Positive Periodic Solutions for Neutral Delay Ratio-Dependent Predator-Prey Model with Holling-Tanner Functional Response
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 response x'(t)=x(t)[r(t)-a(t)x(t-σ(t))-b(t)x...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2011/376862 |
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| _version_ | 1832552393566322688 |
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| author | Guirong Liu Sanhu Wang Jurang Yan |
| author_facet | Guirong Liu Sanhu Wang Jurang Yan |
| author_sort | Guirong Liu |
| collection | DOAJ |
| description | 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 response x'(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)). |
| format | Article |
| id | doaj-art-d2692531d97144e69cbf7ca82e1b88cf |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-d2692531d97144e69cbf7ca82e1b88cf2025-02-03T05:58:46ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252011-01-01201110.1155/2011/376862376862Positive Periodic Solutions for Neutral Delay Ratio-Dependent Predator-Prey Model with Holling-Tanner Functional ResponseGuirong Liu0Sanhu Wang1Jurang Yan2School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, ChinaDepartment of Computer, Luliang University, Luliang, Shanxi 033000, ChinaSchool of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, ChinaBy 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 response x'(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)).http://dx.doi.org/10.1155/2011/376862 |
| spellingShingle | Guirong Liu Sanhu Wang Jurang Yan Positive Periodic Solutions for Neutral Delay Ratio-Dependent Predator-Prey Model with Holling-Tanner Functional Response International Journal of Mathematics and Mathematical Sciences |
| title | Positive Periodic Solutions for Neutral Delay Ratio-Dependent Predator-Prey Model with Holling-Tanner Functional Response |
| title_full | Positive Periodic Solutions for Neutral Delay Ratio-Dependent Predator-Prey Model with Holling-Tanner Functional Response |
| title_fullStr | Positive Periodic Solutions for Neutral Delay Ratio-Dependent Predator-Prey Model with Holling-Tanner Functional Response |
| title_full_unstemmed | Positive Periodic Solutions for Neutral Delay Ratio-Dependent Predator-Prey Model with Holling-Tanner Functional Response |
| title_short | Positive Periodic Solutions for Neutral Delay Ratio-Dependent Predator-Prey Model with Holling-Tanner Functional Response |
| title_sort | positive periodic solutions for neutral delay ratio dependent predator prey model with holling tanner functional response |
| url | http://dx.doi.org/10.1155/2011/376862 |
| work_keys_str_mv | AT guirongliu positiveperiodicsolutionsforneutraldelayratiodependentpredatorpreymodelwithhollingtannerfunctionalresponse AT sanhuwang positiveperiodicsolutionsforneutraldelayratiodependentpredatorpreymodelwithhollingtannerfunctionalresponse AT jurangyan positiveperiodicsolutionsforneutraldelayratiodependentpredatorpreymodelwithhollingtannerfunctionalresponse |