Using a one-dimensional nonlinear oscillator
model, the Duffing oscillator detection model is established.
Holmes, "dynamics of a nonlinear oscillator
with feedback control.
They cover asymptotic expansions and series, asymptotic methods for solving nonlinear equations, the perturbation of nonlinear oscillations, a nonlinear oscillator
in a potential well, auto-resonances in nonlinear systems, asymptotics for loss of stability, and systems of coupled oscillators.
Luongo and Zulli considered a general, nonlinear, multiDOF structure attached to a nonlinear oscillator
with small mass and damping, and a mixed multiple scale/harmonic balance method was proposed to obtain differential equations describing the slow- and fast-flow dynamics of the entire structure .
Bailey, Biomimetic control with a feedback coupled nonlinear oscillator
: insect experiments, design tools, and hexapedal robot adaptation results [Ph.D.
Wang, "Inner resonance of a coupled hyperbolic tangent nonlinear oscillator
arising in a packaging system," Applied Mathematics and Computation, vol.
where T is period of the nonlinear oscillator
, F(u) = [integral] f (u)du.
Marquez, Higher order analytical approximations to a nonlinear oscillator
with discontinuity by He's homotopy perturbation method, Physics Letters A 372 (2008) 2010-2016.
In this paper it is shown how it is possible to realise a simple nonlinear oscillator
and observe the behaviour of the main nonlinear characteristics from a mechanical (and mathematical) point of view.
"It is difficult enough to analyze the dynamics of a single nonlinear oscillator
, let alone a whole population of them."