Collective attention under digital exposure: A dynamical systems approach

Abstract

The widespread use of digital devices has raised growing concerns about its impact on sustained attention at the population level. In this work, we propose a minimal dynamical framework to describe the collective evolution of attention under continuous exposure to screen-mediated environments. We introduce a macroscopic variable representing the average level of sustained attention and model its dynamics as the result of competing mechanisms: intrinsic cognitive recovery and degradation induced by digital stimulation. The digital environment is treated as an external control parameter that continuously perturbs the system, leading to a relaxational dynamics. The proposed mechanisms are consistent with empirical findings on attentional dynamics under digital exposure. We first analyze a linear formulation, which provides an analytically tractable baseline, and then extend the model by incorporating a nonlinear degradation term that captures amplification effects under high-intensity stimulation. We derive an explicit expression for the stationary state and show that the equilibrium attention level decreases monotonically with increasing exposure. An effective potential formulation is introduced, revealing that digital overstimulation progressively deforms the dynamical landscape, shifting the stable state toward regimes of reduced attention without generating multiple equilibria. Importantly, the model does not rely on social contagion or interaction-driven bistability, but instead describes a continuous displacement of the collective cognitive regime under environmental pressure. Our results suggest that the impact of digital technologies on attention may be understood as a gradual macroscopic effect emerging from persistent external stimulation, rather than as a transition between competing behavioral states.

Figures (4)

• Figure 1: (a) Temporal evolution of the attention level $x(t)$ for different values of the digital exposure parameter $T$, showing exponential relaxation toward a unique stationary state. (b) Stationary attention level $x^*$ as a function of $T$, illustrating a continuous decrease with increasing exposure. The inset shows the same data in log-log scale, highlighting the asymptotic behavior $x^*\sim T^{-1}$.
• Figure 2: (a) Temporal evolution of the attention level $x(t)$ for different values of the digital exposure parameter $T$, for a fixed nonlinear coefficient $\beta=1.0$, showing relaxation toward a unique stationary state. (b) Temporal evolution of $x(t)$ for different values of $\beta$, at fixed $T=2.0$, highlighting the role of nonlinear degradation. Larger values of $\beta$ lead to a stronger suppression of the stationary attention level and a faster convergence toward stationary states.
• Figure 3: (a) Stationary attention level $x^*$ as a function of the digital exposure parameter $T$, for a fixed nonlinear coefficient $\beta=1.0$, showing a continuous decrease with increasing exposure. (b) Stationary attention level $x^*$ as a function of $\beta$, for fixed $T=2.0$, highlighting the role of nonlinear degradation. Larger values of $\beta$ lead to a stronger suppression of the stationary attention level.
• Figure 4: (a) Effective potential $V(x)$ for different values of the digital exposure parameter $T$, for fixed $\beta=1.0$, illustrating a continuous deformation of the landscape and a shift of the minimum toward lower values of $x$. (b) Effective potential $V(x)$ for different values of $\beta$, at fixed $T=2.0$, highlighting the effect of nonlinear degradation. The inset shows a zoom near the minimum, clearly illustrating the shift of the equilibrium position as $\beta$ increases. In all cases, the potential remains single-welled, indicating the absence of bistability.