Key role of time-delay and connection topology in shaping the dynamics of noisy genetic regulatory networks

This paper focuses on a paced genetic regulatory small-world network with time-delayed coupling. How the dynamical behaviors including temporal resonance and spatial synchronization evolve under the influence of time-delay and connection topology is explored through numerical simulations. We reveal the phenomenon of delay-induced resonance when the network topology is fixed. For a fixed time-delay, temporal resonance is shown to be degraded by increasing the rewiring probability of the network. On the other hand, for small rewiring probability, temporal resonance can be enhanced by an appropriately tuned small delay but degraded by a large delay, while conversely, temporal resonance is always reduced by time-delay for large rewiring probability. Finally, an optimal spatial synchrony is detected by a proper combination of time-delay and connection topology.