Isochronous synchronization in mutually coupled chaotic circuits.

@article{Wagemakers2007IsochronousSI,
  title={Isochronous synchronization in mutually coupled chaotic circuits.},
  author={Alexandre Wagemakers and Javier M. Buld{\'u} and Miguel A. F. Sanju{\'a}n},
  journal={Chaos},
  year={2007},
  volume={17 2},
  pages={
          023128
        }
}
This paper examines the robustness of isochronous synchronization in simple arrays of bidirectionally coupled systems. First, the achronal synchronization of two mutually chaotic circuits, which are coupled with delay, is analyzed. Next, a third chaotic circuit acting as a relay between the previous two circuits is introduced. We observe that, despite the delay in the coupling path, the outer dynamical systems show isochronous synchronization of their outputs, i.e., display the same dynamics at… 

Figures from this paper

Adaptive Isochronal Synchronization in Mutually Coupled Chaotic Systems

An adaptive feedback scheme is proposed for the stability of isochronal synchronization between two identical chaotic systems with delay-coupled, so this scheme is analytical, and simple to implement in practice.

Isochronal synchronization in networks and chaos-based TDMA communication

A conceptual framework for the application of isochronal synchronization to TDMA communication in networks of delay-coupled chaotic oscillators is introduced and it is argued to have potential to provide gain in simplicity, security and efficiency in communication schemes for autonomous/standalone network applications.

Isochronal synchronization in complex networks - The Lyapunov-Krasovskii theorem and stability in the network parameter space

Isochronal synchronization is a unique phenomenon in which physically distant oscillators wired together relax into zero-lag synchronous behavior over time. Such behavior is observed in natural

Multistability Analysis and Function Projective Synchronization in Relay Coupled Oscillators

The synchronization of systems that act as mediators between two dynamical units that show function projective synchronization (FPS) with each other are presented and it is shown that the coupled systems can achieve function projectives synchronization in a determined time despite the unpredictability of the scaling function.

Enhancing synchronization in chaotic oscillators by induced heterogeneity

Abstract We report enhancing of complete synchronization in identical chaotic oscillators when their interaction is mediated by a mismatched oscillator. The identical oscillators now interact

Synchronization transitions in coupled time-delay electronic circuits with a threshold nonlinearity.

The existence of different kinds of synchronizations observed experimentally is corroborated by numerical simulations and from the changes in the Lyapunov exponents of the coupled time-delay systems.

Synchronization and symmetry breaking of delay-coupled oscillators: on the role of phase and amplitude instabilities

We study the synchronization behavior of Stuart-Landau oscillators coupled with delay, using analytical and numerical methods. We compare the dynamics of one oscillator with delayed feedback, two

N-phase synchronization of asymmetric attractors in a ring of coupled chaotic circuits

This paper suggests ring topology and alternately shifted bias are essential factors of N-phase synchronization.

On the formulation and solution of the isochronal synchronization stability problem in delay-coupled complex networks.

Following this approach, it is shown how the error system can be defined such that its dimension can be the same as (or smaller than) that of the network state vector.

Amplitude and phase effects on the synchronization of delay-coupled oscillators.

Analytical proof is provided that, in case of two mutually coupled elements, the onset of an amplitude instability always results in antiphase oscillations, leading to a leader-laggard behavior in the chaotic regime.

References

SHOWING 1-10 OF 32 REFERENCES

Synchronization by dynamical relaying in electronic circuit arrays.

The synchronization of two chaotic electronic circuits whose dynamics is relayed by a third parameter-matched circuit, to which they are coupled bidirectionally in a linear chain configuration, is experimentally studied.

Isochronal synchrony and bidirectional communication with delay-coupled nonlinear oscillators.

  • B. ZhouR. Roy
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2007
This approach to combine both bidirectional and unidirectional coupling represents an application of generalized synchronization using a mediating drive signal for a spatially distributed and internally synchronized multicomponent system.

Synchronization in chaotic systems.

This chapter describes the linking of two chaotic systems with a common signal or signals and highlights that when the signs of the Lyapunov exponents for the subsystems are all negative the systems are synchronized.

Delays, connection topology, and synchronization of coupled chaotic maps.

It is shown that, similar to the undelayed case, the synchronization of the network depends on the connection topology, characterized by the spectrum of the graph Laplacian, which means that scale-free and random networks are capable of synchronizing despite the delayed flow of information.

From Phase to Lag Synchronization in Coupled Chaotic Oscillators

We study synchronization transitions in a system of two coupled self-sustained chaotic oscillators. We demonstrate that with the increase of coupling strength the system first undergoes the

Random delays and the synchronization of chaotic maps.

It is found that for adequate coupling strength the array is able to synchronize, in spite of the random delays, and the synchronized state is a homogeneous steady state, where the chaotic dynamics of the individual maps is suppressed.

Experimental Observation of Lag Synchronization in Coupled Chaotic Systems

Measurements indicate that due to the influence of noise, lag synchronization appears to occur intermittently in time.

Coherent regimes of mutually coupled Chua's circuits.

The theoretical results indicate that the same predictable change in the collective dynamics can be obtained for large populations of strongly coupled circuits with parameter mismatches.

Hyperchaotic behaviour of two bi‐directionally coupled Chua's circuits

It is shown that hyperchaotic behaviour occurs for proper values of the coupling strength between the two Chua's circuits, and the calculus of conditional Lyapunov exponents is necessary in order to exclude antisynchronization along the tangent manifold.