Theory ◽  
Food Chains ◽  
Positive Periodic Solutions ◽  
Mawhin Continuation Theorem

By using the Mawhin continuation theorem of coincidence degree theory and some results on inequalities, we establish the existence of 2 n positive periodic solutions for n species non‐autonomous Lotka‐Volterra unidirectional food chains with harvesting terms. Two examples are given to illustrate the effectiveness of our results.

Sign in / Sign up

Export Citation Format

Share Document