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

TL;DR

This paper investigates how memory effects in complex systems reshape stability landscapes, influencing resilience, resistance, and regime shift behaviors, with implications for better understanding and managing critical transitions.

Contribution

It introduces a fractional derivative model to incorporate memory into stability landscapes, revealing new behaviors and potential misinterpretations when ignoring memory effects.

Findings

Memory flattens basin floors, slowing recovery.

Memory increases the threshold for stability transitions.

Fitting memory-free models to memory-driven data can lead to misdiagnosis.

Abstract

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.