"Stability Landscape Dancing with Memory"Khalighi, MoeinThis study investigates the impact of memory effects on ecological model stability, employing advanced computational methods and mathematical modeling, including fractional calculus. We analyze univariate bistable models to understand how ecological memory influences system adaptability, stability, resilience, and resistance to environmental changes. Our findings reveal the importance of integrating past and present states for a comprehensive grasp of system dynamics, highlighting memory's critical role in ecological stability, resilience, tipping points, and critical transitions. Incorporating memory effects into ecological models offers a holistic view, enhancing our understanding of system responses to changes and providing insights for ecosystem management and conservation. This research marks a significant advancement in ecological studies, setting the stage for future exploration of memory effects on complex systems. This research delves into the dynamic interplay between memory effects and the stability landscape of ecological models, utilizing advanced computational techniques and mathematical innovations, such as fractional calculus. We conceptualize memory as a choreographer, orchestrating the movements within the stability landscape of univariate bistable ecological models. Through this lens, we examine how the echoes of past environmental interactions shape the system's adaptability, influencing its stability, resilience, and resistance to current and future perturbations. Our exploration reveals that memory does not merely act as a passive repository of past states but actively modifies the stability landscape, akin to a choreographer who shapes the performance of a dance. This modification by memory highlights its pivotal role in governing ecological system attributes, including stability thresholds, resilience capacity, resistance levels, and the criticality of transitions and tipping points. By integrating long-term memory effects into our ecological models, we unveil a more intricate understanding of the stability landscape, thereby enriching our comprehension of ecological dynamics and system responses to environmental changes. Our findings demonstrate the necessity of considering memory effects in ecological modeling, paving the way for future investigations into the impacts of memory on more complex, multivariate systems. |
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