- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 741043, 11 pages
Existence and Stability of Positive Periodic Solutions for a Neutral Multispecies Logarithmic Population Model with Feedback Control and Impulse
1Department of Mathematics, National University of Defense Technology, Changsha 410073, China
2Department of Mathematics, Hengyang Normal University, Hengyang, Hunan 421008, China
Received 14 June 2013; Revised 1 August 2013; Accepted 2 August 2013
Academic Editor: Yong Ren
Copyright © 2013 Zhenguo Luo and Liping Luo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- P. Weng, “Existence and global stability of positive periodic solution of periodic integrodifferential systems with feedback controls,” Computers & Mathematics with Applications, vol. 40, no. 6-7, pp. 747–759, 2000.
- F. Yang and D. Q. Jiang, “Existence and global attractivity of positive periodic solution of a Logistic growth system with feedback control and deviating arguments,” Annals of Differential Equations, vol. 17, no. 4, pp. 337–384, 2001.
- F. Chen, “Positive periodic solutions of neutral Lotka-Volterra system with feedback control,” Applied Mathematics and Computation, vol. 162, no. 3, pp. 1279–1302, 2005.
- C. Wang and J. Shi, “Periodic solution for a delay multispecies logarithmic population model with feedback control,” Applied Mathematics and Computation, vol. 193, no. 1, pp. 257–265, 2007.
- H. Hu, Z. Teng, and H. Jiang, “Permanence of the nonautonomous competitive systems with infinite delay and feedback controls,” Nonlinear Analysis: Real World Applications, vol. 10, no. 4, pp. 2420–2433, 2009.
- J. Yan and A. Zhao, “Oscillation and stability of linear impulsive delay differential equations,” Journal of Mathematical Analysis and Applications, vol. 227, no. 1, pp. 187–194, 1998.
- W. Zhang and M. Fan, “Periodicity in a generalized ecological competition system governed by impulsive differential equations with delays,” Mathematical and Computer Modelling, vol. 39, no. 4-5, pp. 479–493, 2004.
- Q. Wang and B. X. Dai, “Existence of positive periodic solutions for a neutral population model with delays and impulse,” Nonlinear Analysis: Theory, Methods and Applications, vol. 69, pp. 3919–3930, 2008.
- Y. Zhang and J. Sun, “Stability of impulsive functional differential equations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 68, no. 12, pp. 3665–3678, 2008.
- G. Zhu, X. Meng, and L. Chen, “The dynamics of a mutual interference age structured predator-prey model with time delay and impulsive perturbations on predators,” Applied Mathematics and Computation, vol. 216, no. 1, pp. 308–316, 2010.
- D. B. Lakshmikantham and P. Simeonov, Theory of Impulsive Differential Equations, World Scientific Publisher, Singapore, 1989.
- D. Baĭnov and P. Simeonov, Impulsive Differential Equations: Periodic Solutions and Applications, vol. 66, Longman, Harlow, UK, 1993.
- M. Benchohra, J. Henderson, and S. Ntouyas, Impulsive Differential Equations and Inclusions, vol. 2, Hindawi Publishing Corporation, New York, NY, USA, 2006.
- Z. J. Liu, “Positive periodic solutions for a delay multispecies logarithmic population model,” Chinese Journal of Engineering Mathematics, vol. 19, no. 4, pp. 11–16, 2002.
- S. Lu and W. Ge, “Existence of positive periodic solutions for neutral logarithmic population model with multiple delays,” Journal of Computational and Applied Mathematics, vol. 166, no. 2, pp. 371–383, 2004.
- F. Chen, “Periodic solutions and almost periodic solutions for a delay multispecies logarithmic population model,” Applied Mathematics and Computation, vol. 171, no. 2, pp. 760–770, 2005.
- F. Chen, “Periodic solutions and almost periodic solutions of a neutral multispecies logarithmic population model,” Applied Mathematics and Computation, vol. 176, no. 2, pp. 431–441, 2006.
- W. Zhao, “New results of existence and stability of periodic solution for a delay multispecies Logarithmic population model,” Nonlinear Analysis: Real World Applications, vol. 10, no. 1, pp. 544–553, 2009.
- Q. Wang, Y. Wang, and B. Dai, “Existence and uniqueness of positive periodic solutions for a neutral logarithmic population model,” Applied Mathematics and Computation, vol. 213, no. 1, pp. 137–147, 2009.
- Y. Luo and Z. Luo, “Existence of positive periodic solutions for neutral multi-delay logarithmic population model,” Applied Mathematics and Computation, vol. 216, no. 4, pp. 1310–1315, 2010.