On the Conditions for Invariance of the Sets Belonging to the Phase Portraits of Nonlinear Dynamic Systems

2005 ◽  
Vol 66 (6) ◽  
pp. 866-875 ◽  
Author(s):  
V. P. Zhukov
Keyword(s):  
Dynamic Systems ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Systems ◽  
Phase Portraits

scholarly journals Phase Shadows: An Enhanced Representation of Nonlinear Dynamic Systems

2017 ◽  
Vol 27 (14) ◽  
pp. 1730051
Author(s):  
Amalia Luque ◽  
Julio Barbancho ◽  
Javier Fernández Cañete ◽  
Antonio Córdoba
Keyword(s):  
Phase Portrait ◽  
Dynamic Systems ◽  
Limit Cycles ◽  
Nonlinear Dynamic ◽  
Equilibrium Points ◽  
Nonlinear Dynamic Systems ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
System Behavior ◽  
Cylindrical Phase

Many nonlinear dynamic systems have a rotating behavior where an angle defining its state may extend to more than 360[Formula: see text]. In these cases the use of the phase portrait does not properly depict the system’s evolution. Normalized phase portraits or cylindrical phase portraits have been extensively used to overcome the original phase portrait’s disadvantages. In this research a new graphic representation is introduced: the phase shadow. Its use clearly reveals the system behavior while overcoming the drawback of the existing plots. Through the paper the method to obtain the graphic is stated. Additionally, to show the phase shadow’s expressiveness, a rotating pendulum is considered. The work exposes that the new graph is an enhanced representational tool for systems having equilibrium points, limit cycles, chaotic attractors and/or bifurcations.

Model Checking Control Software for Nonlinear Dynamic Systems

2008 ◽  
Author(s):  
James Kapinski ◽  
Alexandre Donze ◽  
Flavio Lerda ◽  
Hitashyam Maka ◽  
Edmund Clarke ◽  
...  
Keyword(s):  
Model Checking ◽  
Dynamic Systems ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Systems ◽  
Control Software

Emulation of Ensembles of Nonlinear Dynamic Systems in Ultrawideband Active Wireless Direct Chaotic Networks

2018 ◽  
Vol 7 (3) ◽  
pp. 38-49
Author(s):  
Yu.V. Andreyev ◽  
◽  
M.Yu. Gerasimov ◽  
A.S. Dmitriev ◽  
R.Yu. Yemelyanov ◽  
...  
Keyword(s):  
Dynamic Systems ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Systems

scholarly journals Developing a deep learning estimator to learn nonlinear dynamic systems

2020 ◽  
Vol 53 (2) ◽  
pp. 158-163
Author(s):  
Kai Wang ◽  
Junghui Chen ◽  
Yalin Wang
Keyword(s):  
Deep Learning ◽  
Dynamic Systems ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Systems

Numerical algorithm for the Mayer problem for nonlinear dynamic systems

1991 ◽  
Vol 54 (2) ◽  
pp. 847-853
Author(s):  
V. A. Bazhenov ◽  
V. I. Gulyaev ◽  
V. L. Koshkin ◽  
I. V. Yarmolenko
Keyword(s):  
Numerical Algorithm ◽  
Dynamic Systems ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Systems ◽  
Mayer Problem
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