Global behaviors and optimal harvesting of a class of impulsive periodic logistic single-species system with continuous periodic control strategy

Boundary Value Problems

Volumn 2008, Issue , 2008, Pages

  Wang, JinRong ^a   Xiang, X ^a   Wei, W ^a  

^a GUIZHOU UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 64249166913     PISSN: 16872762     EISSN: 16872770     Source Type: Journal    
DOI: 10.1155/2008/192353     Document Type: Article

References (39)

1. C. W. Clark, Mathematical Bioeconomics: The Optimal Management of Renewable Resources, Pure and Applied Mathematics, John Wiley & Sons, New York, NY, USA, 1976.
2. X. Song and L. Chen, "Optimal harvesting and stability for a two-species competitive system with stage structure," Mathematical Biosciences, vol. 170, no. 2, pp. 173-186, 2001.
3. R. Marzollo, Ed., Periodic Optimization, Springer, New York, NY, USA, 1972.
4. M. Fan and K. Wang, "Optimal harvesting policy for single population with periodic coefficients," Mathematical Biosciences, vol. 152, no. 2, pp. 165-177, 1998.
5. D. D. Bainov and P. S. Simeonov, Impulsive Differential Equations: Periodic Solutions and Applications, vol. 66 of Pitman Monographs and Surveys in Pure and Applied Mathematics, Longman Scientific & Technical, Harlow, UK, 1993.
6. Y. N. Xiao, D. Z. Cheng, and H. S. Qin, "Optimal impulsive control in periodic ecosystem," Systems & Control Letters, vol. 55, no. 7, pp. 558-565, 2006.
7. V. Lakshmikantham, D. D. Bainov, and P. S. Simeonov, Theory of Impulsive Differential Equations, vol. 6 of Series in Modern Applied Mathematics,World Scientific, Teaneck, NJ, USA, 1989.
8. J. J. Nieto, "An abstract monotone iterative technique," Nonlinear Analysis: Theory, Methods & Applications, vol. 28, no. 12, pp. 1923-1933, 1997.
9. J. Yan, A. Zhao, and J. J. Nieto, "Existence and global attractivity of positive periodic solution of periodic single-species impulsive Lotka-Volterra systems," Mathematical and Computer Modelling, vol. 40, no. 5-6, pp. 509-518, 2004.
10. J.-J. Jiao, L.-S. Chen, J. J. Nieto, and T. Angela, "Permanence and global attractivity of stage-structured predator-prey model with continuous harvesting on predator and impulsive stocking on prey," Applied Mathematics and Mechanics, vol. 29, no. 5, pp. 653-663, 2008.
11. G. Zeng, F. Wang, and J. J. Nieto, "Complexity of a delayed predator-prey model with impulsive harvest and Holling type II functional response," Advances in Complex Systems, vol. 11, no. 1, pp. 77-97, 2008.
12. W. Wang, J. Shen, and J. J. Nieto, "Permanence and periodic solution of predator-prey system with Holling type functional response and impulses," Discrete Dynamics in Nature and Society, vol. 2007, Article ID 81756, 15 pages, 2007.
13. H. Zhang, L. Chen, and J. J. Nieto, "A delayed epidemic model with stage-structure and pulses for pest management strategy," Nonlinear Analysis: Real World Applications, vol. 9, no. 4, pp. 1714-1726, 2008.
14. B. Ahmad and J. J. Nieto, "Existence and approximation of solutions for a class of nonlinear impulsive functional differential equations with anti-periodic boundary conditions," Nonlinear Analysis: Theory, Methods & Applications, vol. 69, no. 10, pp. 3291-3298, 2008.
15. D. Jiang, Y. Yang, J. Chu, and D. O'Regan, "The monotone method for Neumann functional differential equationswith upper and lower solutions in the reverse order," Nonlinear Analysis: Theory, Methods & Applications, vol. 67, no. 10, pp. 2815-2828, 2007.
16. Y. Li, "Global exponential stability of BAM neural networks with delays and impulses," Chaos, Solitons & Fractals, vol. 24, no. 1, pp. 279-285, 2005.
17. M. De la Sen, "Stability of impulsive time-varying systems and compactness of the operators mapping the input space into the state and output spaces," Journal of Mathematical Analysis and Applications, vol. 321, no. 2, pp. 621-650, 2006.
18. L. Yu, J. Zhang, Y. Liao, and J. Ding, "Parameter estimation error bounds for Hammerstein nonlinear finite impulsive response models," Applied Mathematics and Computation, vol. 202, no. 2, pp. 472-480, 2008.
19. T. Jankowski, "Positive solutions to second order four-point boundary value problems for impulsive differential equations," Applied Mathematics and Computation, vol. 202, no. 2, pp. 550-561, 2008.
20. E. M. Hernández, M. Pierri, and G. Goncalves, "Existence results for an impulsive abstract partial differential equation with state-dependent delay," Computers & Mathematics with Applications, vol. 52, no. 3-4, pp. 411-420, 2006.
21. E. M. Hernández, M. Rabello, and H. R. Henríquez, "Existence of solutions for impulsive partial neutral functional differential equations," Journal of Mathematical Analysis and Applications, vol. 331, no. 2, pp. 1135-1158, 2007.
22. E. M. Hernández, R. Sakthivel, and S. T. Aki, "Existence results for impulsive evolution differential equations with state-dependent delay," Electronic Journal of Differential Equations, vol. 2008, no. 28, pp. 1-11, 2008.
23. N. U. Ahmed, "Some remarks on the dynamics of impulsive systems in Banach spaces," Dynamics of Continuous, Discrete and Impulsive Systems. Series A, vol. 8, no. 2, pp. 261-274, 2001.
24. N. U. Ahmed, K. L. Teo, and S. H. Hou, "Nonlinear impulsive systems on infinite dimensional spaces," Nonlinear Analysis: Theory, Methods & Applications, vol. 54, no. 5, pp. 907-925, 2003.
25. X. Xiang and N. U. Ahmed, "Existence of periodic solutions of semilinear evolution equations with time lags," Nonlinear Analysis: Theory, Methods & Applications, vol. 18, no. 11, pp. 1063-1070, 1992.
26. X. Xiang, "Optimal control for a class of strongly nonlinear evolution equations with constraints," Nonlinear Analysis: Theory, Methods & Applications, vol. 47, no. 1, pp. 57-66, 2001.
27. P. Sattayatham, S. Tangmanee, and W. Wei, "On periodic solutions of nonlinear evolution equations in Banach spaces," Journal of Mathematical Analysis and Applications, vol. 276, no. 1, pp. 98-108, 2002.
28. X. Xiang, W. Wei, and Y. Jiang, "Strongly nonlinear impulsive system and necessary conditions of optimality," Dynamics of Continuous, Discrete & Impulsive Systems. Series A, vol. 12, no. 6, pp. 811-824, 2005.
29. W. Wei and X. Xiang, "Necessary conditions of optimal control for a class of strongly nonlinear impulsive equations in Banach spaces," Nonlinear Analysis: Theory, Methods & Applications, vol. 63, no. 5-7, pp. 53-63, 2005.
30. W. Wei, X. Xiang, and Y. Peng, "Nonlinear impulsive integro-differential equations of mixed type and optimal controls," Optimization, vol. 55, no. 1-2, pp. 141-156, 2006.
31. X. Xiang and W. Wei, "Mild solution for a class of nonlinear impulsive evolution inclusions on Banach space," Southeast Asian Bulletin of Mathematics, vol. 30, no. 2, pp. 367-376, 2006.
32. X. Yu, X. Xiang, and W. Wei, "Solution bundle for a class of impulsive differential inclusions on Banach spaces," Journal of Mathematical Analysis and Applications, vol. 327, no. 1, pp. 220-232, 2007.
33. Y. Peng, X. Xiang, and W. Wei, "Nonlinear impulsive integro-differential equations of mixed type with time-varying generating operators and optimal controls," Dynamic Systems and Applications, vol. 16, no. 3, pp. 481-496, 2007.
34. Y. Peng and X. Xiang, "Second order nonlinear impulsive time-variant systems with unbounded perturbation and optimal controls," Journal of Industrial and Management Optimization, vol. 4, no. 1, pp. 17-32, 2008.
35. J. Wang, "Linear impulsive periodic system on Banach spaces," in Proceedings of the 4th International Conference on Impulsive and Hybrid Dynamical Systems, vol. 5, pp. 20-25, Nanning, China, July 2007.
36. J. Wang, X. Xiang, and W. Wei, "Linear impulsive periodic system with time-varying generating operators on Banach space," Advances in Difference Equations, vol. 2007, Article ID 26196, 16 pages, 2007.
37. 0-periodic impulsive perturbations on Banach spaces," Discrete Dynamics in Nature and Society, vol. 2008, Article ID 524945, 16 pages, 2008.
38. N. U. Ahmed, Semigroup Theory with Applications to Systems and Control, vol. 246 of Pitman Research Notes in Mathematics Series, Longman Scientific & Technical, Harlow, UK, 1991.
39. Z.-H. Luo, B.-Z. Guo, and O. Morgül, Stability and Stabilization of Infinite Dimensional Systems with Applications, Communications and Control Engineering Series, Springer, London, UK, 1999.