STIMULUS-INDUCED CHAOTIC SYNCHRONIZATION OF CHUA'S OSCILLATORS

The problem of phase synchronization of Chua's chaotic oscillators is investigated. We consider Chua's circuit when it exhibits a chaotic attractor and apply a single pulse stimulus. It is shown that under certain conditions the system displays self-referential phase reset (SPR) phenomenon. This is a case when the reset phase of the chaotic oscillation is independent on the initial phase, hence on the time moment when the stimulus has been applied. In an ensemble of chaotic oscillators simultaneously stimulated, the SPR yields mutual phase coherence or synchronization between the units. We describe basic dynamical mechanisms of the effect and show how it can be used for controllable cluster formation and for the control of chaotic dynamics.

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PHASE AND LAG SYNCHRONIZATION IN COUPLED FRACTIONAL ORDER CHAOTIC OSCILLATORS

International Journal of Modern Physics B ◽

10.1142/s0217979207038162 ◽

2007 ◽

Vol 21 (30) ◽

pp. 5159-5166 ◽

Cited By ~ 6

Author(s):

CHUNGUANG LI

Keyword(s):

Fractional Order ◽

Coupling Strength ◽

Chaotic Dynamics ◽

Phase Synchronization ◽

Lag Synchronization ◽

Chaotic Oscillators ◽

Integer Order

Chaotic dynamics of fractional (non-integer) order systems have begun to attract much attention in recent years. In this paper, we study the phase and lag synchronization in coupled two fractional order chaotic oscillators. It is shown that with the increase of coupling strength, the system first undergoes a transition to phase synchronization, and when the coupling strength is increased further, another transition to lag synchronization occurs. It is further shown that the system with two chaotic oscillators of different orders can also exhibit phase synchronization phenomena, although the identical synchronization is impossible in this case.

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Top-down control of visual cortex by the frontal eye fields through oscillatory realignment

Nature Communications ◽

10.1038/s41467-021-21979-7 ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

Domenica Veniero ◽

Joachim Gross ◽

Stephanie Morand ◽

Felix Duecker ◽

Alexander T. Sack ◽

...

Keyword(s):

Visual Cortex ◽

Transcranial Magnetic Stimulation ◽

Visual Perception ◽

Magnetic Stimulation ◽

Single Pulse ◽

Frontal Eye Fields ◽

Phase Reset ◽

Top Down ◽

Visual Areas ◽

Beta Frequency

AbstractVoluntary allocation of visual attention is controlled by top-down signals generated within the Frontal Eye Fields (FEFs) that can change the excitability of lower-level visual areas. However, the mechanism through which this control is achieved remains elusive. Here, we emulated the generation of an attentional signal using single-pulse transcranial magnetic stimulation to activate the FEFs and tracked its consequences over the visual cortex. First, we documented changes to brain oscillations using electroencephalography and found evidence for a phase reset over occipital sites at beta frequency. We then probed for perceptual consequences of this top-down triggered phase reset and assessed its anatomical specificity. We show that FEF activation leads to cyclic modulation of visual perception and extrastriate but not primary visual cortex excitability, again at beta frequency. We conclude that top-down signals originating in FEF causally shape visual cortex activity and perception through mechanisms of oscillatory realignment.

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Phase synchronization of chaotic oscillators by external driving

Physica D Nonlinear Phenomena ◽

10.1016/s0167-2789(96)00301-6 ◽

1997 ◽

Vol 104 (3-4) ◽

pp. 219-238 ◽

Cited By ~ 391

Author(s):

Arkady S. Pikovsky ◽

Michael G. Rosenblum ◽

Grigory V. Osipov ◽

Jürgen Kurths

Keyword(s):

Phase Synchronization ◽

Chaotic Oscillators ◽

External Driving

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Experimental Implementation of Networked Chaotic Oscillators Based on Cross-Coupled Inverter Rings in a CMOS Integrated Circuit

Journal of Circuits System and Computers ◽

10.1142/s0218126615501443 ◽

2015 ◽

Vol 24 (09) ◽

pp. 1550144 ◽

Cited By ~ 4

Author(s):

Ludovico Minati

Keyword(s):

Experimental Data ◽

Integrated Circuit ◽

Phase Synchronization ◽

Random Number Generation ◽

Partial Amplitude ◽

Chaotic Oscillator ◽

Chaotic Oscillators ◽

Cmos Integrated Circuit ◽

Experimental Implementation ◽

Small Clusters

A novel chaotic oscillator based on "cross-coupled" inverter rings is presented. The oscillator consists of a 3-ring to which higher odd n-rings are progressively coupled via diodes and pass gates; it does not contain reactive or resistive elements, and is thus suitable for area-efficient implementation on a CMOS integrated circuit. Numerical simulation based on piece-wise linear approximation predicted the generation of positive spikes having approximately constant periodicity but highly variable cycle amplitude. Simulation Program with Integrated Circuit Emphasis (SPICE) simulations and experimental data from a prototype realized on 0.7 μm technology confirmed this finding, and demonstrated increasing correlation dimension (D2) as 5-, 7- and 9-rings were progressively coupled to the 3-ring. Experimental data from a ring of 24 such oscillator cells showed phase synchronization and partial amplitude synchronization (formation of small clusters), emerging depending on DC gate voltage applied at NMOS transistors implementing diffusive coupling between neighboring cells. Thanks to its small area, simple synchronizability and digital controllability, the proposed circuit enables experimental investigation of dynamical complexity in large networks of coupled chaotic oscillators, and may additionally be suitable for applications such as broadband signal and random number generation.

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Phase synchronization in coupled chaotic oscillators with time delay

Physical Review E ◽

10.1103/physreve.66.056203 ◽

2002 ◽

Vol 66 (5) ◽

Cited By ~ 11

Author(s):

J. Y. Chen ◽

K. W. Wong ◽

J. W. Shuai

Keyword(s):

Time Delay ◽

Phase Synchronization ◽

Chaotic Oscillators

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SYNCHRONIZING CHAOTIC ATTRACTORS OF CHUA'S CANONICAL CIRCUIT: THE CASE OF UNCERTAINTY IN CHAOS SYNCHRONIZATION

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127406015829 ◽

2006 ◽

Vol 16 (07) ◽

pp. 1961-1976 ◽

Cited By ~ 5

Author(s):

I. M. KYPRIANIDIS ◽

A. N. BOGIATZI ◽

M. PAPADOPOULOU ◽

I. N. STOUBOULOS ◽

G. N. BOGIATZIS ◽

...

Keyword(s):

Coupling Strength ◽

Chaos Synchronization ◽

Phase Synchronization ◽

Initial Conditions ◽

Chaotic Synchronization ◽

Chaotic Attractors ◽

Coexisting Attractors

In this paper, we have studied the dynamics of two identical resistively coupled Chua's canonical circuits and have found that it is strongly affected by initial conditions, coupling strength and the presence of coexisting attractors. Depending on the coupling variable, chaotic synchronization has been observed both numerically and experimentally. Anti-phase synchronization has also been studied numerically clarifying some aspects of uncertainty in chaos synchronization.

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COOPERATIVE PHASE DYNAMICS IN COUPLED NEPHRONS

International Journal of Modern Physics B ◽

10.1142/s0217979201007233 ◽

2001 ◽

Vol 15 (23) ◽

pp. 3079-3098 ◽

Cited By ~ 20

Author(s):

D. E. POSTNOV ◽

O. V. SOSNOVTSEVA ◽

E. MOSEKILDE ◽

N.-H. HOLSTEIN-RATHLOU

Keyword(s):

Chaotic Dynamics ◽

Phase Synchronization ◽

Functional Unit ◽

Flow Regulation ◽

Tubuloglomerular Feedback ◽

Phase Dynamics ◽

The Individual ◽

Fast Oscillations ◽

Coherent Behavior ◽

Different Time Scales

The individual functional unit of the kidney (the nephron) displays oscillations in its pressure and flow regulation at two different time scales: Relatively fast oscillations associated with the myogenic dynamics of the afferent arteriole, and slower oscillations related with a delay in the tubuloglomerular feedback. Neighboring nephrons interact via vascularly propagated signals. We study the appearance of various forms of coherent behavior in a model of two such interacting nephrons. Among the observed phenomena are in-phase and anti-phase synchronization of chaotic dynamics, multistability, and partial phase synchronization in which the nephrons attain a state of chaotic phase synchronization with respect to their slow dynamics, but the fast dynamics remains desynchronized.

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