Global Stability Analysis of a Nonautonomous Stage-Structured Competitive System with Toxic Effect and Double Maturation Delays
We investigate a nonautonomous two-species competitive system with stage structure and double time delays due to maturation for two species, where toxic effect of toxin liberating species on nontoxic species is considered and the inhibiting effect is zero in absence of either species. Positivity and...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/689573 |
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| _version_ | 1832562789260984320 |
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| author | Chao Liu Yuanke Li |
| author_facet | Chao Liu Yuanke Li |
| author_sort | Chao Liu |
| collection | DOAJ |
| description | We investigate a nonautonomous two-species competitive system with stage structure and double time delays due to maturation for two species, where toxic effect of toxin liberating species on nontoxic species is considered and the inhibiting effect is zero in absence of either species. Positivity and boundedness of solutions are analytically studied. By utilizing some comparison arguments, an iterative technique is proposed to discuss permanence of the species within competitive system. Furthermore, existence of positive periodic solutions is investigated based on continuation theorem of coincidence degree theory. By constructing an appropriate Lyapunov functional, sufficient conditions for global stability of the unique positive periodic solution are analyzed. Numerical simulations are carried out to show consistency with theoretical analysis. |
| format | Article |
| id | doaj-art-184f14c5a3c3487b964ff94cd2f9c2c2 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-184f14c5a3c3487b964ff94cd2f9c2c22025-02-03T01:21:42ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/689573689573Global Stability Analysis of a Nonautonomous Stage-Structured Competitive System with Toxic Effect and Double Maturation DelaysChao Liu0Yuanke Li1Institute of Systems Science, Northeastern University, Shenyang 110004, ChinaInstitute of Systems Science, Northeastern University, Shenyang 110004, ChinaWe investigate a nonautonomous two-species competitive system with stage structure and double time delays due to maturation for two species, where toxic effect of toxin liberating species on nontoxic species is considered and the inhibiting effect is zero in absence of either species. Positivity and boundedness of solutions are analytically studied. By utilizing some comparison arguments, an iterative technique is proposed to discuss permanence of the species within competitive system. Furthermore, existence of positive periodic solutions is investigated based on continuation theorem of coincidence degree theory. By constructing an appropriate Lyapunov functional, sufficient conditions for global stability of the unique positive periodic solution are analyzed. Numerical simulations are carried out to show consistency with theoretical analysis.http://dx.doi.org/10.1155/2014/689573 |
| spellingShingle | Chao Liu Yuanke Li Global Stability Analysis of a Nonautonomous Stage-Structured Competitive System with Toxic Effect and Double Maturation Delays Abstract and Applied Analysis |
| title | Global Stability Analysis of a Nonautonomous Stage-Structured Competitive System with Toxic Effect and Double Maturation Delays |
| title_full | Global Stability Analysis of a Nonautonomous Stage-Structured Competitive System with Toxic Effect and Double Maturation Delays |
| title_fullStr | Global Stability Analysis of a Nonautonomous Stage-Structured Competitive System with Toxic Effect and Double Maturation Delays |
| title_full_unstemmed | Global Stability Analysis of a Nonautonomous Stage-Structured Competitive System with Toxic Effect and Double Maturation Delays |
| title_short | Global Stability Analysis of a Nonautonomous Stage-Structured Competitive System with Toxic Effect and Double Maturation Delays |
| title_sort | global stability analysis of a nonautonomous stage structured competitive system with toxic effect and double maturation delays |
| url | http://dx.doi.org/10.1155/2014/689573 |
| work_keys_str_mv | AT chaoliu globalstabilityanalysisofanonautonomousstagestructuredcompetitivesystemwithtoxiceffectanddoublematurationdelays AT yuankeli globalstabilityanalysisofanonautonomousstagestructuredcompetitivesystemwithtoxiceffectanddoublematurationdelays |