Chandler Ross | Searcharxiv

arXiv2026

Memory reshapes stability landscapes: resilience-resistance tradeoffs and critical transitions

Regime shifts in biology, ecology, and other complex systems are often interpreted through stability landscapes and early warning signals that implicitly assume dynamics without memory effects. Yet many real systems exhibit these effects, thus present dynamics depend on past states and past forcing. Here, we study how memory reshapes bistable stability landscapes and regime shifts using a minimal bistable model with a fractional derivative that controls memory strength. We connect landscape geometry to classical notions of resilience and resistance by quantifying basin curvature and the perturbation magnitude required to cross the unstable threshold, and we track how these quantities evolve in time after perturbations. Memory typically flattens basin floors, slowing recovery, while often increasing the perturbation threshold for stability transitions, revealing a tradeoff between resilience and resistance. Because the landscape becomes history-dependent and time-evolving, memory generates qualitative behaviors that do not appear in memory-free models, including delayed collapse or recovery after stress ends, rebound after apparently successful transition, and broadened hysteresis under gradual parameter change. Finally, we show that fitting a memory-free model to memory-driven data can reproduce trajectories while systematically shifting equilibrium branches and tipping locations, risking incorrect diagnosis and management of regime shifts. These results motivate a moving landscape view and provide practical guidance for interpreting observed anomalies and distinguishing memory-driven effects from noise.

math.DS↗

arXiv2025

Reconstructing ecological community dynamics from limited observations

Ecosystems tend to fluctuate around stable equilibria in response to internal dynamics and environmental factors. Occasionally, they enter an unstable tipping region and collapse into an alternative stable state. Our understanding of how ecological communities vary over time and respond to perturbations depends on our ability to quantify and predict these dynamics. However, the scarcity of long, dense time series data poses a severe bottleneck for characterising community dynamics using existing methods. We overcome this limitation by combining information across multiple short time series using Bayesian inference. By decomposing dynamics into deterministic and stochastic components using Gaussian process priors, we predict stable and tipping regions along the community landscape and quantify resilience while addressing uncertainty. After validation with simulated and real ecological time series, we use the model to question common assumptions underlying classical potential analysis and re-evaluate the stability of previously proposed "tipping elements" in the human gut microbiota.

stat.AP↗