Cite this article as:
Semenov V. V., Vadivasova T. Е., Shell' E. ., Zakharova А. S. Time-delayed Feedback Control of Coherence Resonance. Experimental Study. Izvestiya of Saratov University. New series. Series Physics, 2015, vol. 15, iss. 3, pp. 43-51. DOI: https://doi.org/10.18500/1817-3020-2015-15-3-43-51
Time-delayed Feedback Control of Coherence Resonance. Experimental Study
In the paper a possibility to control the behavior of dynamic systems under conditions of coherent resonance using delayed feedback is proved experimentally. This problem is studied on the classical example of excitable system, which is the FitzHugh – Nagumo oscillator, as well as on the example of the Van der Pol oscillator with hard excitation, which also demonstrates the regime of coherent resonance. In both cases, when changing the delay time the feedback loop can both enhance and suppress the effect of coherent resonance.
1. Hu G., Ditzinger T., Ning C. Z., Haken H. Stochastic resonance without external periodic force// Phys. Rev. Lett. 1993. Vol. 71. P. 807‒810.
2. Pikovsky A., Kurths J. Coherence resonance in a noisedriven excitable system // Phys. Rev. Lett. 1997. Vol. 78. P. 775‒778.
3. Lindner B., Schimansky-Geier L. Analytical approach to the stochastic FitzHugh-Nagumo system and coherence resonance // Phys. Rev. E. 1999. Vol. 60. P. 7270‒ 7276.
4. Lindner B., Garcıa-Ojalvo J., Neiman A. B., Schimansky- Geier L. Effects of noise in excitable systems // Phys. Rep. 2004. Vol. 392. P. 321‒424.
5. FitzHugh R. A. Impulses and physiological states in theoretical models of nerve membrane // Biophys. J. 1961. Vol. 1. P. 445‒466.
6. Nagumo J. S., Arimoto S., Yoshizawa S. An active pulse transmission line simulating nerve axon // Proceedings of the Institute of Radio Engineers. 1962. Vol. 50. P. 2061–2071.
7. Ushakov O. V., Wünsche H. J., Henneberger F., Khovanov I. A., Schimansky-Geier L., Zaks M. A. Coherence resonance near a Hopf bifurcation // Phys. Rev. Lett. 2005. Vol. 95. 123903.
8. Zakharova A., Vadivasova T., Anishchenko V., Koseska A., Kurths J. Stochastic bifurcations and coherencelike resonance in a self-sustained bistable noisy oscillator // Phys. Rev. E. 2010. Vol. 81. 011106.
9. Feoktistov A. , Anishchenko V. Coherence resonance and synchronization of stochastic self-sustained oscillations in hard excitation oscillator // Rus. J. Nonlin. Dyn. 2012. Vol.8. P. 897‒911.
10. Zakharova A., Feoktistov A., Vadivasova T., Schöll E. Coherence resonance and stochastic synchronization in a nonlinear circuit near a subcritical Hopf bifurcation // Eur. Phys. J. Spec. Top. 2013. Vol. 222. P. 2481‒2495.
11. Sethia G. C., Kurths J., Sen A. Coherence resonance in an excitable system with time delay // Phys. Lett. A. 2007. Vol. 364. P. 227–230.
12. Han S. K., Yim T. G., Postnov D. E., Sosnovtseva O. V. Interacting coherence resonance oscillators // Phys. Rev. Lett. 1999. Vol. 83. P. 1771‒1774.
13. Neiman A., Schimansky-Geier L., Cornell-Bel A., Moss F. Noise-enhanced phase synchronization in excitable media // Phys. Rev. Lett. 1999. Vol. 83. P. 4896–4899.
14. Hu B., Zhou Ch. Phase synchronization in coupled nonidentical excitable systems and array-enhanced coherence resonance // Phys. Rev. E. 2000. Vol. 61 (2). P. 1001‒1004.
15. Astakhov S., Feoktistov A., Anishchenko V., Kurths J. Synchronization of multi-frequency noise-induced oscillations // Chaos. 2011. Vol. 21. 047513.
16. Aust R., Hövel P., Hizanidis J., Schöll E. Delay control of coherence resonance in type-I excitable dynamics // Eur. Phys. J. ST. 2010. Vol. 187. P. 77‒85.
17. Janson N. B., Balanov A. G., Schöll E. Delayed feedback as a means of control of noise-induced motion // Phys. Rev. Lett. 2004. Vol. 93 010601.
18. Prager T., Lerch H.-Ph., Schimansky-Geier L., Schöll E. Increase of coherence in excitable systems by delayed feedback // J. Phys. A : Math. Theor. 2007. Vol. 40. P. 11045–11055.
19. Brandstetter S., Dahlem M. A., Schöll E. Interplay of time-delayed feedback control and temporally correlated noise in excitable systems // Philosophical Transactions of the Royal Society A : Mathematical, Physical and Engineering Sciences. 2010. Vol. 368. P. 391‒421.
20. Geffert P. M., Zakharova A., Vüllings A., Just W., Schöll E. Modulating coherence resonance in nonexcitable systems by time-delayed feedback // Eur. Phys. J. B. 2014. Vol. 87. P. 291‒304.
21. Escalera Santos G. J., Escalona J., Parmananda P. Regulating noise-induced spiking using feedback // Phys. Rev. E. 2006. Vol. 73. P. 042102.
22. Semenov V., Feoktistov A., Vadivasova T., Schöoll E., Zakharova A. Time-delayed feedback control of co herence resonance near subcritical Hopf bifurcation : Theory versus experiment // Chaos. 2015. Vol.25. P. 033111.
23. FitzHugh R. Impulses and physiological states in theoretical models of nerve membrane // Biophysical J. 1961. Vol. 1 (6). P. 445–466.
24. Nagumo J. S., Arimoto S., Yoshizawa S. An active pulse transmission line simulating nerve axon // Proceedings of the Institute of Radio Engineers. 1962. Vol. 50. P. 2061–2071.
