  Nonlinear channels play a critical role in realizing dynamical functions.
Neural ionic channels and non-volatile memristors each derive representative
biological and electrical functionalities, such as repetitive firing or pinched
hysteresis. In electromagnetics, saturable channels of amplification or
absorption provide a large nonlinearity for nonequilibrium wave dynamics, from
conventional lasing to mode locking to recent achievements of the
non-reciprocity in complex potentials. Here, we investigate the dynamical phase
diagram of parity-time symmetric systems, governed by competing nonlinear
channels of saturable amplification and absorption. Determined by the relative
strength and saturation level of the channels, three distinctive phases of
fast- and slow-response equilibriums, and an oscillating nonequilibrium are
demonstrated. On phase boundaries, we also reveal the chaotic existence of the
strong oscillation state, which allows the non-reciprocal realization of
repetitive resonator firing with fully tunable time delays. This work will
promote the wave-based realization of nonlinear and chaotic temporal functions,
toward light-based neural systems.
