title: Exceptional points in coupled dissipative dynamical systems.
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.
authors.affiliation: School of Electronics Engineering, Kyungpook National University, Daegu 702-701, Korea.
authors.forename: Jung-Wan
authors.initials: JW
authors.lastname: Ryu
authors.affiliation: National Institute for Mathematical Sciences, Daejeon 305-811, South Korea.
authors.forename: Woo-Sik
authors.initials: WS
authors.lastname: Son
authors.affiliation: National Institute for Mathematical Sciences, Daejeon 305-811, South Korea.
authors.forename: Dong-Uk
authors.initials: DU
authors.lastname: Hwang
authors.affiliation: School of Electronics Engineering, Kyungpook National University, Daegu 702-701, Korea.
authors.forename: Soo-Young
authors.initials: SY
authors.lastname: Lee
authors.affiliation: Department of Physics Education, Pusan National University, Busan 609-735, South Korea.
authors.forename: Sang Wook
authors.initials: SW
authors.lastname: Kim