Rate-Induced Transitions and Noise-Driven Resilience in Vegetation Pattern Dynamics

Abstract. Understanding the resilience and stability of vegetation patterns under changing environmental conditions is crucial for predicting ecosystem responses to climate change. This study investigates the dynamics of vegetation patterns in response to a spatially homogeneous decrease in rainfall across the entire domain. Starting from high-rainfall with a stable homogeneous vegetated state, we applied various rates of rainfall reduction to observe system transitions. We find that rainfall decrease may cause transitions to two or three pulse states, or abrupt shifts to bare soil depending on the rate of change, highlighting the significance of rate-induced tipping (R-tipping) in open dynamical systems.

We identified the pulse creation and destruction timescale (τ_pulse) and the rearrangement timescale (τ_rear) as the critical timescales which govern the system response to gradual environmental changes. The rearrangement timescale, significantly longer than τ_pulse, is relevant for characterising the system behavior under slow perturbations. Dimensional analysis and sensitivity analysis with numerical experiments further validate the fundamental connections between these timescales.

Additionally, we examined the impact of spatially and temporally structured noise on vegetation pattern resilience. Perturbations modeled as Gaussian stochastic processes with specific autocorrelation structures were applied to the system. We find that increased spatial autocorrelation in noise reduces pattern formation, while temporal autocorrelation at critical timescales significantly influences biomass mean and variance. The co-existence of multiple equilibria and unstable states, combined with the presence of ghost attractors enhances system resilience by providing alternative stable configurations under fluctuating conditions.

These findings underscore the importance of considering slow timescales and structured noise in analyzing vegetation dynamics. Understanding these factors is essential for predicting ecosystem resilience and developing strategies to manage vegetation systems under climate variability.