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Horseshoe in a modified Van der Pol-Duffing circuit. (English) Zbl 1171.37314
Using topological “horseshoe theorem” existence of chaos in a modified Van der Pol-Duffing dynamical system is verified.
37D45Strange attractors, chaotic dynamics
[1]Matsumoto, T.; Chua, L. O.; Komuro, M.: The double scroll (nonlinear networks), IEEE trans. Circuits syst. 32, No. 8, 797-818 (1985) · Zbl 0578.94023 · doi:10.1109/TCS.1985.1085791
[2]Inaba, N.; Saito, T.; Mori, S.: Chaotic phenomena in a circuit with negative resistance and an ideal switch of diode, Trans. IEICE 70, 744-755 (1987)
[3]M. Kuramitsu, K. Mori, A simple circuit generating chaos, in: Proceedings of NOLTA, 1994, pp. 93 – 96.
[4]Shinriki, M.; Yamamoto, M.; Mori, S.: Multimode oscillations in a modified van der Pol oscillator containing a positive nonlinear conductance, Proc. IEEE 69, 394-395 (1981)
[5]King, G. P.; Gaito, S. T.: Bistable chaos: I. Unfolding the cusp, Phys. rev. A 46, 3092-3099 (1992)
[6]Matouk, A. E.; Agiza, H. N.: Bifurcations, chaos, and synchronization in ADVP circuit with parallel resistor, J. math. Anal. appl. 341, 259-269 (2008) · Zbl 1131.37037 · doi:10.1016/j.jmaa.2007.09.067
[7]Yang, X. S.; Tang, Y.: Horseshoes in piecewise continuous maps, Chaos soliton. Fract. 19, 841-845 (2004) · Zbl 1053.37006 · doi:10.1016/S0960-0779(03)00202-9
[8]Wiggins, S.: Introduction to applied nonlinear dynamical systems and chaos, (1990)
[9]Robinson, C.: Dynamical systems: stability, symbolic dynamics and chaos, (1995) · Zbl 0853.58001
[10]Yang, X. S.: Metric horseshoe, Chaos soliton. Fract. 20, 1149-1156 (2004) · Zbl 1048.37044 · doi:10.1016/j.chaos.2003.09.035
[11]Yang, X. S.; Huang, Y.: Complex dynamics in simple Hopfield neural networks, Chaos 16 (2006) · Zbl 1146.37371 · doi:10.1063/1.2220476
[12]Yang, X. S.; Li, Q. D.: A horseshoe in a cellular neural network of 4-dimensional autonomous ordinary differential equations, Int. J. Bifurcat. chaos 17, No. 9, 3211-3218 (2007) · Zbl 1185.37202 · doi:10.1142/S0218127407018968
[13]Yang, X. -S.; Li, Q. D.: A computer-assisted proof of chaos in Josephson junctions, Chaos soliton. Fract. 27, 25-30 (2006) · Zbl 1083.37034 · doi:10.1016/j.chaos.2005.04.017
[14]Liao, Z. S.; Huang, Y.: Horseshoe and topological entropy estimate of a class of three-dimensional cellular neural networks, Appl. math. Comput. 197, 382-388 (2008) · Zbl 1134.37012 · doi:10.1016/j.amc.2007.07.077