134 research outputs found
Optimal Phase Description of Chaotic Oscillators
We introduce an optimal phase description of chaotic oscillations by
generalizing the concept of isochrones. On chaotic attractors possessing a
general phase description, we define the optimal isophases as Poincar\'e
surfaces showing return times as constant as possible. The dynamics of the
resultant optimal phase is maximally decoupled of the amplitude dynamics, and
provides a proper description of phase resetting of chaotic oscillations. The
method is illustrated with the R\"ossler and Lorenz systems.Comment: 10 Pages, 14 Figure
Two Scenarios of Breaking Chaotic Phase Synchronization
Two types of phase synchronization (accordingly, two scenarios of breaking
phase synchronization) between coupled stochastic oscillators are shown to
exist depending on the discrepancy between the control parameters of
interacting oscillators, as in the case of classical synchronization of
periodic oscillators. If interacting stochastic oscillators are weakly detuned,
the phase coherency of the attractors persists when phase synchronization
breaks. Conversely, if the control parameters differ considerably, the chaotic
attractor becomes phase-incoherent under the conditions of phase
synchronization break.Comment: 8 pages, 7 figure
Synchronization of chaotic oscillator time scales
This paper deals with the chaotic oscillator synchronization. A new approach
to detect the synchronized behaviour of chaotic oscillators has been proposed.
This approach is based on the analysis of different time scales in the time
series generated by the coupled chaotic oscillators. It has been shown that
complete synchronization, phase synchronization, lag synchronization and
generalized synchronization are the particular cases of the synchronized
behavior called as "time--scale synchronization". The quantitative measure of
chaotic oscillator synchronous behavior has been proposed. This approach has
been applied for the coupled Rossler systems.Comment: 29 pages, 11 figures, published in JETP. 100, 4 (2005) 784-79
Detection of synchronization from univariate data using wavelet transform
A method is proposed for detecting from univariate data the presence of
synchronization of a self-sustained oscillator by external driving with varying
frequency. The method is based on the analysis of difference between the
oscillator instantaneous phases calculated using continuous wavelet transform
at time moments shifted by a certain constant value relative to each other. We
apply our method to a driven asymmetric van der Pol oscillator, experimental
data from a driven electronic oscillator with delayed feedback and human
heartbeat time series. In the latest case, the analysis of the heart rate
variability data reveals synchronous regimes between the respiration and slow
oscillations in blood pressure.Comment: 10 pages, 9 figure
A new approach to partial synchronization in globally coupled rotators
We develop a formalism to analyze the behaviour of pulse--coupled identical
phase oscillators with a specific attention devoted to the onset of partial
synchronization. The method, which allows describing the dynamics both at the
microscopic and macroscopic level, is introduced in a general context, but then
the application to the dynamics of leaky integrate-and-fire (LIF) neurons is
analysed. As a result, we derive a set of delayed equations describing exactly
the LIF behaviour in the thermodynamic limit. We also investigate the weak
coupling regime by means of a perturbative analysis, which reveals that the
evolution rule reduces to a set of ordinary differential equations. Robustness
and generality of the partial synchronization regime is finally tested both by
adding noise and considering different force fields.Comment: 5 pages, 3 eps figure
Synchronization of fractional order chaotic systems
The chaotic dynamics of fractional order systems begin to attract much
attentions in recent years. In this brief report, we study the master-slave
synchronization of fractional order chaotic systems. It is shown that
fractional order chaotic systems can also be synchronized.Comment: 3 pages, 5 figure
Periodicity Manifestations in the Turbulent Regime of Globally Coupled Map Lattice
We revisit the globally coupled map lattice (GCML). We show that in the so
called turbulent regime various periodic cluster attractor states are formed
even though the coupling between the maps are very small relative to the
non-linearity in the element maps.
Most outstanding is a maximally symmetric three cluster attractor in period
three motion (MSCA) due to the foliation of the period three window of the
element logistic maps. An analytic approach is proposed which explains
successfully the systematics of various periodicity manifestations in the
turbulent regime. The linear stability of the period three cluster attractors
is investigated.Comment: 34 pages, 8 Postscript figures, all in GCML-MSCA.Zi
Duration of the Process of Complete Synchronizationof Two Coupled Identical Chaotic Systems
We consider the time required for complete synchronization of two identical
one-way coupled vander Pol-Duffing oscillators occurring in the regime of
dynamic chaos. The influence of the initial phase differ-ence between
oscillators on the duration of the process of complete synchronization has been
studied. At a fixedphase of chaotic oscillations of the self-excited drive
oscillator, the period of time (past the coupling onset) during which the
complete synchronization regime is established depends on the phase of the
self-excited responseoscillatorComment: 4 pages, 2 figure
- …