Databases for the Global Dynamics of Multiparameter Nonlinear Systems

2014 ◽  
Author(s):  
Konstantin Mischaikow
Keyword(s):  
Nonlinear Systems ◽  
Global Dynamics

Transient Vibrations of Nonlinear Systems: Global Dynamics and Chaotic Transients

1993 ◽  
Author(s):  
Mohamed S. Soliman
Keyword(s):  
Steady State ◽  
Nonlinear Systems ◽  
Transient Stability ◽  
Basins Of Attraction ◽  
Global Dynamics ◽  
New Approach ◽  
Damping Characteristics ◽  
Ship Roll ◽  
Chaotic Transients ◽  
Basin Boundaries

Abstract In this paper a new approach in the global transient analysis of nonlinear systems is presented; it has the advantages of being conceptually simpler and at the same time more relevant than one based soley on a stability analysis of the steady-state motions. We address the problem of analysing the global transient stability of nonlinear systems in terms of basins of attraction. We show that at a forcing level that is considerably smaller than that at which the steady state attractor loses its stability, there may exist a rapid erosion and stratification of the basin, signifying a global loss of engineering integrity of the system. This conclusion is reinforced by the fact that basin boundaries can become fractal, resulting in chaotic transients, adding a new degree of uncertainty in the response. The techniques developed are then applied to a ship roll model with cubic and quintic nonlinearities as well as linear plus cubic damping characteristics.

Identification of Continuous-time Nonlinear Systems via Local Gaussian Process Models

2014 ◽  
Vol 134 (11) ◽  
pp. 1708-1715
Author(s):  
Tomohiro Hachino ◽  
Kazuhiro Matsushita ◽  
Hitoshi Takata ◽  
Seiji Fukushima ◽  
Yasutaka Igarashi
Keyword(s):  
Nonlinear Systems ◽  
Gaussian Process ◽  
Continuous Time ◽  
Process Models ◽  
Gaussian Process Models

Modeling of Nonlinear Systems using Genetic Algorithm

2012 ◽  
Vol 132 (6) ◽  
pp. 913-918 ◽  
Author(s):  
Kayoko Hayashi ◽  
Toru Yamamoto ◽  
Kazuo Kawada
Keyword(s):  
Genetic Algorithm ◽  
Nonlinear Systems
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