Modeling Climate Change-Induced Risk Through Tipping Points, Stressors, Resilience, and Bifurcation: A Non-Autonomous Dynamical Systems Approach Using CMIP6

Climate change is accelerating the intensity and frequency of droughts, particularly threatening the resilience of semi-arid socio-ecological systems such as those in the eastern Mediterranean. Traditional drought risk assessments often overlook the complex, non-linear dynamics and abrupt transitions driven by interacting climate stressors and system feedbacks. In this study, we present a non-autonomous dynamical systems model based on coupled Ordinary Differential Equations (ODEs) to quantify climate change-induced risk. The model formalizes the Ecological-Climatic Strain Index (ECSI) as a function of four normalized state variables: Climate Stressor (CS), Resilience Capacity (RC), Tipping Point Probability (TPP), and Bifurcation Transition Index (BTI). By employing non-linear functions and conditional regimes, the model captures threshold behaviors, regime bifurcations, and critical transitions, including Normal, Crisis, Recovery, and Transformative Crisis states. To test the model’s applicability, we applied it to Türkiye using CMIP6-derived SPEI-12 data under the SSP5-8.5 scenario (2015–2100). The results reveal widespread increases in CS and TPP, particularly after 2050, signaling heightened exposure to abrupt ecological transitions. Meanwhile, RC declines across all grids, indicating diminishing adaptive capacity, while ECSI intensifies sharply by the late 21st century—highlighting rising systemic fragility. Spatial heterogeneity is also evident: Grid 16 demonstrates early and severe collapse trajectories, while Grid 33 exhibits relatively greater resilience. These findings illustrate how integrating tipping dynamics, resilience loss, and bifurcation signals into risk modeling can enable earlier detection of critical transitions and inform proactive, location-specific adaptation strategies. This modeling framework offers a transferable tool for assessing climate risk in drought-prone systems globally.