Dynamics of climate and ecological models with effects of global warming time delay and fear effect within the frame of fractional calculus

Abstract

This thesis addresses the complex dynamics of climate and ecological systems using advanced mathematical and computational techniques. By blending fractional calculus, mathematical modeling, numerical methods and data-driven approaches, it provides new insights into environmental phenomena and their nonlinear dynamics. A modifed surface energy balance-mass balance model of the Cryosphere is studied to observe the eand#64256;ect of climate change on the model s dynamics, highlighting the interplay of energy and#64258;uxes and mass balance in response to environmental changes. newlineThe Lorenz-84 atmospheric propagation model is extended to incorporate global newlinewarmingeand#64256;ects, imedelaysand chaoscontrol strategies, oand#64256;eringvaluableperspectives newlineon atmospheric predictability and management. The study further investigates newlinesynchronization, control and multiscale dynamics in a modifed Samardzija-Greller newlinepredator-prey model, uncovering the eand#64256;ects of time-scale separation on ecological newlineinteractions. Behavioral factors, such as fear eand#64256;ects and predator-taxis sensitivity, newlineare also analyzed in a unique ecological model, revealing their critical roles in newlineecological stability and biodiversity conservation. Finally, stochastic and fractional environmental models are developed and applied to real-world data, predicting key environmental indicators such as air pollution levels, forest carbon sequestration, and river water quality. This work not only advances theoretical models but also bridges the gap between mathematical frameworks and practical applications, providing a foundation for future research and policy-making in climate and ecological dynamics.