Mixing adaptive rules in a bilayer Erdős-Rényi network

In many natural networked systems, adaptation is an essential mechanism of self-organization. Usually, network elements interact through either interdependent, high coupling at high coherence, or competitive, low coupling at high coherence, adaptive rules. The former rule supports explosive synchronization, while the latter is associated with continuous transition. Due to inherent heterogeneity of the real networks, one has to understand the transition under the mixing of such adaptive rules. Here, we address this problem from a multilayer perspective and explore the impact of multiplexing on hysteresis region associated with explosive transitions in complex networks.