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Fronts in a bistable medium with two global constraints: Oscillatory instability and large-amplitude limit-cycle motion
Phys. Rev. E 58, 5586 – Published 1 November, 1998
DOI: https://doi.org/10.1103/PhysRevE.58.5586
Abstract
We study the propagation of fronts in a reaction-diffusion model of a bistable medium with two global constraints. The model applies to lateral current density fronts in three-electrode bistable semiconductor systems driven by the main and gate circuits. When taken separately, these constraints provide positive and negative feedbacks on front dynamics leading to accelerated and decelerated fronts, respectively. Under two constraints, there is an interplay between positive and negative feedback resulting in an oscillatory instability of a stationary front and large-amplitude limit-cycle motion. The instability occurs purely due to the global coupling and is not sensitive to the effect of the boundaries.
References (26)
- F. J. Elmer, Phys. Rev. A 41, 4174 (1990); Z. Phys. B 87, 377 (1992).
- L. Schimansky-Geier, Ch. Zülicke, and E. Schöll, Z. Phys. B 84, 433 (1991); Physica A 188, 436 (1992).
- F.-J. Niedernostheide, R. Dohmen, H. Willebrand, B. S. Kerner, and H.-G. Purwins, Physica D 69, 425 (1993).
- D. Battogtokh and A. S. Mikhailov, Physica D 90, 84 (1996).
- M. Falcke, H. Engel, and M. Neufeld, Phys. Rev. E 52, 98 (1995); ibid.M. Falcke and H. Engel, 56, 635 (1997).
- Self-Organization in Activator-Inhibitor-Systems: Semiconductors, Gas Discharge, and Chemical Active Media, edited by H. Engel, F.-J. Niedernostheide, H. G. Purwins, and E. Schöll (Wissenschaft und Technik Verlag, Berlin, 1996).
- I. Schebesch and H. Engel, in Self-Organization in Activator-Inhibitor-Systems: Semiconductors, Gas Discharge, and Chemical Active Media (Ref. [6]), p. 120.
- F. Mertens, R. Imbihl, and A. Mikhailov, J. Chem. Phys. 101, 9903 (1994).
- F.-J. Niedernostheide, M. Or-Guil, M. Kleinkes, and H.-G. Purwins, Phys. Rev. E 55, 4107 (1997).
- N. Mazouz, G. Flätgen, and K. Krischer, Phys. Rev. E 55, 2260 (1997).
- H. Hempel, I. Schebesch, and L. Schimansky-Geier, Eur. Phys. J. B 2, 399 (1998).
- E. Schöll, Nonequilibrium Phase Transitions in Semiconductors (Springer, Berlin, 1987).
- A. Alekseev, S. Bose, P. Rodin, and E. Schöll, Phys. Rev. E 57, 2640 (1998).
- A. Wacker and E. Schöll, Z. Phys. B 93, 431 (1994); S. Bose, A. Wacker, and E. Schöll, Phys. Lett. A 195, 144 (1994); F.-J. Niedernostheide, H. J. Schulze, S. Bose, A. Wacker, and E. Schöll, Phys. Rev. E 54, 1253 (1996).
- M. Meixner, P. Rodin, and E. Schöll, Phys. Status Solidi B 204, 493 (1997); Phys. Rev. E 58, 2796 (1998).
- Proceeding of the International Symposium on Power Semiconductor Devices, Davos, Switzerland, May 31 - June 2, 1994, edited by W. Fichtner and A. Jaecklin (Swiss Federal Institute of Technology ETH, Zürich, 1994).
- D. Ruwisch, M. Bode, H.-J. Schulze and F.-J. Niedernostheide, in Nonlinear Physics of Complex Systems, edited by J. Parisi and W. Zimmermann, Lecture Notes in Physics Vol. 476 (Springer, Berlin, 1996), p. 194.
- C. Radehaus and H. Willebrand, in Nonlinear Dynamics and Pattern Formation in Semiconductors and Devices, edited by F.-J. Niedernostheide (Springer, Berlin, 1995).
- A. Gorbatyuk and P. Rodin, Z. Phys. B 104, 45 (1997).
- A. Gorbatyuk and P. Rodin, Solid-State Electron. 35, 1359 (1992).
- E. Ben-Jacob, H. Brand, G. Dee, L. Kramer, and J. S. Langer, Physica D 14, 348 (1985).
- A. S. Mikhailov, Foundation of Synergetics (Springer, Berlin, 1994), Vol. 1.
- M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 4.: Analysis of Operators (Academic Press, New York, 1972).
- A. Martin, M. Lerch, P. Simmonds, and L. Eaves, Appl. Phys. Lett. 64, 1248 (1994).
- A. Wacker and E. Schöll, J. Appl. Phys. 78, 7352 (1995).
- D. Ruwisch (private communication).