2006/03/28 by Madhurjya P. Bora, Bora, Madhurjya P., Dipak Sarmah +1
Chemistry · Mathematics · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #Chemistry #Computational Physics (physics.comp-ph) #Computer science #Control theory (sociology) #FOS: Physical sciences #Instability #Invariant manifold #Limit (mathematics) #Limit cycle #Magnetic confinement fusion research #Mathematical analysis #Mathematics #Mechanics #Oscillation (cell signaling) #Physics #Plasma #Plasma Physics (physics.plasm-ph) #Quantum mechanics #Relaxation (psychology) #Sawtooth wave #Slow manifold #Statistical physics #nlin.CD #physics.comp-ph #physics.plasm-ph
paper · pdf · doi:10.48550/arxiv.nlin/0603065
published in arXiv (Cornell University) (Cornell University) · 26 pages, 14 EPS figures. accepted for publication in Communications in Nonlinear Science and Numerical Simulations
arxiv created 2006/03/28 · openalex publication_date 2006/03/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A minimal (low-dimensional) dynamical model of the sawtooth oscillations is presented. It is assumed that the sawtooth is triggered by a thermal instability which causes the plasma temperature in the central part of the plasma to drop suddenly, leading to the sawtooth crash. It is shown that this model possesses an isolated limit cycle which exhibits relaxation oscillation, in the appropriate parameter regime, which is the typical characteristics of sawtooth oscillations. It is further shown that the invariant manifold of the model is actually the slow manifold of the relaxation oscillation.