Exceptional points in coupled dissipative dynamical systems

Jung-Wan Ryu, Woo-Sik Son, Dong-Uk Hwang, Soo-Young Lee, and Sang Wook Kim
Phys. Rev. E 91, 052910 – Published 13 May 2015

Abstract

We study the transient behavior in coupled dissipative dynamical systems based on the linear analysis around the steady state. We find that the transient time is minimized at a specific set of system parameters and show that at this parameter set, two eigenvalues and two eigenvectors of the Jacobian matrix coalesce at the same time; this degenerate point is called the exceptional point. For the case of coupled limit-cycle oscillators, we investigate the transient behavior into the amplitude death state, and clarify that the exceptional point is associated with a critical point of frequency locking, as well as the transition of the envelope oscillation.

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  • Received 11 February 2015

DOI:https://doi.org/10.1103/PhysRevE.91.052910

©2015 American Physical Society

Authors & Affiliations

Jung-Wan Ryu1, Woo-Sik Son2, Dong-Uk Hwang2, Soo-Young Lee1, and Sang Wook Kim3,*

  • 1School of Electronics Engineering, Kyungpook National University, Daegu 702-701, Korea
  • 2National Institute for Mathematical Sciences, Daejeon 305-811, South Korea
  • 3Department of Physics Education, Pusan National University, Busan 609-735, South Korea

  • *swkim0412@pusan.ac.kr

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Vol. 91, Iss. 5 — May 2015

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