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.
- Received 11 February 2015
DOI:https://doi.org/10.1103/PhysRevE.91.052910
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