TORUS HYSTERESIS

DOI: https://doi.org/10.15407/rpra19.03.267

D. M. Vavriv, A. Yu. Nimets

Abstract


Theoretical studies of the dynamics of a nonlinear oscillator with cubic and quadratic nonlinearities simultaneously excited by low- and high-frequency external forcing are presented. A new mechanism of the appearance of bistability and hysteresis due to such an interaction is discovered. This mechanism manifests as the bistability and hysteresis of tori formed in the oscillator phase space. A comparative analysis of the oscillator behavior under the resonant harmonic excitation and under the dual frequency excitation is made.

Key words: oscillator, bistability, hysteresis, phase-plane portrait, limit cycle, torus   

Manuscript submitted 08.05.2014

Radio phys. radio astron. 2014, 19(3): 267-275

 

REFERENCES

1. GIBBS, H., 1988. Optical Bistability: Controlling Light with Light. Moskow: Mir Publ. (in Russian).

2. KRASNOSEL'SKII, M. A. and POKROVSKII, A. V., 1983. Systems with Hysteresis. Moscow: Nauka Publ. (in Russian).

3. BOZORTH, R., 1956. Ferromagnetism. Moskow: Inostran. lit. Publ. (in Russian).

4. SOLOMON, M. J., 2003. Hysteresis meets the cell cycle. Proc. Nat. Acad. Sci. USA. vol. 100, no. 3, pp. 771–772.

5. GUIDI, G. M. and GOLDBETER, A., 1997. Bistability without Hysteresis in Chemical Reaction Systems: A Theoretical Analysis of Irreversible Transitions between Multiple Steady States. J. Phys. Chem. A. vol. 101, is. 49, pp. 9367–9376. DOI: 10.1021/ jp972244k

6. MIGULIN, V.V., MEDVEDEV, V.Y., MUSTEL, E.R., and PARIGIN, V.N., 19. Basic Theory of Oscillations, Moscow: Nauka Publ. (in Russian).

7. VAVRIV, D. M. and SHYGIMAGA, D. V., 2000, Chaos in Duffing Oscillator with High- and Low-Frequency External Forcing. Radio Phys. Radio Astron., vol. 5, no. 3, pp. 256–265 (in Russian).

8. MITROPOL'SKII, Yu. A., 1955. Nonstationary Processes in Nonlinear Oscillatory Systems. Kiev: Izd. Akad. Nauk Ukr. SSR Publ. (in Russian).

9. VAVRIV, D. M. and OKSASOGLU, A., 1994. Stability of varactorcircuits. Electron. Lett. vol. 30, is. 6, pp. 462–463. DOI: https://doi.org/10.1049/el:19940347

10. BELOGORTSEV, A. V., VAVRIV, D. M., and TRETYAKOV, O. A., 1994. Destruction of quasiperiodic oscillations in weakly nonlinear systems. Appl. Mech. Rev. vol. 46, no. 7, pp. 372–384. DOI: https://doi.org/10.1115/1.3120366 

 


Keywords


oscillator; bistability; hysteresis; phase-plane portrait; limit cycle; torus

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