Agricultural crops are vital for human survival, forming the backbone of global food supply. However, the rising atmospheric carbon dioxide ( ) level and the increasing temperature relative to the pre-industrial level are poised to impact the yields of essential staple food crops significantly. In this research, we propose and analyze a nonlinear mathematical model to investigate the effects of elevated and temperature on crop yield. Our model assumes that rising levels elevate the global average temperature, and the surface temperature initially boosts the growth rate of crops until a threshold is reached, after which the growth rate declines. We also incorporate seasonal variations into the model and perform a comprehensive analytical and numerical analysis of both the autonomous and associated nonautonomous systems. Our findings reveal a critical threshold for anthropogenic emissions, beyond which the crop yield starts to decrease. Notably, crops with high-temperature tolerance demonstrate higher yields even under elevated conditions, suggesting a viable strategy for mitigating climate change impacts: developing or utilizing crop varieties with enhanced temperature tolerance. Moreover, our analysis of the nonautonomous system uncovers periodic solutions when the corresponding autonomous system is stable. The nonautonomous system also exhibits complex dynamics, including higher-period oscillations and chaos, when the autonomous system undergoes limit-cycle oscillations. This study provides valuable insights into the interplay between level, global average surface temperature, and crop yield, offering potential strategies for safeguarding agricultural productivity in the face of climate change.
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