Georgia Institute of Technology College of Sciences

Symmetries are  fundamental concepts in modern physics and biology. Spontaneous symmetry breaking often leads to fascinating  dynamical patterns such as  chimera states in which structurally and dynamically identical oscillators  split into coherent and incoherent clusters.  Solitary states in which one oscillator separates from the coherent cluster and oscillates with a different frequency represent  “weak” chimeras. While a rigorous stability analysis of a “strong” chimera with a multi-oscillator incoherent cluster  is typically out of reach for finite-size networks, solitary states offer a unique test bed for the development of stability approaches to large chimeras. In this talk, we will present such an approach and study the stability of solitary states in Kuramoto networks of identical 2D phase oscillators with inertia and a phase-lagged coupling.   We will derive asymptotic stability conditions for such solitary states as a function of inertia, network size, and phase lag that may yield either attractive or repulsive coupling. Counterintuitively, our analysis demonstrates that (i) increasing the size of the coherent cluster can promote the stability of the solitary state in the attractive coupling case and (ii) the solitary state can be stable in small-size networks with all repulsive coupling. We also discuss the implications of our analysis for the emergence of rotatory chimeras and splay states. This is a joint work with V. Munyaev, M. Bolotov, L. Smirnov, and G. Osipov.