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 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.

6 pages, 7 figures

References in corpus (4)

• The physics of exceptional points
• Visualization of Branch Points in PT-Symmetric Waveguides
• Exceptional Points in Atomic Spectra
• Total and partial amplitude death in networks of diffusively coupled oscillators

Cited by in corpus (7)

• Stabilization of acoustic modes using Helmholtz and Quarter-Wave resonators tuned at exceptional points
• Stochastic thermodynamics of inertial-like Stuart-Landau dimer
• Experimental observation of exceptional points in coupled pendulums
• Energetic cost for speedy synchronization in non-Hermitian quantum dynamics
• Amplitude death in a ring of nonidentical nonlinear oscillators with unidirectional coupling
• Reconfiguration of quantum states in $\mathcal{P}T$-symmetric quasi-one dimensional lattices
• Nonreciprocity induced spatiotemporal chaos: Reactive vs dissipative routes