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.
