Existence and attractivity of a periodic solution for a ratio-dependent Leslie system with feedback controls

Nonlinear Analysis: Real World Applications

Volumn 12, Issue 1, 2011, Pages 24-33

  Wang, Qi ^a   Jizhou, ^a   Wang, Zhijie ^a   Ding, Minmin ^a   Zhang, Hongyan ^a  

^a ANHUI UNIVERSITY   (China)

Author keywords

Coincidence degree; Global attractivity; Leslie system; Lyapunov functional; Periodic solution; Ratio dependent

Indexed keywords

COINCIDENCE DEGREE; GLOBAL ATTRACTIVITY; LESLIE SYSTEM; LYAPUNOV FUNCTIONALS; PERIODIC SOLUTION; RATIO-DEPENDENT;

FEEDBACK CONTROL; LYAPUNOV FUNCTIONS;

PROBLEM SOLVING;

EID: 77958016606     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2010.05.032     Document Type: Article

References (37)

1. P.H. Leslie Some further notes on the use of matrices in population mathematics Biometrika 35 1948 213 245
2. Haifeng Huo, and Wantong Li Stable periodic solution of the discrete periodic LeslieNewer predatorprey model Mathematical and Computer Modelling 40 2004 261 269
3. F.D. Chen Permanence in nonautonomous multi-species predatorprey system with feedback controls Computers & Mathematics with Applications 173 2006 694 709
4. Hongjian Guo, and Xinyu Song An impulsive predatorprey system with modified LeslieGower and Holling type II schemes Chaos, Solitons and Fractals 36 2008 1320 1331
5. Yiping Chen, Zhijun Liu, and Mainul Haque Analysis of a LeslieGower-type preypredator model with periodic impulsive perturbations Communications in Nonlinear Science and Numerical Simulation 14 2009 3412 3423
6. A.F. Nindjin, M.A. Aziz-Alaoui, and M. Cadivel Analysis of a predatorprey model with modified LeslieGower and Hollingtype II schemes with time delay Nonlinear Analysis: Real World Applications 7 2006 1104 1118
7. Yongli Song, Sanling Yuan, and Jianming Zhang Bifurcation analysis in the delayed LeslieGower predatorprey system Applied Mathematical Modelling 33 2009 4049 4061
8. Yilong Li, and Dongmei Xiao Bifurcations of a predatorprey system of Holling, and Leslie types Chaos, Solitons and Fractals 34 2007 606 620
9. M.A. Aziz-Alaoui, and M. Daher Okiye Boundedness and global stability for a predatorprey model with modified LeslieGower and Holling-type II schemes Applied Mathematics Letters 16 2003 1069 1075
10. Tapan Saha, and Charugopal Chakrabarti Dynamical analysis of a delayed ratio-dependent HollingTanner predatorprey model Journal of Mathematical Analysis and Applications 358 2009 389 402
11. Sunita Gakkhar, and Brahampal Singh Dynamics of modified LeslieGower-type preypredator model with seasonally varying parameters Chaos, Solitons and Fractals 27 2006 1239 1255
12. Yihong Du, Rui Peng, and Mingxin Wang Effect of a protection zone in the diffusive Leslie predatorprey model Journal of Differential Equations 246 2009 3932 3956
13. Fei Chen, and Xiaohong Cao Existence of almost periodic solution in a ratio-dependent Leslie system with feedback controls Journal of Mathematical Analysis and Applications 341 2008 1399 1412
14. Liujuan Chen, and Fengde Chen Global stability of a LeslieGower predatorprey model with feedback controls Applied Mathematics Letters 22 2009 1330 1334
15. Radouane Yafia, Fatiha El Adnani, and Hamad Talibi Alaoui Limit cycle and numerical similations for small and large delays in a predatorprey model with modified LeslieGower and Holling-type II schemes Nonlinear Analysis: Real World Applications 9 2008 2055 2067
16. Fengde Chen, Liujuan Chen, and Xiangdong Xie On a LeslieGower predatorprey model incorporating a prey refuge Nonlinear Analysis: Real World Applications 10 2009 2905 2908
17. Sanling Yuan, and Yongli Song Stability and Hopf bifurcations in a delayed LeslieGower predatorprey system Journal of Mathematical Analysis and Applications 355 2009 82 100
18. M.A. Aziz-Alaoui Study of a LeslieGower-type tritrophic population model Chaos, Solitons and Fractals 14 2002 1275 1293
19. Pablo Aguirre, Eduardo Gonz'alez-Olivares, and Eduardo S'aez Two limit cycles in a LeslieGower predatorprey model with additive Allee effect Nonlinear Analysis: Real World Applications 10 2009 1401 1416
20. Chunyan Ji, Daqing Jiang, and Ningzhong Shi Analysis of a predatorprey model with modified LeslieGower and Holling-type II schemes with stochastic perturbation Journal of Mathematical Analysis and Applications 359 2009 482 498
21. A.F. Nindjin, and M.A. Aziz-Alaoui Persistence and global stability in a delayed LeslieGower type three species food chain Journal of Mathematical Analysis and Applications 340 2008 340 357
22. Haifeng Huo, and Wantong Li Periodic solutions of delayed LeslieGower predatorprey models Applied Mathematics and Computation 155 2004 591 605
23. Xiaoquan Ding, and Jifa Jiang Periodicity in a generalized semi-ratio-dependent predatorprey system with time delays and impulses Journal of Mathematical Analysis and Applications 360 2009 223 234
24. Xiaoquan Ding, and Fangfang Wang Positive periodic solution for a semi-ratio-dependent predatorprey system with diffusion and time delays Nonlinear Analysis: Real World Applications 9 2008 239 249
25. Xinyu Song, and Yongfeng Li Dynamic behaviors of the periodic predatorprey model with modified LeslieGower Holling-type II schemes and impulsive effect Nonlinear Analysis: Real World Applications 9 2008 64 79
26. S.B. Hsu, and T.W. Huang Global stability for a class of predatorprey system SIAM Journal on Applied Mathematics 55 3 1995 763 783
27. S.B. Hsu, and T.W. Huang A ratio-dependent food chain model and its applications to biological control Mathematical Biosciences 181 2003 55 83
28. K.S. Cheng, S.B. Hsu, and S.S. Lin Some results on global stability of a predatorprey model Journal of Mathematical Biology 12 1981 115 126
29. P.H. Leslie Some further notes on the use of matrices in population mathematics Biometrika 35 1948 213 245
30. M. Fan, K. Wang, Patricia J.Y. Wong, and Ravi P. Agarwal Periodicity and stability in periodic n-species LotkaVolterra competition system with feedback controls and deviating arguments Acta Mathematica Sinica 19 4 2003 801 822
31. M. Fan, and K. Wang Global existence of positive periodic solutions of predatorprey systems with infinite delays Journal of Mathematical Analysis and Applications 262 2001 1 11
32. P. Weng, and D. Jiang Existence and global stability of positive periodic solution of n-species LotkaVolterra competition system with feedback controls and deviating arguments Far East Journal of Mathematical Sciences (FJMS) 7 1 2002 45 65
33. Q. Wang, M. Fan, and K. Wang Dynamics of a class of nonautonomous semi-ratio-dependent predatorprey systems with functional responses Journal of Mathematics and Applications 278 2003 443 471
34. R. Xu, and L.S. Chen Persistence and stability of two-species ratio-dependent predatorprey system of delay in a two patch environment Computers & Mathematics with Applications 40 45 2000 577 588
35. Qi Wang, Binxiang Dai, and Yuming Chen Multiple periodic solutions of an impulsive predatorprey model with Holling-type IV functional response Mathematical and Computer Modelling 49 2009 1829 1836
36. R.E. Gaines, and J.L. Mawhin Coincidence Degree and Nonlinear Differential Equations 1977 Springer-Verlag New York
37. I. Barbalat Systems d'equations differentielle d'oscillations nonlineaires Revue Roumaine de Mathmatique Pures et Appliques 4 1959 267 270