Synchronization and Communication with Chaotic Time-Delay

Synchronization and Communication withChaotic Time-Delay Electronic Circuit Systems

David T. Sodaitis*, Vasily Dronov,Min-Young Kim, Atsushi Uchida,

and Rajarshi Roy

Institute for Research in Electronicsand Applied Physics (IREAP)

University of Maryland

* University of New Hampshire

TREND 2003

Investigation of dependence ofsynchronization on parametermismatch and delay time.

Objectives

Demonstration of synchronization ofchaos in two Mackey-Glass electroniccircuits with delayed feedback byexperiment and PSPICE simulation.

Circuit implementation of Mackey-Glass delayed system.

)()(1

)()( tbxtxtax

dttdx

n −−+

−=

ττ

2.0=a 1.0=b 10=n

The Mackey-Glass System

The Mackey-Glass mathematical model1:a delay differential equation

typical parameter values:

1) M.C. Mackey and L. Glass, Science 197, 287 (1977).

Phase Portrait of the Mackey Glass System

τ =10

Analog electronic circuit 2

Nonlinearfunction

Delay line

R

C

2) A. Namajunas, K. Pyragas, and A. Tamasevicius, Phys. Lett. A 201, 42 (1995).

Implementation

Circuit Schematic

Nonlinear Device

Linear Gain Stage

Delay Line

PSPICE Simulation vs. Circuit

Identical Synchronization

Synchronization Error

Communications Encryption

Drive

Response

One-way Coupling

Message

Subtraction yieldsback Message

Time Delay

Time Delay

Conclusions

We have investigated the dynamics ofa Mackey-Glass electronic circuit byexperiment and PSPICE simulation.

The degree of synchronization isdegraded with increase of parametermismatch and delay time, which wehypothesize is related to thedimensionality of the chaoticattractor.

Synchronization of chaos in twoMackey-Glass circuits has beenobserved.