Species permanence and dynamical behavior analysis of an impulsively controlled ecological system with distributed time delay

Computers and Mathematics with Applications

Volumn 59, Issue 12, 2010, Pages 3824-3835

  Yu, Hengguo ^a   Zhong, Shouming ^a   Agarwal, Ravi P ^b,c   Xiong, Lianglin ^d  

^a UNIVERSITY OF ELECTRONIC SCIENCE AND TECHNOLOGY OF CHINA   (China)

^b Florida Institute of Technology ^*  (United States)

^c KING FAHD UNIVERSITY OF PETROLEUM AND MINERALS   (Saudi Arabia)

^d YUNNAN MINZU UNIVERSITY   (China)

Author keywords

Distributed time delay; Dynamical behavior; Globally asymptotically stable; Impulsive harvest; Periodic solution; The largest Lyapunov exponent

Indexed keywords

DISTRIBUTED TIME DELAYS; DYNAMICAL BEHAVIORS; GLOBALLY ASYMPTOTICALLY STABLE; LARGEST LYAPUNOV EXPONENT; PERIODIC SOLUTION;

ASYMPTOTIC ANALYSIS; BIFURCATION (MATHEMATICS); CASCADE CONTROL SYSTEMS; DYNAMICS; ECOLOGY; HARVESTING; LYAPUNOV FUNCTIONS; ORDINARY DIFFERENTIAL EQUATIONS; PROBLEM SOLVING; STRUCTURES (BUILT OBJECTS); TIME DELAY;

LYAPUNOV METHODS;

EID: 77953229337     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2010.04.018     Document Type: Article

References (30)

1. Holt R.D. Predation, apparent competition, and the structure of prey communities. Theor. Popul. Biol. 12 (1977) 197-229
2. Holt R.D. On the evolutionary stability of sink populations. Evol. Ecol. 11 (1997) 723-731
3. Holt R.D. Spatial heterogeneity, indirect interactions, and the coexistence of prey species. Am. Nat. 124 (1984) 377-406
4. Holt R.D., and Lawton J.H. The ecological consequences of shared nature enemies. Annu. Rev. Ecol. Syst. 25 (1994) 495-520
5. Kar T.K. Stability analysis of a prey-predator model in corporating a prey refuge. Commun. Nonlinear Sci. Numer. Simul. 10 (2005) 681-691
6. Gakkhar S., and Naji R.K. Order and chaos in s food web consisting of a predator and two independent preys. Commun. Nonlinear Sci. Numer. Simul. 10 (2005) 105-120
7. Harmon J.P., and Andow D.A. Indirect effects between shared prey, predictions for biological control. Biocontrol 49 (2004) 605-626
8. Wang H., and Wang W. The dynamical complexity of a Ivler-type prey-predator system with impulsive effect. Chaos Solitons Fractals 38 (2008) 1168-1176
9. Pang G., and Chen L. Dynamic analysis of a pest-epidemic model with impulsive control. Math. Comput. Simulation 79 (2008) 72-84
10. Wang X., and Song X. Mathematical models for the control of a pest population by infected pest. Comput. Math. Appl. 56 (2008) 266-278
11. Dong L., and Chen L. Opitmal harvesting policies for periodic Gompertz systems. Nonlinear Anal. RWA 8 (2007) 572-578
12. Wang W., Wang H., and Li Z. Chaotic behavior of a three-species Beddington-type system with impulsive perturbation. Chaos Solitons Fractals 37 (2008) 438-443
13. Georgescu P., Zhang H., and Chen L. Bifurcation of nontrivial periodic solution for an impulsively controlled pest management model. Appl. Math. Comput. 202 (2008) 675-685
14. Song X., and Li Y. Dynamic behavior of the periodic predator-prey model with modified Leslie-Gower Holling-type II schemes and impulsive effects. Nonlinear Anal. RWA 9 (2008) 64-79
15. Lakshmikantham V., Bainov D.D., and Simeonov P.C. Theory of Impulsive Differential Equations (1989), World Scientific, Singapore
16. Bainov D.D., and Simeonov P.C. Impulsive Differential Equations: Asymptotic Properties of the Solutions (1993), World Scientific, Singapore
17. Zhang H., Chen L., and Jiao J. A delayed epidemic model with stage-structure and pulses for pest management strategy. Nonlinear Anal. RWA 9 (2008) 1714-1726
18. Guo H., and Chen L. The effects of impulsive harvest on a predator-prey system with distributed time delay. Commun. Nonlinear Sci. Numer. Simul. 14 (2009) 2301-2309
19. Zhang H., Georgescu P., and Chen L. An impulsive predator-prey system with Beddington-DeAngelis functional response and time delay. Int. J. Biomath. 1 (2008) 1-17
20. Grond F., Diebner H.H., Sahle S., and Mathias A. A robust, locally interpretable algorithm for Lyapunov exponents. Chaos Solitons Fractals 16 (2003) 841-852
21. Sportt J.G. Chaos and Time-Series Analysis (2003), Oxford University Press pp. 116-117
22. Rosenstein M.T., Collins J.J., and De Luca C.J. A practical method for calculating largest Lyapunov exponents from small data sets. Physica D 65 (1993) 117-134
23. Lv S., and Zhao M. The dynamic complexity of a three species food chain model. Chaos Solitons Fractals 37 (2008) 1469-1480
24. Lv S., and Zhao M. The dynamic complexity of a host-parasitoid model with a lower bound for the host. Chaos Solitons Fractals 36 (2008) 911-919
25. Yu H., Zhao M., Lv S., and Zhu L. Dynamic complexity of a parasitoid-host-parasitoid ecological model. Chaos Solitons Fractals 39 (2009) 39-48
26. Zhao M., Yu H.G., and Zhu J. Effects of a population floor on the persistence of chaos in a mutual interference host-parasitoid model. Chaos Solitons Fractals 42 (2009) 1245-1250
27. Zhao M., and Zhang L.M. Permanence and chaos in a host-parasitoid model with prolonged diapause for the host. Commun. Nonlinear Sci. Numer. Simul. 14 (2009) 4197-4203
28. Zhao M., and Lv S.J. Chaos in a three-species food chain model with a Beddington-DeAngelis functional response. Chaos Solitons Fractals 50 (2009) 1622-1635
29. Talebinejad M., Chan A.D.C., Miri A., and Dansereau R.M. Fractal analysis of surface electromyography signals: a novel power spectrum-based method. J. Electromyogr. Kines. 19 (2009) 840-850
30. Masoller C., Sicaedi schifino A.C., and Romanelli L. Charaterization of strange attractors of Lorenz model of general circulation of the atmospher. Chaos Solitons Fractals 6 (1995) 357-366