Coexistence of interdependence and competition in adaptive multilayer network

In dynamical networks, the presence of adaptation establishing the relationship between the coherence of local populations and unit's effective coupling provides the explosive transition - an abrupt transition from incoherence to coherence and vice versa through the hysteresis loop. Explosive transition is even possible under the coexistence of two opposite types of adaptation - interdependence and competition, wherein growing the competitive population dramatically narrows the area of hysteresis. Here, we demonstrate that considering a mixed adaptive model from a multilayer perspective expands the hysteresis region and shifts both forward and backward transition boundaries to the higher values of coupling strength as compared with a monolayer case. We show that this is due to greater robustness of the multilayer network against the intralayer topology and lower sensitivity to the amplification of the pre-bifurcation noise, i.e., spurious fluctuations of local coherence, in the vicinity of a tipping point as opposed to a single-layer network. (c) 2021 Elsevier Ltd. All rights reserved.

Automated summary

This study investigates the relationship between adaptation, coherence, and coupling in dynamical networks, discussing the abrupt transition from incoherence to coherence and the coexistence of two types of adaptation. It shows that a mixed adaptive model from a multilayer perspective expands the hysteresis region and shifts transition boundaries, demonstrating the greater robustness of multilayer networks to topology and lower sensitivity to noise.