Title: Spontaneous symmetry breaking due to the trade-off between attractive and repulsive couplings,
Abstract: Spontaneous symmetry breaking (SSB) is an important phenomenon observed in
various fields including physics and biology. In this connection, we here show
that the trade-off between attractive and repulsive couplings can induce
spontaneous symmetry breaking in a homogeneous system of coupled oscillators.
With a simple model of a system of two coupled Stuart-Landau oscillators, we
demonstrate how the tendency of attractive coupling in inducing in-phase
synchronized (IPS) oscillations and the tendency of repulsive coupling in
inducing out-of-phase synchronized (OPS) oscillations compete with each other
and give rise to symmetry breaking oscillatory (SBO) states and interesting
multistabilities. Further, we provide explicit expressions for synchronized and
anti-synchronized oscillatory states as well as the so called oscillation death
(OD) state and study their stability. If the Hopf bifurcation parameter
(${\lambda}$) is greater than the natural frequency ($\omega$) of the system,
the attractive coupling favours the emergence of an anti-symmetric OD state via
a Hopf bifurcation whereas the repulsive coupling favours the emergence of a
similar state through a saddle-node bifurcation. We show that an increase in
the repulsive coupling not only destabilizes the IPS state but also facilitates
the re-entrance of the IPS state.