Subharmonic resonance and chaos in forced excitable systems |
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Authors: | Hans G Othmer Min Xie |
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Institution: | (1) Department of Mathematics, University of Utah, Salt Lake City,UT, 84112, USA. e-mail:othmer@math.utah.edu, US |
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Abstract: | Forced excitable systems arise in a number of biological and physiological applications and have been studied analytically
and computationally by numerous authors. Existence and stability of harmonic and subharmonic solutions of a forced piecewise-linear
Fitzhugh-Nagumo-like system were studied in Othmer ad Watanabe (1994) and in Xie et al. (1996). The results of those papers
were for small and moderate amplitude forcing. In this paper we study the existence of subharmonic solutions of this system
under large-amplitude forcing. As in the case of intermediate-amplitude forcing, bistability between 1 : 1 and 2 : 1 solutions
is possible for some parameters. In the case of large-amplitude forcing, bistability between 2 : 2 and 2 : 1 solutions, which
does not occur in the case of intermediate-amplitude forcing, is also possible for some parameters. We identify several new
canonical return maps for a singular system, and we show that chaotic dynamics can occur in some regions of parameter space.
We also prove that there is a direct transition from 2 : 2 phase-locking to chaos after the first period-doubling bifurcation,
rather than via the infinite sequence of period doublings seen in a smooth quadratic interval map. Coexistence of chaotic
dynamics and stable phase-locking can also occur.
Received: 6 July 1998 / Revised version: 2 October 1998 |
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Keywords: | : Phase locking Fitzhugh-Nagumo |
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