Stability and Hopf bifurcation of a delay eco‐epidemiological model with nonlinear incidence rate
In this paper, a three‐dimensional eco‐epidemiological model with delay is considered. The stability of the two equilibria, the existence of Hopf bifurcation and the permanence are investigated. It is found that Hopf bifurcation occurs when the delay τ passes a sequence of critical values. Moreover,...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Vilnius Gediminas Technical University
2010-11-01
|
| Series: | Mathematical Modelling and Analysis |
| Subjects: | |
| Online Access: | https://journals.vgtu.lt/index.php/MMA/article/view/6043 |
| _version_ | 1818787349288452096 |
|---|---|
| author | Xueyong Zhou Jingan Cui |
| author_facet | Xueyong Zhou Jingan Cui |
| author_sort | Xueyong Zhou |
| collection | DOAJ |
| description | In this paper, a three‐dimensional eco‐epidemiological model with delay is considered. The stability of the two equilibria, the existence of Hopf bifurcation and the permanence are investigated. It is found that Hopf bifurcation occurs when the delay τ passes a sequence of critical values. Moreover, by applying Nyquist criterion, the length of delay is estimated for which the stability continues to hold. Numerical simulation with a hypothetical set of data has been done to support the analytical results.
This work is supported by the National Natural Science Foundation of China (No. 10771104 and No.10471117), Program for Innovative Research Team (in Science and Technology) in University of Henan Province (No. 2010IRTSTHN006) and Program for Key Laboratory of Simulation and Control for Population Ecology in Xinyang Normal University (No. 201004) and Natural Science Foundation of the Education Department of Henan Province (No. 2009B1100200 and No. 2010A110017)
First published online: 10 Feb 2011 |
| first_indexed | 2024-12-18T14:06:22Z |
| format | Article |
| id | doaj.art-8f126f80144b469f931b804e229e80f9 |
| institution | Directory Open Access Journal |
| issn | 1392-6292 1648-3510 |
| language | English |
| last_indexed | 2024-12-18T14:06:22Z |
| publishDate | 2010-11-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj.art-8f126f80144b469f931b804e229e80f92022-12-21T21:05:13ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102010-11-0115410.3846/1392-6292.2010.15.547-569Stability and Hopf bifurcation of a delay eco‐epidemiological model with nonlinear incidence rateXueyong Zhou0Jingan Cui1School of Mathematical Sciences, Nanjing Normal University Nanjing 210046, Jiangsu, P.R. China; College of Mathematics and Information Science, Xinyang Normal University Xinyang 464000, Henan, P.R. ChinaSchool of Science, Beijing University of Civil Engineering and Architecture Beijing 100044, P.R.ChinaIn this paper, a three‐dimensional eco‐epidemiological model with delay is considered. The stability of the two equilibria, the existence of Hopf bifurcation and the permanence are investigated. It is found that Hopf bifurcation occurs when the delay τ passes a sequence of critical values. Moreover, by applying Nyquist criterion, the length of delay is estimated for which the stability continues to hold. Numerical simulation with a hypothetical set of data has been done to support the analytical results. This work is supported by the National Natural Science Foundation of China (No. 10771104 and No.10471117), Program for Innovative Research Team (in Science and Technology) in University of Henan Province (No. 2010IRTSTHN006) and Program for Key Laboratory of Simulation and Control for Population Ecology in Xinyang Normal University (No. 201004) and Natural Science Foundation of the Education Department of Henan Province (No. 2009B1100200 and No. 2010A110017) First published online: 10 Feb 2011https://journals.vgtu.lt/index.php/MMA/article/view/6043predator‐prey modeleco‐epidemiologydelayHopf bifurcation |
| spellingShingle | Xueyong Zhou Jingan Cui Stability and Hopf bifurcation of a delay eco‐epidemiological model with nonlinear incidence rate Mathematical Modelling and Analysis predator‐prey model eco‐epidemiology delay Hopf bifurcation |
| title | Stability and Hopf bifurcation of a delay eco‐epidemiological model with nonlinear incidence rate |
| title_full | Stability and Hopf bifurcation of a delay eco‐epidemiological model with nonlinear incidence rate |
| title_fullStr | Stability and Hopf bifurcation of a delay eco‐epidemiological model with nonlinear incidence rate |
| title_full_unstemmed | Stability and Hopf bifurcation of a delay eco‐epidemiological model with nonlinear incidence rate |
| title_short | Stability and Hopf bifurcation of a delay eco‐epidemiological model with nonlinear incidence rate |
| title_sort | stability and hopf bifurcation of a delay eco epidemiological model with nonlinear incidence rate |
| topic | predator‐prey model eco‐epidemiology delay Hopf bifurcation |
| url | https://journals.vgtu.lt/index.php/MMA/article/view/6043 |
| work_keys_str_mv | AT xueyongzhou stabilityandhopfbifurcationofadelayecoepidemiologicalmodelwithnonlinearincidencerate AT jingancui stabilityandhopfbifurcationofadelayecoepidemiologicalmodelwithnonlinearincidencerate |