Dynamical systems design of nonlinear oscillators using phase reduction approach

2012 ◽  
Author(s):  
Kazuki Nakada ◽  
Keiji Miura ◽  
Tetsuya Asai ◽  
Hisa-aki Tanaka
Keyword(s):  
Dynamical Systems ◽  
Systems Design ◽  
Nonlinear Oscillators ◽  
Phase Reduction ◽  
Reduction Approach

scholarly journals Phase reduction theory for hybrid nonlinear oscillators

2017 ◽  
Vol 95 (1) ◽  
Author(s):  
Sho Shirasaka ◽  
Wataru Kurebayashi ◽  
Hiroya Nakao
Keyword(s):  
Nonlinear Oscillators ◽  
Reduction Theory ◽  
Phase Reduction

Quadratic and Cubic Nonlinear Oscillators with Damping and Their Applications

2016 ◽  
Vol 26 (03) ◽  
pp. 1650050
Author(s):  
Jibin Li ◽  
Zhaosheng Feng
Keyword(s):  
Dynamical Systems ◽  
Normal Form ◽  
Exact Solutions ◽  
Traveling Wave ◽  
Kdv Equation ◽  
Traveling Wave Solutions ◽  
Nonlinear Oscillators ◽  
Qualitative Theory ◽  
Wave Solutions ◽  
Explicit Representations

We apply the qualitative theory of dynamical systems to study exact solutions and the dynamics of quadratic and cubic nonlinear oscillators with damping. Under certain parametric conditions, we also consider the van der Waals normal form, Chaffee–Infante equation, compound Burgers–KdV equation and Burgers–KdV equation for explicit representations of kink-profile wave solutions and unbounded traveling wave solutions.

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