Darboux first integrals and linearizability of quadratic–quintic Duffing–van der Pol oscillators

2021 ◽  
pp. 104215
Author(s):  
Maria V. Demina ◽  
Dmitry I. Sinelshchikov
Keyword(s):  
First Integrals ◽  
Van Der Pol ◽  
Van Der Pol Oscillators ◽  
Darboux First Integrals

Asymptotic Wave Solutions for the Model of a Medium with Van Der Pol Oscillators

2014 ◽  
Vol 59 (9) ◽  
pp. 932-938
Author(s):  
V.A. Danylenko ◽  
◽  
S.I. Skurativskyi ◽  
I.A. Skurativska ◽  
◽  
...  
Keyword(s):  
Van Der Pol ◽  
Wave Solutions ◽  
Van Der Pol Oscillators

scholarly journals Modal synchronization of coupled bistable van der Pol oscillators

2021 ◽  
Vol 143 ◽  
pp. 110555
Author(s):  
I.B. Shiroky ◽  
O.V. Gendelman
Keyword(s):  
Van Der Pol ◽  
Van Der Pol Oscillators

scholarly journals Uncovering Droop Control Laws Embedded Within the Nonlinear Dynamics of Van der Pol Oscillators

2017 ◽  
Vol 4 (2) ◽  
pp. 347-358 ◽  
Author(s):  
Mohit Sinha ◽  
Florian Dorfler ◽  
Brian B. Johnson ◽  
Sairaj V. Dhople
Keyword(s):  
Nonlinear Dynamics ◽  
Droop Control ◽  
Van Der Pol ◽  
Control Laws ◽  
Van Der Pol Oscillators

scholarly journals Dynamics of hierarchical weighted networks of van der Pol oscillators

2020 ◽  
Vol 30 (12) ◽  
pp. 123146
Author(s):  
Daniel Monsivais-Velazquez ◽  
Kunal Bhattacharya ◽  
Rafael A. Barrio ◽  
Philip K. Maini ◽  
Kimmo K. Kaski
Keyword(s):  
Van Der Pol ◽  
Weighted Networks ◽  
Van Der Pol Oscillators

On the non-integrability of a family of Duffing-van der Pol oscillators

1993 ◽  
Vol 26 (23) ◽  
pp. 6927-6942 ◽  
Author(s):  
T C Bountis ◽  
L B Drossos ◽  
M Lakshmanan ◽  
S Parthasarathy
Keyword(s):  
Van Der Pol ◽  
Van Der Pol Oscillators

HIGH-DIMENSIONAL CHAOS IN DISSIPATIVE AND DRIVEN DYNAMICAL SYSTEMS

2009 ◽  
Vol 19 (09) ◽  
pp. 2823-2869 ◽  
Author(s):  
Z. E. MUSIELAK ◽  
D. E. MUSIELAK
Keyword(s):  
Dynamical Systems ◽  
Degrees Of Freedom ◽  
Nonlinear Dynamical Systems ◽  
High Dimensional ◽  
Van Der Pol ◽  
Nonlinear Dynamical ◽  
Onset Of Chaos ◽  
General Rules ◽  
Van Der Pol Oscillators ◽  
Control And Synchronization

Studies of nonlinear dynamical systems with many degrees of freedom show that the behavior of these systems is significantly different as compared with the behavior of systems with less than two degrees of freedom. These findings motivated us to carry out a survey of research focusing on the behavior of high-dimensional chaos, which include onset of chaos, routes to chaos and the persistence of chaos. This paper reports on various methods of generating and investigating nonlinear, dissipative and driven dynamical systems that exhibit high-dimensional chaos, and reviews recent results in this new field of research. We study high-dimensional Lorenz, Duffing, Rössler and Van der Pol oscillators, modified canonical Chua's circuits, and other dynamical systems and maps, and we formulate general rules of high-dimensional chaos. Basic techniques of chaos control and synchronization developed for high-dimensional dynamical systems are also reviewed.

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