scholarly journals CORRIGENDUM: Fenichel Theory for Multiple Time Scale Singular Perturbation Problems

2019 ◽  
Vol 18 (2) ◽  
pp. 1223-1223
Author(s):  
Pedro Toniol Cardin ◽  
Marco Antonio Teixeira
Keyword(s):  
Singular Perturbation ◽  
Time Scale ◽  
Singular Perturbation Problems ◽  
Multiple Time ◽  
Multiple Time Scale ◽  
Perturbation Problems ◽  
Fenichel Theory

scholarly journals Viscosity methods for large deviations estimates of multiscale stochastic processes

2018 ◽  
Vol 24 (2) ◽  
pp. 605-637 ◽  
Author(s):  
Daria Ghilli
Keyword(s):  
Singular Perturbation ◽  
Large Deviations ◽  
Stochastic Processes ◽  
Stochastic Volatility ◽  
Time Scale ◽  
Stochastic Systems ◽  
Singular Perturbation Problems ◽  
Hjb Equations ◽  
Large Deviations Estimates ◽  
Perturbation Problems

We study singular perturbation problems for second order HJB equations in an unbounded setting. The main applications are large deviations estimates for the short maturity asymptotics of stochastic systems affected by a stochastic volatility, where the volatility is modelled by a process evolving at a faster time scale and satisfying some condition implying ergodicity.

BIFURCATIONS OF RELAXATION OSCILLATIONS NEAR FOLDED SADDLES

2005 ◽  
Vol 15 (11) ◽  
pp. 3411-3421 ◽  
Author(s):  
JOHN GUCKENHEIMER ◽  
KATHLEEN HOFFMAN ◽  
WARREN WECKESSER
Keyword(s):  
Perturbation Theory ◽  
Dynamical Systems ◽  
Singular Perturbation ◽  
Time Scale ◽  
Singular Limit ◽  
Singular Perturbation Theory ◽  
Multiple Time ◽  
Multiple Time Scale ◽  
Relaxation Oscillations ◽  
Geometric Methods

Relaxation oscillations are periodic orbits of multiple time scale dynamical systems that contain both slow and fast segments. The slow–fast decomposition of these orbits is defined in the singular limit. Geometric methods in singular perturbation theory classify degeneracies of these decompositions that occur in generic one-parameter families of relaxation oscillations. This paper investigates the bifurcations that are associated with one type of degeneracy that occurs in systems with two slow variables, in which relaxation oscillations become homoclinic to a folded saddle.

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