- 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 732321, 9 pages
Homoclinic Bifurcations in Planar Piecewise-Linear Systems
1Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
2Central University of Finance and Economics, School of Applied Mathematics, Beijing 100084, China
Received 25 January 2013; Accepted 29 August 2013
Academic Editor: Rob Sturman
Copyright © 2013 Bin Xu et al. 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. di Bernardo, C. J. Budd, A. R. Champneys, and P. Kowalczyk, Piecewise-Smooth Dynamical Systems, vol. 163 of Applied Mathematical Sciences, Springer, London, UK, 2008.
- M. di Bernardo, D. J. Pagano, and E. Ponce, “Nonhyperbolic boundary equilibrium bifurcations in planar Filippov systems: a case study approach,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 18, no. 5, pp. 1377–1392, 2008.
- R. Lum and L. O. Chua, “Global properties of continuous piecewise linear vector fields—part I: simplest case in ℝ2,” International Journal of Circuit Theory and Applications, vol. 19, no. 3, pp. 251–307, 1991.
- E. Freire, E. Ponce, F. Rodrigo, and F. Torres, “A piecewise linear electronic circuit with a multiplicity of bifurcations,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 14, no. 11, pp. 3871–3881, 2004.
- D. Simpson, Bifurcations in Piece-Wise Continuous Systems, World Scientific, 2010.
- E. Freire, E. Ponce, F. Rodrigo, and F. Torres, “Bifurcation sets of continuous piecewise linear systems with two zones,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 8, no. 11, pp. 2073–2097, 1998.
- D. J. W. Simpson and J. D. Meiss, “Andronov-Hopf bifurcations in planar, piecewise-smooth, continuous flows,” Physics Letters A, vol. 371, no. 3, pp. 213–220, 2007.
- C. D. Mitrovski and Lj. M. Kocarev, “Periodic trajectories in piecewise-linear maps,” IEEE Transactions on Circuits and Systems. I., vol. 48, no. 10, pp. 1244–1252, 2001.
- J. M. Gonçalves, “Regions of stability for limit cycle oscillations in piecewise linear systems,” IEEE Transactions on Automatic Control, vol. 50, no. 11, pp. 1877–1882, 2005.
- Y. Xiong and M. Han, “Bifurcation of limit cycles by perturbing a piecewise linear Hamiltonian system,” Abstract and Applied Analysis, vol. 2013, Article ID 575390, 19 pages, 2013.
- F. Liang, M. Han, and V. G. Romanovski, “Bifurcation of limit cycles by perturbing a piecewise linear Hamiltonian system with a homoclinic loop,” Nonlinear Analysis: Theory, Methods & Applications, vol. 75, no. 11, pp. 4355–4374, 2012.
- R. I. Leine and H. Nijmeijer, Dynamics and Bifurcations of Non-Smooth Mechanical Systems, vol. 18 of Lecture Notes in Applied and Computational Mechanics, Springer, Berlin, Germany, 2004.
- L. Perko, Differential Equations and Dynamical Systems, vol. 7 of Texts in Applied Mathematics, Springer, New York, NY, USA, 3rd edition, 2001.