Effect of processing delay on bifurcation delay in a network of slow-fast oscillators

Bifurcation delay or slow passage effect occurs in dynamical systems with slow-fast time-varying parameters. In this work, we report the impact of processing delay on bifurcation delay in a network of locally coupled slow-fast systems with self-feedback delay. We report that the network exhibits coexisting coherent (synchronized) and incoherent (desynchronized) states among the oscillators as a function of various parameters like self-feedback delay, processing delay, and amplitude of the external current. In particular, we show the decrease of the synchronized region (control of synchronization) for (i) a fixed value of processing delay with varying self-feedback delay and (ii) fixed self-feedback delay with increasing processing delay. In contrast, we observe the increase of the synchronized region (control of desynchronization) for fixed processing delay and self-feedback delay while varying the amplitude of the external current. Finally, we have also analyzed the effect of processing delay on bifurcation delay with the presence of noise and we report that the inhomogeneity in the additional noise does not affect the asymmetry in a bifurcation delay.