Dynamic Environment Coupling Induced Synchronized States in Coupled Time-Delayed Electronic Circuits

R. Suresh, K. Srinivasan, D. V. Senthilkumar, K. Murali, M. Lakshmanan*, J. Kurths

*Corresponding author for this work

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

We experimentally demonstrate the effect of dynamic environment coupling in a system of coupled piecewise linear time-delay electronic circuits with mutual and subsystem coupling configurations. Time-delay systems are essentially infinite-dimensional systems with complex phase-space properties. Dynamic environmental coupling with mutual coupling configuration has been recently theoretically shown to induce complete (CS) and inverse synchronizations (IS) [Resmi et al., 2010] in low-dimensional dynamical systems described by ordinary differential equations (ODEs), for which no experimental confirmation exists. In this paper, we investigate the effect of dynamic environment for the first time in mutual as well as subsystem coupling configurations in coupled time-delay differential equations theoretically and experimentally. Depending upon the coupling strength and the nature of feedback, we observe a transition from asynchronization to CS via phase synchronization and from asynchronization to IS via inverse-phase synchronization in both coupling configurations. The results are corroborated by snapshots of the time evolution, phase projection plots and localized sets as observed from the oscilloscope. Further, the synchronization is also confirmed numerically from the largest Lyapunov exponents, correlation of probability of recurrence and correlation coefficient of the coupled time-delay system. We also present a linear stability analysis and obtain conditions for different synchronized states.

Original languageEnglish
Article number1450067
Number of pages16
JournalInternational Journal of Bifurcation and Chaos
Volume24
Issue number5
DOIs
Publication statusPublished - May 2014

Keywords

  • dynamic environment coupling
  • phase and inverse-phase synchronization
  • complete and inverse synchronization
  • piecewise linear time-delay systems
  • phase synchronization
  • chaotic oscillators

Cite this

Dynamic Environment Coupling Induced Synchronized States in Coupled Time-Delayed Electronic Circuits. / Suresh, R.; Srinivasan, K.; Senthilkumar, D. V.; Murali, K.; Lakshmanan, M.; Kurths, J.

In: International Journal of Bifurcation and Chaos, Vol. 24, No. 5, 1450067, 05.2014.

Research output: Contribution to journalArticle

Suresh, R. ; Srinivasan, K. ; Senthilkumar, D. V. ; Murali, K. ; Lakshmanan, M. ; Kurths, J. / Dynamic Environment Coupling Induced Synchronized States in Coupled Time-Delayed Electronic Circuits. In: International Journal of Bifurcation and Chaos. 2014 ; Vol. 24, No. 5.
@article{0aeca58d7bd04cdb9afa23e6aefb297f,
title = "Dynamic Environment Coupling Induced Synchronized States in Coupled Time-Delayed Electronic Circuits",
abstract = "We experimentally demonstrate the effect of dynamic environment coupling in a system of coupled piecewise linear time-delay electronic circuits with mutual and subsystem coupling configurations. Time-delay systems are essentially infinite-dimensional systems with complex phase-space properties. Dynamic environmental coupling with mutual coupling configuration has been recently theoretically shown to induce complete (CS) and inverse synchronizations (IS) [Resmi et al., 2010] in low-dimensional dynamical systems described by ordinary differential equations (ODEs), for which no experimental confirmation exists. In this paper, we investigate the effect of dynamic environment for the first time in mutual as well as subsystem coupling configurations in coupled time-delay differential equations theoretically and experimentally. Depending upon the coupling strength and the nature of feedback, we observe a transition from asynchronization to CS via phase synchronization and from asynchronization to IS via inverse-phase synchronization in both coupling configurations. The results are corroborated by snapshots of the time evolution, phase projection plots and localized sets as observed from the oscilloscope. Further, the synchronization is also confirmed numerically from the largest Lyapunov exponents, correlation of probability of recurrence and correlation coefficient of the coupled time-delay system. We also present a linear stability analysis and obtain conditions for different synchronized states.",
keywords = "dynamic environment coupling, phase and inverse-phase synchronization, complete and inverse synchronization, piecewise linear time-delay systems, phase synchronization, chaotic oscillators",
author = "R. Suresh and K. Srinivasan and Senthilkumar, {D. V.} and K. Murali and M. Lakshmanan and J. Kurths",
year = "2014",
month = "5",
doi = "10.1142/S0218127414500679",
language = "English",
volume = "24",
journal = "International Journal of Bifurcation and Chaos",
issn = "0218-1274",
publisher = "WORLD SCIENTIFIC PUBL CO PTE LTD",
number = "5",

}

TY - JOUR

T1 - Dynamic Environment Coupling Induced Synchronized States in Coupled Time-Delayed Electronic Circuits

AU - Suresh, R.

AU - Srinivasan, K.

AU - Senthilkumar, D. V.

AU - Murali, K.

AU - Lakshmanan, M.

AU - Kurths, J.

PY - 2014/5

Y1 - 2014/5

N2 - We experimentally demonstrate the effect of dynamic environment coupling in a system of coupled piecewise linear time-delay electronic circuits with mutual and subsystem coupling configurations. Time-delay systems are essentially infinite-dimensional systems with complex phase-space properties. Dynamic environmental coupling with mutual coupling configuration has been recently theoretically shown to induce complete (CS) and inverse synchronizations (IS) [Resmi et al., 2010] in low-dimensional dynamical systems described by ordinary differential equations (ODEs), for which no experimental confirmation exists. In this paper, we investigate the effect of dynamic environment for the first time in mutual as well as subsystem coupling configurations in coupled time-delay differential equations theoretically and experimentally. Depending upon the coupling strength and the nature of feedback, we observe a transition from asynchronization to CS via phase synchronization and from asynchronization to IS via inverse-phase synchronization in both coupling configurations. The results are corroborated by snapshots of the time evolution, phase projection plots and localized sets as observed from the oscilloscope. Further, the synchronization is also confirmed numerically from the largest Lyapunov exponents, correlation of probability of recurrence and correlation coefficient of the coupled time-delay system. We also present a linear stability analysis and obtain conditions for different synchronized states.

AB - We experimentally demonstrate the effect of dynamic environment coupling in a system of coupled piecewise linear time-delay electronic circuits with mutual and subsystem coupling configurations. Time-delay systems are essentially infinite-dimensional systems with complex phase-space properties. Dynamic environmental coupling with mutual coupling configuration has been recently theoretically shown to induce complete (CS) and inverse synchronizations (IS) [Resmi et al., 2010] in low-dimensional dynamical systems described by ordinary differential equations (ODEs), for which no experimental confirmation exists. In this paper, we investigate the effect of dynamic environment for the first time in mutual as well as subsystem coupling configurations in coupled time-delay differential equations theoretically and experimentally. Depending upon the coupling strength and the nature of feedback, we observe a transition from asynchronization to CS via phase synchronization and from asynchronization to IS via inverse-phase synchronization in both coupling configurations. The results are corroborated by snapshots of the time evolution, phase projection plots and localized sets as observed from the oscilloscope. Further, the synchronization is also confirmed numerically from the largest Lyapunov exponents, correlation of probability of recurrence and correlation coefficient of the coupled time-delay system. We also present a linear stability analysis and obtain conditions for different synchronized states.

KW - dynamic environment coupling

KW - phase and inverse-phase synchronization

KW - complete and inverse synchronization

KW - piecewise linear time-delay systems

KW - phase synchronization

KW - chaotic oscillators

U2 - 10.1142/S0218127414500679

DO - 10.1142/S0218127414500679

M3 - Article

VL - 24

JO - International Journal of Bifurcation and Chaos

JF - International Journal of Bifurcation and Chaos

SN - 0218-1274

IS - 5

M1 - 1450067

ER -