- 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
Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 385419, 9 pages
Bifurcation of Limit Cycles of a Class of Piecewise Linear Differential Systems in with Three Zones
Department of Electronics and Information Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
Received 1 March 2013; Accepted 16 April 2013
Academic Editor: Qingdu Li
Copyright © 2013 Yanyan Cheng. 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.
- J. Llibre and M. A. Texeira, “On the stable limit cycle of a weight-driven pendulum clock,” European Journal of Physics, vol. 31, no. 1, pp. 249–1254, 2010.
- M. Vidyasagar, Nonlinear Systems Analysis, Poelltice-Hall, 2nd edition, 1993.
- 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, Theory and applications.
- V. Carmona, E. Freire, E. Ponce, and F. Torres, “Bifurcation of invariant cones in piecewise linear homogeneous systems,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 15, no. 8, pp. 2469–2484, 2005.
- S. Huan and X.-S. Yang, “Generalized Hopf bifurcation emerged from a corner in general planar piecewise smooth systems,” Nonlinear Analysis. Theory, Methods & Applications, vol. 75, no. 17, pp. 6260–6274, 2012.
- C. Chritopher and C. Li, Limit Cycles in Differential Equations, Birkhauser, Boston, Mass, USA, 2007.
- S.-M. Huan and X.-S. Yang, “On the number of limit cycles in general planar piecewise linear systems,” Discrete and Continuous Dynamical Systems A, vol. 32, no. 6, pp. 2147–2164, 2012.
- J. Li, “Hilbert's 16th problem and bifurcations of planar polynomial vector fields,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 13, no. 1, pp. 47–106, 2003.
- J. Llibre and A. Makhlouf, “Bifurcation of limit cycles from a two-dimensional center inside ,” Nonlinear Analysis. Theory, Methods & Applications, vol. 72, no. 3-4, pp. 1387–1392, 2010.
- E. Freire, E. Ponce, and J. Ros, “The focus-center-limit cycle bifurcation in symmetric 3D piecewise linear systems,” SIAM Journal on Applied Mathematics, vol. 65, no. 6, pp. 1933–1951, 2005.
- V. Carmona, S. Fernández-García, F. Fernández-Sánchez, E. García-Medina, and A. E. Teruel, “Reversible periodic orbits in a class of 3D continuous piecewise linear systems of differential equations,” Nonlinear Analysis. Theory, Methods & Applications, vol. 75, no. 15, pp. 5866–5883, 2012.
- A. Buică and J. Llibre, “Bifurcation of limit cycles from a four-dimensional center in control systems,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 15, no. 8, pp. 2653–2662, 2005.
- C. A. Buzzi, J. Llibre, and J. C. Medrado, “On the limit cycles of a class of piecewise linear differential systems in with two zones,” Mathematics and Computers in Simulation, vol. 82, no. 4, pp. 533–539, 2011.
- C. A. Buzzi, J. Llibre, J. C. Medrado, and J. Torregrosa, “Bifurcation of limit cycles from a centre in in resonance 1:N,” Dynamical Systems, vol. 24, no. 1, pp. 123–137, 2009.
- P. T. Cardin, T. de Carvalho, and J. Llibre, “Bifurcation of limit cycles from an -dimensional linear center inside a class of piecewise linear differential systems,” Nonlinear Analysis. Theory, Methods & Applications, vol. 75, no. 1, pp. 143–152, 2012.
- J. Llibre, E. Ponce, and J. Ros, “Algebraic determination of limit cycles in a family of three-dimensional piecewise linear differential systems,” Nonlinear Analysis. Theory, Methods & Applications, vol. 74, no. 17, pp. 6712–6727, 2011.
- A. Buică and J. Llibre, “Averaging methods for finding periodic orbits via Brouwer degree,” Bulletin des Sciences Mathématiques, vol. 128, no. 1, pp. 7–22, 2004.
- A. Buică, J. Llibre, and O. Makarenkov, “Asymptotic stability of periodic solutions for nonsmooth differential equations with application to the nonsmooth van der Pol oscillator,” SIAM Journal on Mathematical Analysis, vol. 40, no. 6, pp. 2478–2495, 2009.
- F. E. Browder, “Fixed point theory and nonlinear problems,” American Mathematical Society, vol. 9, no. 1, pp. 1–39, 1983.