Road to chaos in a Duflng oscillator with time delay loop

• Autorzy: Borkowski Łukasz

Identyfikatory

DOI

10.2478/mme-2021-0013

• Języki publikacji: EN

Abstrakty

EN

This article examines a single Duffing oscillator with a time delay loop. The research aims to check the impact of the time delay value on the nature of the solution, in particular the scenario of transition to a chaotic solution. Dynamic tools such as bifurcation diagrams, phase portraits, Poincaré maps, and FFT analysis will be used to evaluate the obtained results.

Słowa kluczowe

EN

Duffing oscillator; time delay loop; bifurcation diagram; phase portraits; Poincare maps

PL

oscylator Duffinga; pętla opóźnienia; diagram bifurkacji; portret fazowy; mapy Poincaré

• Wydawca: Wydawnictwo Politechniki Łódzkiej
• Czasopismo: Mechanics and Mechanical Engineering
• Rocznik: 2021
• Tom: Vol. 25, nr 1
• Strony: 84--87
• Opis fizyczny: Bibliogr. 20 poz., rys., wykr.

Twórcy

autor

Borkowski Łukasz

• Lodz University of Technology, Department of Strength of Materials, Stefanowskiego 1/15, Lodz, 90-924, Poland

Bibliografia

• [1] Parker, T. S., & Chua, L. O.: Chaos: A tutorial for engineers, Proceedings of the IEEE, 75(8), 982-1008, 1987.
• [2] Pyragas, K.: Continuous control of chaos by self-controlling feedback, Physics Letters A, 170(6), 421-428, 1992.
• [3] Schöll, E., Schuster, H. G.: Handbook of chaos control, John Wiley & Sons, 2000.
• [4] Afraimovich, V. S., Verichev, N. N., & Rabinovich, M. I.: Stochastic synchronization of oscillation in dissipative systems, Radiophysics and Quantum Electronics, 29(9), 795-803, 1986.
• [5] Pecora, L. M., & Carroll, T. L.: Synchronization in chaotic systems, Physical review letters, 64(8), 821, 1990.
• [6] Landau, L. D.: On the problem of turbulence, CR Acad. Sci. URSS, 44(31), 1-314, 1944.
• [7] Hopf, E.: A mathematical example displaying features of turbulence, Communications on Pure and Applied Mathematics, 1(4), 303-322, 1948.
• [8] Newhouse, S., Ruelle, D., Takens, F.: Occurrence of strange Axiom A attractors near quasi periodic flows on Tm, m≥3, Communications in Mathematical Physics, 64(1), 35-40, 1978.
• [9] Ruelle, D., & Takens, F.: On the nature of turbulence, Communications in Mathematical Physics, 20(3), 167-192, 1971.
• [10] Feigenbaum, M. J.: Quantitative universality for a class of nonlinear transformations, Journal of Statistical Physics, 19(1), 25-52, 1978.
• [11] Feigenbaum, M. J.: The universal metric properties of nonlinear transformations, Journal of Statistical Physics, 21(6), 669-706, 1979.
• [12] Pomeau, Y., Manneville, P.: Intermittent transition to turbulence in dissipative dynamical systems, Communications in Mathematical Physics, 74(2), 189-197, 1980.
• [13] Manneville, P., Pomeau, Y.: Different ways to turbulence in dissipative dynamical systems, Physica D: Nonlinear Phenomena, 1(2), 219-226, 1980.
• [14] Mackey, M. C., Glass, L.: Oscillation and chaos in physiological control systems, Science, 197(4300), 287-289, 1977.
• [15] Doyne Farmer, J.: Chaotic attractors of an infinite-dimensional dynamical system, Physica D: Nonlinear Phenomena, 4(3), 366- 393, 1982.
• [16] Lu, H., He, Z.: Chaotic behavior in first-order autonomous continuous-time systems with delay. Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on, 43(8), 700-702, 1996.
• [17] Awrejcewicz, J.,Wojewoda, J.: Observation of chaos in a nonlinear oscillator with delay: a numerical study., KSME Journal, 3(1), 15, 1989.
• [18] Maccari, A.: Vibration control for the primary resonance of the Van der Pol oscillator by a time delay state feedback, International journal of non-linear mechanics, 38(1), 123-131, 2003.
• [19] Yu, P., Yuan, Y., Xu, J.: Study of double Hopf bifurcation and chaos for an oscillator with time delayed feedback, Communications in Nonlinear Science and Numerical Simulation, 7(1), 69-91, 2002.
• [20] Xu, J., Chung, K.W.: Effects of time delayed position feedback on a Van der Pol-Duflng oscillator, Physica D: Nonlinear Phenomena, 180(1), 17-39, 2003.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).