Network temporality can promote and suppress information spreading.

Temporality is an essential characteristic of many real-world networks and dramatically affects the spreading dynamics on networks. In this paper, we propose an information spreading model on temporal networks with heterogeneous populations. Individuals are divided into activists and bigots to describe the willingness to accept the information. Through a developed discrete Markov chain approach and extensive numerical simulations, we discuss the phase diagram of the model and the effects of network temporality. From the phase diagram, we find that the outbreak phase transition is continuous when bigots are relatively rare, and a hysteresis loop emerges when there are a sufficient number of bigots. The network temporality does not qualitatively alter the phase diagram. However, we find that the network temporality affects the spreading outbreak size by either promoting or suppressing, which relies on the heterogeneities of population and of degree distribution. Specifically, in networks with homogeneous and weak heterogeneous degree distribution, the network temporality suppresses (promotes) the information spreading for small (large) values of information transmission probability. In networks with strong heterogeneous degree distribution, the network temporality always promotes the information spreading when activists dominate the population, or there are relatively fewer activists. Finally, we also find the optimal network evolution scale, under which the network information spreading is maximized.