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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 848613, 7 pages
Duffing-Type Oscillator with a Bounded from above Potential in the Presence of Saddle-Center Bifurcation and Singular Perturbation: Frequency Control
Faculty of Materials Science and Technology, Slovak University of Technology in Bratislava, Hajdoczyho 1, 917 01 Trnava, Slovakia
Received 21 June 2013; Revised 9 August 2013; Accepted 21 August 2013
Academic Editor: Elena Braverman
Copyright © 2013 Robert Vrabel 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.
- Z. Feng, G. Chen, and S.-B. Hsu, “A qualitative study of the damped Duffing equation and applications,” Discrete and Continuous Dynamical Systems B, vol. 6, no. 5, pp. 1097–1112, 2006.
- A. Litvak-Hinenzon and V. Rom-Kedar, “Symmetry-breaking perturbations and strange attractors,” Physical Review E, vol. 55, no. 5, pp. 4964–4978, 1997.
- V. Ryabov and K. Fukushima, “Analysis of homoclinic bifurcation in Duffing oscillator under two-frequency excitation: peculiarity of using Melnikov method in combination with averaging technique,” Proceedings of the Chaotic Modeling & Simulation International Conference (CHaos '10), 2010.
- X. Wei, M. F. Randrianandrasana, M. Ward, and D. Lowe, “Nonlinear dynamics of a periodically driven Duffing resonator coupled to a Van der Pol oscillator,” Mathematical Problems in Engineering, Article ID 248328, 16 pages, 2011.
- X. Yue, W. Xu, and Y. Zhang, “Global bifurcation analysis of Rayleigh-Duffing oscillator through the composite cell coordinate system method,” Nonlinear Dynamics, vol. 69, no. 1-2, pp. 437–457, 2012.
- A. H. Nayfeh and D. T. Mook, Nonlinear Oscillations, Pure and Applied Mathematics, Wiley-Interscience, New York, NY, USA, 1979.
- S. Lenci and G. Rega, “Optimal control of nonregular dynamics in a Duffing oscillator,” Nonlinear Dynamics, vol. 33, no. 1, pp. 71–86, 2003.
- A. Sharma, V. Patidar, G. Purohit, and K. K. Sud, “Effects on the bifurcation and chaos in forced Duffing oscillator due to nonlinear damping,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 6, pp. 2254–2269, 2012.
- E. Tamaseviciute, A. Tamasevicius, G. Mykolaitis, S. Bumeliene, and E. Lind-berg, “Analogue electrical circuit for simulation of the duffing-holmes equation,” Nonlinear Analysis: Modelling and Control, vol. 13, no. 2, pp. 241–252, 2008.
- V. Sauli, “Bethe-Salpeter study of radially excited vector quarkonia,” Physical Review D, vol. 86, Article ID 096004, 6 pages, 2012.
- V. K. Dolmatov, J. L. King, and J. C. Oglesby, “Diffuse versus square-well confining potentials in modelling A@C60 atoms,” Journal of Physics B, vol. 45, Article ID 105102, 2012.
- C. K. R. T. Jones, “Geometric singular perturbation theory,” in C.I.M.E. Lectures, Montecatini Terme, vol. 1609 of Lecture Notes in Mathematics, pp. 44–118, Springer, Heidelberg, Germany, 1995.
- R. Vrabel and M. Abas, “Frequency control of singularly perturbed forced Duffing's oscillator,” Journal of Dynamical and Control Systems, vol. 17, no. 3, pp. 451–467, 2011.
- S.-N. Chow, C. Z. Li, and D. Wang, Normal Forms and Bifurcation of Planar Vector Fields, Cambridge University Press, Cambridge, UK, 1994.
- D. Xiao and S. Ruan, “Bogdanov-Takens bifurcations in predator-prey systems with constant rate harvesting,” Fields Institute Communications, vol. 21, pp. 493–506, 1999.
- V. Gelfreich, “Splitting of a small separatrix loop near the saddle-center bifurcation in area-preserving maps,” Physica D, vol. 136, no. 3-4, pp. 266–279, 2000.