Coupling conditions for globally stable and robust synchrony of chaotic systems

Suman Saha, Arindam Mishra, E. Padmanaban, Sourav K. Bhowmick, Prodyot K. Roy, Bivas Dam, and Syamal K. Dana
Phys. Rev. E 95, 062204 – Published 9 June 2017
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Abstract

We propose a set of general coupling conditions to select a coupling profile (a set of coupling matrices) from the linear flow matrix of dynamical systems for realizing global stability of complete synchronization (CS) in identical systems and robustness to parameter perturbation. The coupling matrices define the coupling links between any two oscillators in a network that consists of a conventional diffusive coupling link (self-coupling link) as well as a cross-coupling link. The addition of a selective cross-coupling link in particular plays constructive roles that ensure the global stability of synchrony and furthermore enables robustness of synchrony against small to nonsmall parameter perturbation. We elaborate the general conditions for the selection of coupling profiles for two coupled systems, three- and four-node network motifs analytically as well as numerically using benchmark models, the Lorenz system, the Hindmarsh-Rose neuron model, the Shimizu-Morioka laser model, the Rössler system, and a Sprott system. The role of the cross-coupling link is, particularly, exemplified with an example of a larger network, where it saves the network from a breakdown of synchrony against large parameter perturbation in any node. The perturbed node in the network transits from CS to generalized synchronization (GS) when all the other nodes remain in CS. The GS is manifested by an amplified response of the perturbed node in a coherent state.

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  • Received 23 August 2016
  • Revised 5 May 2017

DOI:https://doi.org/10.1103/PhysRevE.95.062204

©2017 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear Dynamics

Authors & Affiliations

Suman Saha1,2,3,*, Arindam Mishra4,†, E. Padmanaban5,6, Sourav K. Bhowmick2,6, Prodyot K. Roy6,7, Bivas Dam1, and Syamal K. Dana6,8,‡

  • 1Department of Instrumentation and Electronics Engineering, Jadavpur University, Kolkata 700090, India
  • 2Department of Electronics, Asutosh College, Kolkata 700026, India
  • 3Dumkal Institute of Engineering and Technology, Murshidabad 742406, India
  • 4Department of Physics, Jadavpur University, Kolkata 700032, India
  • 5CSIR-Indian Institute of Chemical Biology, Kolkata 700032, India
  • 6Center for Complex System Research Kolkata, Kolkata 700094, India
  • 7Department of Mathematics, Presidency University, Kolkata 700073, India
  • 8Department of Mathematics, Jadavpur University, Kolkata 700032, India

  • *ecesuman06@gmail.com
  • arindammishra@gmail.com
  • syamaldana@gmail.com

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Issue

Vol. 95, Iss. 6 — June 2017

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