Abstract
For a system of van der Pol-like oscillators, Lyapunov functions valid in the greater part of phase space are given. They allow a finite region of attraction to be defined. Any attractor has to be within the rigorously estimated bounds. Under a special choice of the interaction matrices the attractive region can be squeezed to zero. In this case the asymptotic behaviour is given by a conservative system of nonlinear oscillators which acts as attractor. Though this system does not possess, in general, a Hamiltonian formulation, Gibbs statistics is possible due to the proof of a Liouville theorem and the existence of a positive invariant or `shell` condition. The `canonical` distribution on the attractor is remarkably simple despite nonlinearities. Finally the connection of the van der Pol-like system and of the attractive region with turbulence and fluctuation spectra in fluids and plasmas is discussed. (orig.)
Citation Formats
Tasso, H.
Lyapunov stability of large systems of van der Pol-like oscillators and connection with turbulence and fluctuations spectra.
Germany: N. p.,
1993.
Web.
Tasso, H.
Lyapunov stability of large systems of van der Pol-like oscillators and connection with turbulence and fluctuations spectra.
Germany.
Tasso, H.
1993.
"Lyapunov stability of large systems of van der Pol-like oscillators and connection with turbulence and fluctuations spectra."
Germany.
@misc{etde_10135119,
title = {Lyapunov stability of large systems of van der Pol-like oscillators and connection with turbulence and fluctuations spectra}
author = {Tasso, H}
abstractNote = {For a system of van der Pol-like oscillators, Lyapunov functions valid in the greater part of phase space are given. They allow a finite region of attraction to be defined. Any attractor has to be within the rigorously estimated bounds. Under a special choice of the interaction matrices the attractive region can be squeezed to zero. In this case the asymptotic behaviour is given by a conservative system of nonlinear oscillators which acts as attractor. Though this system does not possess, in general, a Hamiltonian formulation, Gibbs statistics is possible due to the proof of a Liouville theorem and the existence of a positive invariant or `shell` condition. The `canonical` distribution on the attractor is remarkably simple despite nonlinearities. Finally the connection of the van der Pol-like system and of the attractive region with turbulence and fluctuation spectra in fluids and plasmas is discussed. (orig.)}
place = {Germany}
year = {1993}
month = {Apr}
}
title = {Lyapunov stability of large systems of van der Pol-like oscillators and connection with turbulence and fluctuations spectra}
author = {Tasso, H}
abstractNote = {For a system of van der Pol-like oscillators, Lyapunov functions valid in the greater part of phase space are given. They allow a finite region of attraction to be defined. Any attractor has to be within the rigorously estimated bounds. Under a special choice of the interaction matrices the attractive region can be squeezed to zero. In this case the asymptotic behaviour is given by a conservative system of nonlinear oscillators which acts as attractor. Though this system does not possess, in general, a Hamiltonian formulation, Gibbs statistics is possible due to the proof of a Liouville theorem and the existence of a positive invariant or `shell` condition. The `canonical` distribution on the attractor is remarkably simple despite nonlinearities. Finally the connection of the van der Pol-like system and of the attractive region with turbulence and fluctuation spectra in fluids and plasmas is discussed. (orig.)}
place = {Germany}
year = {1993}
month = {Apr}
}