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Subharmonic resonance and chaos in forced excitable systems
1Department of Mathematics, University of Utah, Salt Lake City, UT 84112, USA. othemer@math.utah.edu
Journal of Mathematical Biology
|August 14, 1999
Summary
This study investigates large-amplitude forcing in Fitzhugh-Nagumo-like systems, revealing new bistability phenomena and direct transitions to chaos. It identifies novel return maps and conditions for chaotic dynamics alongside stable phase-locking.
Area of Science:
- Mathematical Biology
- Dynamical Systems
- Computational Neuroscience
Background:
- Forced excitable systems are crucial in biological and physiological applications.
- Previous research analyzed harmonic and subharmonic solutions for small/moderate forcing amplitudes in Fitzhugh-Nagumo-like systems.
- The behavior under large-amplitude forcing remained less understood.
Purpose of the Study:
- To investigate the existence of subharmonic solutions in a forced piecewise-linear Fitzhugh-Nagumo-like system under large-amplitude forcing.
- To identify new dynamical behaviors and parameter regimes not observed with smaller forcing amplitudes.
- To characterize the transition to chaotic dynamics.
Main Methods:
- Analysis of a forced piecewise-linear Fitzhugh-Nagumo-like system.
- Identification of canonical return maps for a singular system.
- Computational and analytical investigation of system dynamics under varying forcing amplitudes.
Main Results:
- Bistability between 1:1 and 2:1 solutions occurs, similar to intermediate forcing.
- New bistability between 2:2 and 2:1 solutions is observed under large-amplitude forcing.
- Chaotic dynamics are identified in specific parameter regions, with direct transitions from 2:2 phase-locking to chaos via period-doubling bifurcations.
- Coexistence of chaotic dynamics and stable phase-locking is possible.
Conclusions:
- Large-amplitude forcing introduces novel bistability regimes in Fitzhugh-Nagumo-like systems.
- The system exhibits direct transitions to chaos, differing from smooth maps.
- Understanding these dynamics is crucial for applications involving forced excitable systems.
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