×

Synchronization of solutions of Duffing-type equations with random perturbations. (English) Zbl 1293.34069

The authors study an equation representing the motion of a particle with specified initial position and initial velocity, and with velocity perturbed by random perturbations at random times. Their concern is with the establishing of conditions under which the sample paths of similar particles are almost identical after a long time.

MSC:

34F05 Ordinary differential equations and systems with randomness
34D06 Synchronization of solutions to ordinary differential equations
Full Text: DOI

References:

[1] Huygens, C., The Pendulum Clock or, Geometrical Demonstrations Concerning the Motion of Pendula as Applied to Clocks (1986), Iowa State Univ. Press: Iowa State Univ. Press Ames
[2] Arenas, A.; Díaz-Guilerac, A.; Kurths, J.; Moreno, Y.; Zhoug, Ch., Synchronization in complex networks, Phys. Rep., 469, 93-153 (2008)
[3] Wu, B. C.W., Synchronization in Complex Networks of Nonlinear Dynamical Systems (2007), World Scientific: World Scientific Singapore · Zbl 1135.34002
[4] Pecora, L. M.; Carroll, T. L., Synchronization in chaotic systems, Phys. Rev. Lett., 64, 8, 821-824 (1990) · Zbl 0938.37019
[5] Carroll, T. L.; Pecora, L. M., Synchronized chaotic circuit, IEEE Trans. Circuits Syst., 38, 4, 453-456 (1991)
[6] Moskalenko, O. I.; Hramov, A. E.; Koronovskii, A. A.; Ovchinnikov, A. A., Effect of noise on generalized synchronization of chaos: theory and experiment, Eur. Phys. J. B, 82, 1, 69-82 (2011)
[7] Dmitriev, B. S.; Zharkov, Yu. D.; Koronovskii, A. A.; Khramov, A. E.; Skorokhodov, V. N., Experimental and theoretical investigations of the influence of the external noise on dynamics of a klystron oscillator, J. Commun. Technol. Electron., 57, 1, 45-53 (2012)
[8] Zhou, J.; Chen, Z., Further results on complete synchronization for noise-perturbed chaotic systems, Phys. Lett. A, 372, 33, 5394-5401 (2008) · Zbl 1223.34068
[9] Sun, Z.; Yang, X., Generating and enhancing lag synchronization of chaotic systems by white noise, Chaos, 21, 3, 033114-033123 (2011) · Zbl 1317.34089
[10] Kaulakys, B.; Ivanauskas, F.; Meškauskas, T., Synchronization of chaotic systems driven by identical noise, Internat. J. Bifur. Chaos, 9, 3, 533-539 (1999) · Zbl 0972.37507
[11] Ambrazevičius, A.; Ivanauskas, F.; Pragarauskas, H., On Duffing equation with random perturbations, Nonlinear Anal. Model. Control, 15, 2, 129-138 (2010) · Zbl 1218.34067
[12] Guckenheimer, J.; Holmes, P., Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (1983), Springer-Verlag · Zbl 0515.34001
[13] Wiggins, S., Introduction to Applied Nonlinear Dynamical Systems and Chaos (1991), Springer-Verlag
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.