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.

EXISTENCE OF MULTIPLE PERIODIC SOLUTIONS TO LOTKA–VOLTERRA NETWORK-LIKE FOOD-CHAIN SYSTEM WITH DELAYS AND IMPULSES ON TIME SCALES

2014 ◽  
Vol 07 (01) ◽  
pp. 1450003 ◽  
Author(s):  
KAIHONG ZHAO ◽  
LIANG DING ◽  
FENGZAO YANG
Keyword(s):  
Periodic Solutions ◽  
Time Scales ◽  
Food Chain ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Continuation Theorem ◽  
Mawhin’S Continuation Theorem ◽  
Chain System ◽  
Multiple Periodic Solutions ◽  
General Kind

In this paper, we have studied a general kind of n-species Lotka–Volterra network-like food-chain system with delays and impulses on time scales. Applying Mawhin's continuation theorem of coincidence degree theory and some skills of inequalities, some sufficient criteria have been established to guarantee the existence of at least 2n periodic solutions to this model. One example is given to illustrate the effectiveness of our results.

MULTIPLE POSITIVE PERIODIC SOLUTIONS TO m-LAYER PERIODIC LOTKA–VOLTERRA NETWORK-LIKE MULTIDIRECTIONAL FOOD-CHAIN WITH HARVESTING TERMS

2011 ◽  
Vol 09 (01) ◽  
pp. 71-96 ◽  
Author(s):  
YONGKUN LI ◽  
KAIHONG ZHAO
Keyword(s):  
Periodic Solutions ◽  
Food Chain ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Continuation Theorem ◽  
Coincidence Degree Theory ◽  
Positive Periodic Solutions ◽  
Mawhin’S Continuation Theorem

An m-layer peiodic Lotka–Volterra network-like multidirectional food-chain with harvesting terms is proposed in this paper. By applying Mawhin's continuation theorem of coincidence degree theory and some skills of the inequalities, sufficient conditions which guarantee the existence of [Formula: see text] positive periodic solutions of the system are obtained. An example is given to illustrate the effectiveness of our results.

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 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 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 Existence of Multiple Positive Periodic Solutions to Two Species Parasitical Model with Impulsive Effects and Harvesting Terms

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Zhouhong Li
Keyword(s):  
Periodic Solutions ◽  
Positive Solutions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Continuation Theorem ◽  
Impulsive Effects ◽  
Coincidence Degree Theory ◽  
Positive Periodic Solutions ◽  
Mawhin’S Continuation Theorem

By applying Mawhin’s continuation theorem of coincidence degree theory and some skills of inequalities, we establish the existence of four positive solutions for two species parasitical system with impulsive effects and harvesting terms. Finally, an example is given to illustrate the effectiveness of our results.

scholarly journals Positive periodic solutions of a discrete mutualism model with time delays

2005 ◽  
Vol 2005 (4) ◽  
pp. 499-506 ◽  
Author(s):  
Yongkun Li
Keyword(s):  
Periodic Solutions ◽  
Time Delays ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Continuation Theorem ◽  
Coincidence Degree Theory ◽  
Positive Periodic Solutions ◽  
Mawhin’S Continuation Theorem ◽  
Mutualism Model

A discrete periodic mutualism model with time delays is investigated. By using Gaines and Mawhin's continuation theorem of coincidence degree theory, the existence of positive periodic solutions of the model is established.

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.

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