# 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…

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## References

SHOWING 1-10 OF 32 REFERENCES

### Synchronization by dynamical relaying in electronic circuit arrays.

- PhysicsChaos
- 2006

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.

- PhysicsPhysical 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.

### Zero-lag long-range synchronization via dynamical relaying.

- PhysicsPhysical review letters
- 2006

The results show that zero-lag synchronized chaotic dynamical states can occur over long distances through relaying, without restriction by the amount of delay.

### Synchronization in chaotic systems.

- PhysicsPhysical review letters
- 1990

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.

- Computer SciencePhysical review letters
- 2004

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

- Physics
- 1997

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.

- PhysicsPhysical review letters
- 2005

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

- PhysicsInt. J. Bifurc. Chaos
- 2000

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.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2006

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.