A hybrid evolutionary algorithm for the symbolic modeling of multiple-time-scale dynamical systems

2015 ◽  
Vol 8 (4) ◽  
pp. 149-164 ◽  
Author(s):  
Theodore W. Cornforth ◽  
Hod Lipson
Keyword(s):  
Dynamical Systems ◽  
Evolutionary Algorithm ◽  
Time Scale ◽  
Multiple Time ◽  
Multiple Time Scale ◽  
Symbolic Modeling ◽  
Hybrid Evolutionary Algorithm

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.

Sign in / Sign up

Export Citation Format

Share Document