24,198 research outputs found
Energy Conservative Limit Cycle Oscillations
This paper shows how globally attractive limit cycle oscillations can be induced in a system with a nonlinear feedback element. Based on the same principle as the Van der Pol oscillator, the feedback behaves as a negative damping for low velocities but as an ordinary damper for high velocities. This nonlinear damper can be physically implemented with a continuous variable transmission and a spring, storing energy in the spring when the damping is positive and reusing it when the damping is negative. The resulting mechanism has a natural limit cycle oscillation that is energy conservative and can be used for the development of robust, dynamic walking robots
Phase reduction of stochastic limit cycle oscillators
We point out that the phase reduction of stochastic limit cycle oscillators
has been done incorrectly in the literature. We present a correct phase
reduction method for oscillators driven by weak external white Gaussian noises.
Numerical evidence demonstrates that the present phase equation properly
approximates the dynamics of the original full oscillator system.Comment: 4 pages, 2 figure
Synchronization of coupled stochastic limit cycle oscillators
For a class of coupled limit cycle oscillators, we give a condition on a
linear coupling operator that is necessary and sufficient for exponential
stability of the synchronous solution. We show that with certain modifications
our method of analysis applies to networks with partial, time-dependent, and
nonlinear coupling schemes, as well as to ensembles of local systems with
nonperiodic attractors. We also study robustness of synchrony to noise. To this
end, we analytically estimate the degree of coherence of the network
oscillations in the presence of noise. Our estimate of coherence highlights the
main ingredients of stochastic stability of the synchronous regime. In
particular, it quantifies the contribution of the network topology. The
estimate of coherence for the randomly perturbed network can be used as means
for analytic inference of degree of stability of the synchronous solution of
the unperturbed deterministic network. Furthermore, we show that in large
networks, the effects of noise on the dynamics of each oscillator can be
effectively controlled by varying the strength of coupling, which provides a
powerful mechanism of denoising. This suggests that the organization of
oscillators in a coupled network may play an important role in maintaining
robust oscillations in random environment. The analysis is complemented with
the results of numerical simulations of a neuronal network.
PACS: 05.45.Xt, 05.40.Ca
Keywords: synchronization, coupled oscillators, denoising, robustness to
noise, compartmental modelComment: major revisions; two new section
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