Analysis of a stage structured predator-prey Gompertz model with disturbing pulse and delay

Applied Mathematical Modelling

Volumn 33, Issue 11, 2009, Pages 4231-4240

  Wang, Xia ^a   Song, Qiang ^b   Song, Xinyu ^a  

^a XINYANG NORMAL UNIVERSITY   (China)

^b Xinyang Vocational and Technical College   (China)

Author keywords

Permanence; Predator eradication; Predator prey; Stage structure; Time delay

Indexed keywords

DYNAMICS OF SYSTEM; ECOLOGICAL STUDIES; GLOBAL ATTRACTIVITY; GOMPERTZ MODEL; IMPULSIVE CATCHING; MATURATION TIME DELAY; PERIODIC SOLUTION; PERMANENCE; PEST MANAGEMENT; PREDATOR-ERADICATION; PREDATOR-PREY; STAGE STRUCTURE; STAGE STRUCTURED; SUFFICIENT CONDITIONS;

PERIODIC STRUCTURES; TIME DELAY;

MAMMALS;

EID: 67649619205     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2009.03.005     Document Type: Article

References (21)

1. Huffaker C.B. New Technology of Pest Control (1980), Wiley, New York
2. Gourley S.A., and Kuang Y. A stage structured predator-prey model and its dependence on through-stage delay and death rate. J. Math. Biol. 49 (2004) 188-200
3. d'Onofrio A. Pulse vaccination strategy in the SIR epidemic model: global asymptotic stable eradication in presence of vaccine failures. Math. Comput. Modell. 36 (2002) 473-489
4. Jiao J.J., Meng X.Z., and Chen L.L. A stage-structured Holling mass defence predator-prey model with impulsive perturbations on predators. Appl. Math. Comput. 189 (2007) 1448-1458
5. Meng X.Z., Jiao J.J., and Chen L.L. The dynamics of an age structured predator-prey model with disturbing pulse and time delays. Nonlinear Anal. Real World Appl. 9 (2008) 547-561
6. Liu K.Y., Meng X.Z., and Chen L.L. A new stage structured predator-prey Gomportz model with time delay and impulsive perturbations on the prey. Appl. Math. Comput. 196 (2008) 705-719
7. Liu S.Q., Chen L.S., and Luo G.L. Extinction and permanence in competitive stage-structured system with time-delay. Nonlinear Anal. 51 (2002) 1347-1361
8. Liu S.Q., Chen L.S., Luo G.L., and Jiang Y.L. Asymptotic behaviors of competitive Lotka-Volterra system with stage structure. J. Math. Anal. Appl. 271 (2002) 124-138
9. Wang X., and Song X.Y. Mathematical models for the control of a pest population by infected pest. Comput. Math. Appl. 56 (2008) 266-278
10. Song X.Y., and Cui J.A. The stage-structured predator-prey system with delay and harvesting. Appl. Anal. 81 (2002) 1127-1142
11. Liu B., and Chen L.S. The periodic competing Lotka-Volterra model with impulsive effect. IMA J. Math. Med. Biol. 21 (2004) 129-145
12. Liu B., Zhang Y.J., and Chen L.S. The dynamical behaviors of a Lotka-Volterra predator-prey model concerning integrated pest management. Nonlinear Anal. Real World Appl. 6 (2005) 227-243
13. Tang S.Y., and Chen L.S. The effect of seasonal harvesting on stage-structured population models. J. Math. Biol. 48 (2004) 357-374
14. Wang W.D., and Chen L.S. A predator-prey system with stage-structure for predator. Comput. Math. Appl. 33 (1997) 83-91
15. Meng X.Z., Chen L.L., and Li Q.X. The dynamics of a impulsive delay predator-prey model with variable coefficients. Appl. Math. Comput. 198 (2008) 361-374
16. Zhang H., Jiao J.J., and Chen L.L. Pest management through continuous and impulsive control strategies. Biosystems 90 (2007) 350-361
17. Liu X.N., and Ballinger G. Boundedness for impulsive delay differential equations and applications to population growth models. Nonlinear Anal. 53 (2003) 1041-1062
18. Leonid B., and Elena B. Linearized oscillation theory for a nonlinear delay impulsive equation. J. Comput. Appl. Math. 161 (2003) 477-495
19. Yan J.R. Stability for impulsive delay differential equations. Nonlinear Anal. 63 (2005) 66-80
20. Lakshmikantham V., Bainov D., and Simeonov P. Theory of Impulsive Differential Equations (1989), World Scientific, Singapore
21. Kuang Y. Delay Differential Equations with Applications in Population Dynamics (1993), Academic Press, San Diego, CA