A Differential Equations Analysis of Renewable Energy Consumption Resilience for Climate Risk Mitigation

Abstract Climate change gives rise to escalating disruptions to energy systems, requiring resilient strategies for fostering sustainable consumption. Renewable energy provides a vital adaptive capability for mitigating climate threats. Using a three-phase data of energy consumption from 2000–2025, this study employs a set of differential equations to explore the dynamics of renewable-fossil energy consumption in the face of climate uncertainty. The results show that, there is high growth in energy consumption due to high value of energy intensity and high technology advancement in leveraging fossil fuels technology as indicated that, in the period from 2010 to 2020, the empirical outcomes unveil decrease to energy intensity \(\:(\sigma\:\:=\:1.39)\). Additionally, at higher amount of carbon emissions of \(\:\lambda\:=0.19\), the rate of fossil fuel consumptions goes into diminishing there is a sharp increase of renewable energy as an optimal substitute. This study concludes that, the increase of energy intensity influenced the rise in fossil energy consumption. Nevertheless, the rise of technological advancement toward renewable sources enhanced the renewable energy consumption. The results of this work further emphasize that promoting the consumption resilience of renewable energy necessitates not only improving climate resilience, but also promoting less cost in energy integration. This context offers a quantitative basis for suggesting strategies that align renewable energy growth with long-term climate risk mitigation goals.