In this paper, different nonlinear dynamics analysis techniques are employed to unveil the rich nonlinear phenomena of the electromagnetic system. In particular, bifurcation diagrams, time responses, phase portraits, Poincare maps, power spectrum analysis, and the construction of basins of attraction are all powerful and effective tools for nonlinear dynamics problems. We also employ the method of Lyapunov exponents to show the occurrence of chaotic motion and to verify those numerical simulation results. Finally, two cases of a chaotic electromagnetic system being effectively controlled by a reference signal or being synchronized to another nonlinear electromagnetic system are presented.<\/p>\r\n","references":"[1] S. C. Chang, T. C. Tung, \"Identification of a non-linear electromagnetic\r\nsystem: an experimental study,\" Journal of Sound and Vibration, vol. 214, pp. 853-872, 1998.\r\n[2] A. Wolf, J. B. Swift, H. Swinney and J. A. Vastano, \"Determining\r\nLyapunov exponents from a time series,\" Physica D, vol. 16, pp. 285-317, 1985.\r\n[3] E. Ott, C. Grebogi and J. A. Yorke, \"Controlling chaos,\" Physical Review Letters, vol. 64, pp. 1196-1199, 1990.\r\n[4] W. L. Ditto, S. N. Rauseo and M. L. Spano, \"Experimental control of\r\nchaos,\" Physical Review Letters, vol. 65, pp. 3211-3214, 1990.\r\n[5] E. R. Hunt, \"Stabilizing high-period orbits in a chaotic system: The diode\r\nresonator,\" Physical Review Letters, vol. 67, pp. 1953-1955, 1991.\r\n[6] Y. C. Lai, M. Ding and C. Grebogi, \"Controlling Hamiltonian chaos,\"\r\nPhysical Review E, vol. 67, pp. 86-92, 1993.\r\n[7] C. Cai, Z. Xu, W. Xu and B. Feng, \"Notch filter feedback control in a\r\nclass of chaotic systems,\" Automatica, vol. 38, pp. 695-701, 2002.\r\n[8] C. Cai, Z. Xu and W. Xu, \"Converting chaos into periodic motion by\r\nfeedback control,\" Automatica, vol. 38, pp. 1927-1933, 2002.\r\n[9] C. C. Fun, P. C. Tung, \"Experimental and analytical study of dither signals in a class of chaotic system,\" Physics Letters A, vol. 229, pp. 228-234, 1997.\r\n[10] L. M. Pecora and T. L. Carroll, \"Synchronization in Chaotic Systems,\"\r\nPhysical Review Letters, vol. 64, pp. 821-823, 1990.\r\n[11] J. K. John and R. E. Amritkar, \"Synchronization by feedback and\r\nadaptive control,\" International Journal of Bifurcation and Chaos, vol. 4,\r\npp. 1687-1695, 1994.\r\n[12] S. Li and Y. P. Tian, \"Finite time synchronization of chaotic systems,\"\r\nChaos, Solitons & Fractals, vol. 15, pp. 303-310, 2003.\r\n[13] E. W. Bai and K. E. Lonngren, \"Synchronization and Chaos of Chaotic\r\nSystems,\" Chaos, Solitons & Fractals, vol. 10, pp. 1571-1575, 1999.\r\n[14] T. L. Carroll, L. M. Pecora, \"Synchronizing Chaotic Circuits,\" IEEE\r\nTrans. Circ Syst. I, vol. 38, pp. 453-456, 1991.\r\n[15] T. L. Liao and S. H. Tsai, \"Adaptive Synchronization of Chaotic Suystem\r\nand its Application to Secure Communications,\" Chaos, Solitons &\r\nFractals, vol. 11, pp. 1387-1396, 2000.\r\n[16] IMSL, Inc, User-s manual - IMSL MATH\/LIBRARY, 1989, pp. 633.\r\n[17] J. L. Kaplan, J. A. Yorke, Chaotic behavior of multidimensional\r\ndifference equations, Lecture Notes in Mathematics. New York: Springer-Verlag, 1979, pp.228-237.\r\n[18] W. Szemplinska-Stupnicka, G. Iooss and F. C. Moon, Chaotic Motions in\r\nNonlinear Dynamical Systems. New York: Springer-Verlag, 1988.\r\n[19] C. Y. Tseng, P. C. Tung, \"Stability, bifurcation, and chaos of a structure\r\nwith a non-linear actuator,\" Japanese Journal of Applied Physics, vol. 34, pp. 3766-3774, 1995.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 65, 2012"}