Excitable systems with noise and delay, with applications to control: Renewal theory approach

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 77, Issue 3, 2008, Pages

  Pototsky, Andrey ^a   Janson, Natalia ^a  

^a LOUGHBOROUGH UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

FUNCTIONS; PARAMETER ESTIMATION; RANDOM PROCESSES; SPURIOUS SIGNAL NOISE; TIME DELAY;

BISTABLE SYSTEMS; EXCITABLE SYSTEMS;

ELECTRIC EXCITATION;

EID: 40949137738     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.77.031113     Document Type: Article

References (22)

1. B. Lindner, J. Garcia-Ojalvo, A. Neiman, and L. Schimansky-Geier, Phys. Rep. PRPLCM 0370-1573 10.1016/j.physrep.2003.10.015 392, 321 (2004).
2. B. Lindner and L. Schimansky-Geier, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.61.6103 61, 6103 (2000).
3. A. Neiman, P. I. Saparin, and L. Stone, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.56.270 56, 270 (1997).
4. D. R. Cox, Renewal Theory (Methuen, London, 1970).
5. I. Goychuk, P. Hänggi, J. L. Vega, and S. Miret-Artes, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.71.061906 71, 061906 (2005).
6. T. Prager and L. Schimansky-Geier, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.230601 91, 230601 (2003).
7. V. I. Melnikov, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.48.2481 48, 2481 (1993).
8. N. B. Janson, A. G. Balanov, and E. Schöll, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.010601 93, 010601 (2004).
9. K. Pyragas, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(92)90745-8 170, 421 (1992).
10. A. G. Balanov, N. B. Janson, and E. Schöll, Physica D PDNPDT 0167-2789 10.1016/j.physd.2004.05.008 199, 1 (2004).
11. E. Schöll, A. G. Balanov, N. B. Janson, and A. Neiman, Stochastics Dyn. ZZZZZZ 0219-4937 5, 281 (2005).
12. N. B. Janson, A. G. Balanov, and E. Schöll, Handbook of Chaos Control (Wiley-VCH, Weinheim, 2007), pp. 223-273.
13. A. Amann, W. Just, and E. Schöll, Physica A PHYADX 0378-4371 10.1016/j.physa.2005.12.073 373, 191 (2007).
14. T. Prager, H.-P. Lerch, L. Schimansky-Geier, and E. Schöll, J. Phys. A JPHAC5 0305-4470 10.1088/1751-8113/40/36/005 40, 11045 (2007).
15. B. McNamara and K. Wiesenfeld, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.39.4854 39, 4854 (1989).
16. T. Piwonski, J. Houlihan, T. Busch, and G. Huyet, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.040601 95, 040601 (2005).
17. H. Kramers, Physica (Amsterdam) PHYSAG 0031-8914 10.1016/S0031-8914(40) 90098-2 7, 284 (1940).
18. A. R. Bulsara and L. Gammaitoni, Phys. Today PHTOAD 0031-9228 49, 39 (1996).
19. C. W. Gardiner, Handbook of Stochastic Methods (Springer-Verlag, Berlin, 2004).
20. I. Goychuk and P. Hänggi, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.69.021104 69, 021104 (2004).
21. A. Pototsky and N. B. Janson, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.76.056208 76, 056208 (2007).
22. A. S. Pikovsky and J. Kurths, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.78.775 78, 775 (1997).