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Nonlinear channels play a critical role in realizing dynamical functions.Neural ionic channels and non-volatile memristors each derive representativebiological and electrical functionalities, such as repetitive firing or pinchedhysteresis. In electromagnetics, saturable channels of amplification orabsorption provide a large nonlinearity for nonequilibrium wave dynamics, fromconventional lasing to mode locking to recent achievements of thenon-reciprocity in complex potentials. Here, we investigate the dynamical phasediagram of parity-time symmetric systems, governed by competing nonlinearchannels of saturable amplification and absorption. Determined by the relativestrength and saturation level of the channels, three distinctive phases offast- and slow-response equilibriums, and an oscillating nonequilibrium aredemonstrated. On phase boundaries, we also reveal the chaotic existence of thestrong oscillation state, which allows the non-reciprocal realization ofrepetitive resonator firing with fully tunable time delays. This work willpromote the wave-based realization of nonlinear and chaotic temporal functions,toward light-based neural systems.

Dynamical phase diagram of parity-time symmetry with competing saturable channels