RELAXATION OSCILLATIONS IN SINGULARLY PERTURBED GENERALIZED LIENARD SYSTEMS WITH NON-GENERIC TURNING POINTS
نویسندگان
چکیده
منابع مشابه
Canard Solutions at Non-generic Turning Points
This paper deals with singular perturbation problems for vector fields on 2-dimensional manifolds. “Canard solutions” are solutions that, starting near an attracting normally hyperbolic branch of the singular curve, cross a “turning point” and follow for a while a normally repelling branch of the singular curve. Following the geometric ideas developed by Dumortier and Roussarie in 1996 for the ...
متن کاملA review on singularly perturbed differential equations with turning points and interior layers
Singular perturbation problems with turning points arise as mathematical models for various physical phenomena. The problem with interior turning point represent one-dimensional version of stationary convectiondiffusion problems with a dominant convective term and a speed field that changes its sign in the catch basin. Boundary turning point problems, on the other hand, arise in geophysics and ...
متن کاملBlue-sky Catastrophe in Singularly Perturbed Systems
We show that the blue-sky catastrophe, which creates a stable periodic orbit of unboundedly increasing length, is a typical phenomenon for singularly perturbed (multi-scale) systems with at least two fast variables. Three distinct mechanisms of this bifurcation are described. We argue that it is behind the transition from periodic spiking to periodic bursting oscillations. 2000 Math. Subj. Clas...
متن کاملNumerical method for a system of second order singularly perturbed turning point problems
In this paper, a parameter uniform numerical method based on Shishkin mesh is suggested to solve a system of second order singularly perturbed differential equations with a turning point exhibiting boundary layers. It is assumed that both equations have a turning point at the same point. An appropriate piecewise uniform mesh is considered and a classical finite difference scheme is applied on t...
متن کاملMonotone Relaxation Iterates and Applications to Semilinear Singularly Perturbed Problems
This paper deals with monotone relaxation iterates for solving nonlinear monotone difference schemes of elliptic type. The monotone ω-Jacobi and SUR (Successive Under-Relaxation) methods are constructed. The monotone methods solve only linear discrete systems at each iterative step and converge monotonically to the exact solution of the nonlinear monotone difference schemes. Convergent rates of...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Modelling and Analysis
سال: 2017
ISSN: 1392-6292,1648-3510
DOI: 10.3846/13926292.2017.1315344