- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 767526, 10 pages
Periodicity and Permanence of a Discrete Impulsive Lotka-Volterra Predator-Prey Model Concerning Integrated Pest Management
1College of Science, Northeast Forestry University, Harbin 150040, China
2Forestry Engineering Mobile Station, Northeast Forestry University, Harbin 150040, China
3College of Mechanical and Electrical Engineering, Northeast Forestry University, Harbin 150040, China
Received 18 September 2013; Revised 23 November 2013; Accepted 25 November 2013
Academic Editor: Stefan Balint
Copyright © 2013 Chang Tan and Jun Cao. 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.
- V. Lakshmikantham, D. D. Baĭnov, and P. S. Simeonov, Theory of Impulsive Differential Equations, vol. 6, World Scientific Publishing, Teaneck, NJ, USA, 1989.
- V. Lakshmikantham, X. Liu, and S. Sathananthan, “Impulsive integro-differential equations and extension of Lyapunov's method,” Applicable Analysis, vol. 32, no. 3-4, pp. 203–214, 1989.
- D. Baĭnov and P. Simeonov, Impulsive Differential Equations: Periodic Solutions and Applications, vol. 66 of Pitman Monographs and Surveys in Pure and Applied Mathematics, Longman, Harlow, UK, 1993.
- K. Gopalsamy and B. G. Zhang, “On delay differential equations with impulses,” Journal of Mathematical Analysis and Applications, vol. 139, no. 1, pp. 110–122, 1989.
- H. Liang, M. Liu, and M. Song, “Extinction and permanence of the numerical solution of a two-prey one-predator system with impulsive effect,” International Journal of Computer Mathematics, vol. 88, no. 6, pp. 1305–1325, 2011.
- S. Elaydi, An Introduction to Difference Equations, Springer, New York, NY, USA, 3rd edition, 2005.
- J. M. Cushing and S. M. Henson, “Global dynamics of some periodically forced, monotone difference equations,” Journal of Difference Equations and Applications, vol. 7, no. 6, pp. 859–872, 2001.
- S. Mohamad, “Global exponential stability in discrete-time analogues of delayed cellular neural networks,” Journal of Difference Equations and Applications, vol. 9, no. 6, pp. 559–575, 2003.
- S. Mohamad and A. G. Naim, “Discrete-time analogues of integrodifferential equations modelling bidirectional neural networks,” Journal of Computational and Applied Mathematics, vol. 138, no. 1, pp. 1–20, 2002.
- K. Murakami, “Stability for non-hyperbolic fixed points of scalar difference equations,” Journal of Mathematical Analysis and Applications, vol. 310, no. 2, pp. 492–505, 2005.
- A. M. Stuart and A. R. Humphries, Dynamical Systems and Numerical Analysis, vol. 2, Cambridge University Press, Cambridge, UK, 1996.
- Q. Zhang, “On a linear delay difference equation with impulses,” Annals of Differential Equations, vol. 18, no. 2, pp. 197–204, 2002.
- Z. He and X. Zhang, “Monotone iterative technique for first order impulsive difference equations with periodic boundary conditions,” Applied Mathematics and Computation, vol. 156, no. 3, pp. 605–620, 2004.
- R. Z. Abdullin, “Stability of nonlinear difference equations with pulse actions: a comparison method,” Automation and Remote Control 1, vol. 61, no. 11, pp. 1796–1807, 2000.
- R. Z. Abdullin, “Stability of difference equations with impulsive actions at the instants of time dependent on the state vector,” Automation and Remote Control 1, vol. 58, no. 7, pp. 1092–1100, 1997.
- B. Liu and D. J. Hill, “Uniform stability and ISS of discrete-time impulsive hybrid systems,” Nonlinear Analysis: Hybrid Systems, vol. 4, no. 2, pp. 319–333, 2010.
- S. Mohamad and K. Gopalsamy, “Exponential stability of continuous-time and discrete-time cellular neural networks with delays,” Applied Mathematics and Computation, vol. 135, no. 1, pp. 17–38, 2003.
- S. Mohamad and K. Gopalsamy, “Dynamics of a class of discrete-time neural networks and their continuous-time counterparts,” Mathematics and Computers in Simulation, vol. 53, no. 1-2, pp. 1–39, 2000.
- B. Liu, Y. Zhang, and L. Chen, “The dynamical behaviors of a Lotka-Volterra predator-prey model concerning integrated pest management,” Nonlinear Analysis: Real World Applications, vol. 6, no. 2, pp. 227–243, 2005.
- Z. Zhang and X. Liu, “Robust stability of uncertain discrete impulsive switching systems,” Computers & Mathematics with Applications, vol. 58, no. 2, pp. 380–389, 2009.
- S. Wu, C. Li, X. Liao, and S. Duan, “Exponential stability of impulsive discrete systems with time delay and applications in stochastic neural networks: a Razumikhin approach,” Neurocomputing, vol. 82, pp. 29–36, 2012.
- Y. Zhang, “Exponential stability of impulsive discrete systems with time delays,” Applied Mathematics Letters of Rapid Publication, vol. 25, no. 12, pp. 2290–2297, 2012.