Stability and Hopf bifurcation analysis of an eco-epidemiological model with delay

Journal of the Franklin Institute

Volumn 347, Issue 9, 2010, Pages 1654-1680

  Zhou, Xueyong ^a,b   Cui, Jingan ^c  

^a NANJING NORMAL UNIVERSITY   (China)

^b XINYANG NORMAL UNIVERSITY   (China)

^c BEIJING UNIVERSITY OF CIVIL ENGINEERING AND ARCHITECTURE   (China)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTICAL STABILITY; BIFURCATION PERIODIC SOLUTIONS; CENTER MANIFOLD THEORY; CRITICAL VALUE; EPIDEMIOLOGICAL MODELS; EXPLICIT FORMULA; HOPF BIFURCATION ANALYSIS; NORMAL FORM THEORY; NUMERICAL SIMULATION; PLANAR EQUILIBRIUM; POSITIVE EQUILIBRIUM; STABILITY SWITCH;

STABILITY;

HOPF BIFURCATION;

EID: 77958089819     PISSN: 00160032     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jfranklin.2010.08.001     Document Type: Article

References (21)

1. E. Beretta, and Y. Kuang Geometric stability switch criteria in delay differential systems with delay dependent parameters SIAM J. Math. Anal. 33 2002 1144 1165
2. J. Chattopadhyay, and O. Arino A predatorprey model with disease in the prey Nonlinear Anal. 36 1999 747 766
3. J. Chattopadhyay, and N. Bairagi Pelicans at risk in Salton Seaan eco-epidemiological model Ecol. Modelling 136 2001 103 112
4. D. Greenhalgh Some results for a SEIR epidemic model with density dependence in the death rate IMA J. Math. Appl. Med. Biol. 9 1992 67 106
5. J.K. Hale Theory of Functional Differential Equations 1977 Springer-Verlag New York/Heidelberg/Berlin
6. B. Hassard, N. Kazarinoff, and Y. Wan Theory and Application of Hopf Bifurcation 1981 Cambridge University Press Cambridge
7. N.D. Hayes Roots of the transcendental equation associated with a certain difference-differential equation J. London Math. Soc. 25 1950 226 232
8. S.B. Hsu, and T.W. Hwang Hopf bifurcation analysis for a predatorprey system of Holling and Leslie type Taiwan J. Math. 3 1999 35 53
9. X.C. Huang Stability of a general predatorprey model J. Franklin Inst. 327 5 1990 751 769
10. T.W. Hwang Uniqueness of limit cycle for Gause-type predatorprey systems J. Math. Anal. Appl. 238 1999 179 195
11. W. Krajewski, and U. Viaro Locating the equilibrium points of a predatorprey model by means of affine state feedback J. Franklin Inst. 345 5 2008 489 498
12. Y. Kuang Delay Differential Equations with Applications in Population Dynamics 1993 Academic Press San Diego
13. Y. Kuang, and E. Beretta Global qualitative analysis of a ratio-dependent predatorprey system J. Math. Biol. 36 1998 389 406
14. M.Y. Li, H.L. Smith, and L. Wang Global dynamics of an SEIR epidemic model with vertical transmission SIAM J. Appl. Math. 62 2001 58 69
15. C. Liu, Q.L. Zhang, and X.D. Duan Dynamical behavior in a harvested differential-algebraic prey-predator model with discrete time delay and stage structure J. Franklin Inst. 346 10 2009 1038 1059
16. W.M. Liu, H.W. Hethcote, and S.A. Levin Dynamical behavior of epidemiological models with nonlinear incidence rate J. Math. Biol. 25 1987 359 380
17. Y. Qu, and J.J. Wei Bifurcation analysis in a predatorprey system with stage-structure and harvesting J. Franklin Inst. 347 7 2010 1097 1113
18. S.G. Ruan, and J.J. Wei On the zeros of a third degree exponential polynomial with applications to a delayed model for the control of testosterone secretion IMA J. Math. Appl. Med. Biol. 18 2001 41 52
19. Y.N. Xiao, and L.S. Chen Analysis of a three species eco-epidemiological model J. Math. Anal. Appl. 258 2 2001 733 754
20. X. Zhang, Q.L. Zhang, and V. Sreeram Bifurcation analysis and control of a discrete harvested prey-predator system with BeddingtonDeAngelis functional response J. Franklin Inst. 347 7 2010 1076 1096
21. X.Y. Zhou, X.Y. Shi, and X.Y. Song Analysis of a delay prey-predator model with disease in the prey species only J. Korean Math. Soc. 46 4 2009 713 731