Staged-structured Lotka-Volterra predator-prey models for pest management

Applied Mathematics and Computation

Volumn 203, Issue 1, 2008, Pages 258-265

  Shi, Ruiqing ^a,b   Chen, Lansun ^a  

^a DALIAN UNIVERSITY OF TECHNOLOGY   (China)

^b SHANXI NORMAL UNIVERSITY   (China)

Author keywords

Biological control; Impulsive; Pest eradication equilibrium; Pest eradication periodic solution; Stage structured

Indexed keywords

IMPULSE RESPONSE; PERTURBATION TECHNIQUES; PHASE EQUILIBRIA;

AMPLITUDE PERTURBATION; BIOLOGICAL CONTROL; BIOLOGICAL CONTROLS; COMPARISON TECHNIQUES; FLOQUET'S THEOREM; GLOBAL ASYMPTOTICAL STABILITY; IMPULSIVE; IMPULSIVE SYSTEMS; LIAPUNOV STABILITY; LOCAL STABILITY; LOTKA-VOLTERRA; PERIODIC SOLUTIONS; PEST MANAGEMENT; PEST-ERADICATION EQUILIBRIUM; PEST-ERADICATION PERIODIC SOLUTION; PREDATOR-PREY MODELING; STAGE STRUCTURED; STAGE STRUCTURES; SUFFICIENT CONDITIONS; TRIVIAL EQUILIBRIUM;

SYSTEM STABILITY;

EID: 50249100273     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2008.04.032     Document Type: Article

References (19)

1. Song X.Y., and Chen L.S. Optimal harvesting policy and stability for single-species growth model with stage structure. Journal of Systems Science and Complexity 15 (2002) 194-201
2. Xiao Y.N., and Chen L.S. Stabilizing effect of cannibalism on a structured competitive system. Acta Mathematics 22A 2 (2002) 210-216 (in Chinese)
3. Song X.Y., and Chen L.S. Modelling and analysis of a single-species system with stage structure and harvesting. Mathematics and Computer Modelling 36 (2002) 67-82
4. Song X.Y., and Chen L.S. Optimal harvesting and stability for a predator-prey system with stage structure. Acta Mathematical Applicate Sinica 18 (2002) 423-430
5. Lu Z.H., and Chen L.S. Global attractivity of nonautonomous inshore-offshore fishing models with stage-structure. Applicable Analysis 81 (2002) 589-605
6. Liu S.Q., Chen L.S., and Agarwal R. Recent progress on stage-structured population dynamics. Mathematics and Computer Modelling 36 (2002) 1319-1360
7. Liu S.Q., Chen L.S., and Liu Z.J. Extinction and permanence in nonautonomous competitive system with stage structure. Journal of Mathematical Analysis and Applications 274 (2002) 667-684
8. Liu S.Q., Chen L.S., and Luo G.L. Extinction and permance in competitive stage-structured system with time delays. Nonlinear Analysis 51 (2002) 1347-1361
9. Tang S.Y., and Chen L.S. Multiple attractors in stage-structured population models with birth pulses. Bulletin of Mathematical Biology 65 (2003) 479-495
10. Xiao Y.N., and Chen L.S. On an SIS epidemic model with stage structure. Journal of Systems Science and Complexity 16 (2003) 275-288
11. Xiao Y.N., and Chen L.S. An SIS epidemic models with stage structure and a delay. Acta Mathematical Applicate Sinica (English Series) 18 4 (2002) 607-618
12. Aiello W.G., and Freedman H.I. A time delay model of single-species growth with stage structure. Mathematical Biosciences 101 (1990) 139-153
13. Aiello W.G., Freedman H.I., and Wu J. Analysis of a model representing stage-structured population growth with state-dependent time delay. SIAM Journal on Applied Mathematics 52 (1992) 855-869
14. Wang W.D., and Chen L.S. A predator-prey system with stage structure for predator. Computers Mathematics with Applications 33 (1997) 83-91
15. In: Lakshmikantham V., Bainov D.D., and Simeonov P. (Eds). Theory of Impulsive Differential Equations (1989), World Scientific, Singapore
16. D. Bainov, P. Simeonov (Eds.), Impulsive Differential Equations: Periodic Solutions and Applications, Pitman Monographs and Surveys in Pure and Applied Mathematics, vol. 66, 1993.
17. Xiao Y.N., Chen L.S., and Bosh F.V.D. Dynamical behavior for stage-structured SIR infectious disease model. Nonlinear Analysis: RWA 3 (2002) 175-190
18. Lu Z.H., Gang S.J., and Chen L.S. Analysis of an SI epidemic with nonlinear transmission and stage structure. Acta Mathematics Sinica 4 (2003) 440-446
19. Liu X.N., and Chen L.S. Complex dynamics of Holling type II Lotka-Volterra predator-prey system with impulsive perturbations on the predator. Chaos Solitons and Fractals 16 (2003) 311-320