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.
For explaining the VA procedure, we consider a general nonlinear oscillator
in the form of Eq.
Marquez, Higher order analytical approximations to a nonlinear oscillator
with discontinuity by He's homotopy perturbation method, Physics Letters A 372 (2008) 2010-2016.
Concerning the organization of this paper, next an introduction to chaos is presented, then a description of the created software is exposed and after that the application to the case of the damped nonlinear oscillator
with variable damping is reported.
The Virtual Lab has been successfully applied to investigate the transition to chaos in the damped and forced nonlinear oscillator
, with variable (increasing) applied force.
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.
Li, "Heteroclinic bifurcation of strongly nonlinear oscillator
," Chinese Physics Letters, vol.
We consider a generalized nonlinear oscillator
in the form
ot = p/4, and setting R(t =p/4o ) = 0, we can obtain an approximate frequency-amplitude relationship of the studied nonlinear oscillator
In this paper we consider the following nonlinear oscillator
In the near future, the circuit simulator will include nonlinear oscillator
, noise (including phase and mixer noise) and stability analyses.