A multi-layer dynamic model of information propagation considering individual three-phase linear modulated behaviors

The propagation of individual behaviors has emerged as a significant phenomenon influencing social trust and stability. To thoroughly investigate this, we propose a multi-layer dynamic model that captures non-monotonic responses in behavior spread. This model highlights that behavioral intensity is suppressed in the middle state interval but promoted in the low and high state intervals, employing a threshold modeling approach. We perform a detailed mathematical analysis of the dynamics of individual behaviors using a three-phase linear modulation (TPLM), developing an edge-based compartmental theory that aligns remarkably well with simulation results. Our analysis and numerical simulations reveal that these modulated behaviors significantly impact dynamics, as measured by the final adoption size. Notably, we observe a phenomenon in the order of the phase transition from second-order continuous to first-order discontinuous, mediated by the behavioral parameters. This transition can be triggered by adjusting parameters and structural perturbations, such as altering individuals’ adoption thresholds or increasing network heterogeneity. • This study examines TPLM dynamics via non-monotonic spread in double-layer networks. • The threshold model with TPLM behaviors is established. • The behavioral threshold is proposed by a N-shaped probability function. • The phase transition on final adoption size is affected by TPLM behaviors.