Double Periodic Solutions for a Ratio-Dependent Predator-Prey System with Harvesting Terms on Time Scales

Double Periodic Solutions for a Ratio-Dependent Predator-Prey System with Harvesting Terms on Time Scales

We investigate a nonautonomous ratio-dependent predator-prey model with Beddington-DeAngelis functional response and multiple harvesting (or exploited) terms on time scales. By means of using a continuation theorem based on coincidence degree theory, we obtain sufficient criteria for the existence o...

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Main Author: Zhenjie Liu
Format: Article
Language:English
Published: Hindawi Limited 2009-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2009/243974
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spelling doaj-d66f18e5dd9144ffbc7938ce30b195542020-11-24T23:18:48ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2009-01-01200910.1155/2009/243974243974Double Periodic Solutions for a Ratio-Dependent Predator-Prey System with Harvesting Terms on Time ScalesZhenjie Liu0School of Mathematics and Computer, Harbin University, Harbin, Heilongjiang 150086, ChinaWe investigate a nonautonomous ratio-dependent predator-prey model with Beddington-DeAngelis functional response and multiple harvesting (or exploited) terms on time scales. By means of using a continuation theorem based on coincidence degree theory, we obtain sufficient criteria for the existence of at least two periodic solutions for the system. Moreover, when the time scale 𝕋 is chosen as ℝ or ℤ, the existence of the periodic solutions of the corresponding continuous and discrete models follows. Therefore, the methods are unified to provide the existence of the desired solutions for the continuous differential equations and discrete difference equations.http://dx.doi.org/10.1155/2009/243974
collection DOAJ
language English
format Article
sources DOAJ
author Zhenjie Liu
spellingShingle Zhenjie Liu
Double Periodic Solutions for a Ratio-Dependent Predator-Prey System with Harvesting Terms on Time Scales
Discrete Dynamics in Nature and Society
author_facet Zhenjie Liu
author_sort Zhenjie Liu
title Double Periodic Solutions for a Ratio-Dependent Predator-Prey System with Harvesting Terms on Time Scales
title_short Double Periodic Solutions for a Ratio-Dependent Predator-Prey System with Harvesting Terms on Time Scales
title_full Double Periodic Solutions for a Ratio-Dependent Predator-Prey System with Harvesting Terms on Time Scales
title_fullStr Double Periodic Solutions for a Ratio-Dependent Predator-Prey System with Harvesting Terms on Time Scales
title_full_unstemmed Double Periodic Solutions for a Ratio-Dependent Predator-Prey System with Harvesting Terms on Time Scales
title_sort double periodic solutions for a ratio-dependent predator-prey system with harvesting terms on time scales
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1026-0226
1607-887X
publishDate 2009-01-01
description We investigate a nonautonomous ratio-dependent predator-prey model with Beddington-DeAngelis functional response and multiple harvesting (or exploited) terms on time scales. By means of using a continuation theorem based on coincidence degree theory, we obtain sufficient criteria for the existence of at least two periodic solutions for the system. Moreover, when the time scale 𝕋 is chosen as ℝ or ℤ, the existence of the periodic solutions of the corresponding continuous and discrete models follows. Therefore, the methods are unified to provide the existence of the desired solutions for the continuous differential equations and discrete difference equations.
url http://dx.doi.org/10.1155/2009/243974
work_keys_str_mv AT zhenjieliu doubleperiodicsolutionsforaratiodependentpredatorpreysystemwithharvestingtermsontimescales
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