2 research outputs found
Edge of chaos as critical local symmetry breaking in dissipative nonautonomous systems
The fully nonlinear notion of resonance -- in
the general context of dissipative systems subjected to
potentials is discussed. It is demonstrated that there is an exact local
invariant associated with each geometrical resonance solution which reduces to
the system's energy when the potential is steady. The geometrical resonance
solutions represent a \textit{local symmetry} whose critical breaking leads to
a new analytical criterion for the order-chaos threshold. This physical
criterion is deduced in the co-moving frame from the local energy conservation
over the shortest significant timescale. Remarkably, the new criterion for the
onset of chaos is shown to be valid over large regions of parameter space, thus
being useful beyond the perturbative regime and the scope of current
mathematical techniques
Stochastic resonance with different periodic forces in overdamped two coupled anharmonic oscillators
We study the stochastic resonance phenomenon in the overdamped two coupled
anharmonic oscillators with Gaussian noise and driven by different external
periodic forces. We consider (i) sine, (ii) square, (iii) symmetric saw-tooth,
(iv) asymmetric saw-tooth, (v) modulus of sine and (vi) rectified sinusoidal
forces. The external periodic forces and Gaussian noise term are added to one
of the two state variables of the system. The effect of each force is studied
separately. In the absence of noise term, when the amplitude of the applied
periodic force is varied cross-well motion is realized above a critical value
() of . This is found for all the forces except the modulus
of sine and rectified sinusoidal forces.Stochastic resonance is observed in the
presence of noise and periodic forces. The effect of different forces is
compared. The logarithmic plot of mean residence time
against where is the intensity of the noise and
is the value of at which cross-well motion is initiated
shows a sharp knee-like structure for all the forces. Signal-to-noise ratio is
found to be maximum at the noise intensity at which mean
residence time is half of the period of the driving force for the forces such
as sine, square, symmetric saw-tooth and asymmetric saw-tooth waves. With
modulus of sine wave and rectified sine wave, the peaks at a value of
for which sum of in two wells of the potential of the system is
half of the period of the driving force. For the chosen values of and
, signal-to-noise ratio is found to be maximum for square wave while it
is minimum for modulus of sine and rectified sinusoidal waves.Comment: 13 figures,27 page