Stochastic resonance and dynamic event-triggered impulsive control of a variable-order fractional information diffusion system with hybrid noise

The processes and control of information diffusion have received significant attention in the information age. Considering the prevalent environmental noise and individual memory, this paper constructs a variable-order fractional information diffusion model on heterogeneous networks, incorporating internal Gaussian white noise and external Lévy noise. Since the introduction of noise leading to stochastic resonance, we define a metric of generalized signal-to-noise ratio (GSNR) to measure the gain effect of noise on the system. To effectively suppress the spread of negative information and promote the dissemination of positive information within the constraints of limited resources, the dynamic event-triggered impulsive control (DETIC) is designed to the variable-order fractional negative–positive information diffusion model with short memory induced by internal and external noise, where it successfully prevent impulse signals from disrupting the non-locality of the fractional-order operator. Besides, the exclusion of Zeno behavior and the stability of the controlled system are proved and it is demonstrated that the minimum execution interval are not less than the corresponding static event-triggered mechanism. Employing the particle swarm optimization (PSO) algorithm, we determine the optimal noise intensities based on the GSNR, along with the optimal DETIC. Comparative experiments and the instance show that the combination of optimal noise intensities and optimal DETIC achieve the best results in suppressing the diffusion of negative information and promoting the dissemination of positive information, which provides valuable guidance for controlling the information diffusion.