- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- 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 382592, 11 pages
Poincaré Map and Periodic Solutions of First-Order Impulsive Differential Equations on Moebius Stripe
Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
Received 12 December 2012; Accepted 1 January 2013
Academic Editor: Yonghui Xia
Copyright © 2013 Yefeng He and Yepeng Xing. 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.
- M. Akhmet, Principles of Discontinuous Dynamical Systems, Springer, New York, NY, USA, 2010.
- D. D. Bainov and P. S. Simenov, Impulsive Differential Equations: Periodic Solutions and Applications, Longman Scientific and Technical, Harlow, UK, 1993.
- S. Djebali, L. Górniewicz, and A. Ouahab, “First-order periodic impulsive semilinear differential inclusions: existence and structure of solution sets,” Mathematical and Computer Modelling, vol. 52, no. 5-6, pp. 683–714, 2010.
- X. L. Fu, B. Q. Yan, and Y. S. Liu, Theory of Impulsive Differential System, Science Press, Beijing, China, 2005.
- V. Lakshmikantham, D. D. Baĭnov, and P. S. Simeonov, Theory of Impulsive Differential Equations, vol. 6 of Series in Modern Applied Mathematics, World Scientific Publishing, Singapore, 1989.
- Y. Liu, “Further results on periodic boundary value problems for nonlinear first order impulsive functional differential equations,” Journal of Mathematical Analysis and Applications, vol. 327, no. 1, pp. 435–452, 2007.
- J. Li and J. Shen, “Periodic boundary value problems for impulsive differential-difference equations,” Indian Journal of Pure and Applied Mathematics, vol. 35, no. 11, pp. 1265–1277, 2004.
- A. M. Samoilenko and N. A. Perestyuk, Impulsive Differential Equations, World Scientic Publishing, Singapore, 1995.
- J. Shen, “New maximum principles for first-order impulsive boundary value problems,” Applied Mathematics Letters, vol. 16, no. 1, pp. 105–112, 2003.
- E. M. Bonotto, “LaSalle's theorems in impulsive semidynamical systems,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 5-6, pp. 2291–2297, 2009.
- E. M. Bonotto and M. Federson, “Limit sets and the Poincaré-Bendixson theorem in impulsive semidynamical systems,” Journal of Differential Equations, vol. 244, no. 9, pp. 2334–2349, 2008.
- J. W. Grizzle, G. Abba, and F. Plestan, “Asymptotically stable walking for biped robots: analysis via systems with impulse effects,” IEEE Transactions on Automatic Control, vol. 46, no. 1, pp. 51–64, 2001.
- I. A. Hiskens, “Stability of hybrid system limit cycles: application to the Compass Gait Biped Robot,” in Proceedings of the 40th lEEE Conference on Decision and Control, Oriando, Fla, USA, December 2001.
- B. Morris and J. W. Grizzle, “Hybrid invariant manifolds in systems with impulse effects with application to periodic locomotion in bipedal robots,” IEEE Transactions on Automatic Control, vol. 54, no. 8, pp. 1751–1764, 2009.
- K. G. Dishlieva, “Differentiability of solutions of impulsive differential equations with respect to the impulsive perturbations,” Nonlinear Analysis: Real World Applications, vol. 12, no. 6, pp. 3541–3551, 2011.
- G. Jiang and Q. Lu, “Impulsive state feedback control of a predator-prey model,” Journal of Computational and Applied Mathematics, vol. 200, no. 1, pp. 193–207, 2007.
- L. Nie, Z. Teng, L. Hu, and J. Peng, “Qualitative analysis of a modified Leslie-Gower and Holling-type II predator-prey model with state dependent impulsive effects,” Nonlinear Analysis: Real World Applications, vol. 11, no. 3, pp. 1364–1373, 2010.
- Z. Teng, L. Nie, and X. Fang, “The periodic solutions for general periodic impulsive population systems of functional differential equations and its applications,” Computers & Mathematics with Applications, vol. 61, no. 9, pp. 2690–2703, 2011.
- M. Han and S. Gu, Theory and Method of Nonlinear System, Science Press, Beijing, China, 2001.
- Z. Hu and M. Han, “Periodic solutions and bifurcations of first-order periodic impulsive differential equations,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 19, no. 8, pp. 2515–2530, 2009.