Bifurcation Analysis of Temperature Effects in Lake Eutrophication

Over the past 20 years, rising global temperatures have accelerated the biological processes in lake systems and potentially intensify the lake eutrophication. This poses a challenge to establishing sustainable lake management strategies. To address this issue, this paper develops an algae-phosphorus model which incorporates the temperature effects to assess how warming influences lake eutrophication dynamics. We incorporate differential equations in formulating the model. A eutrophic lake, Tasik Harapan is chosen as the case study. Both XPPAUT and MatCont are used in conducting co-dimension one and co-dimension two bifurcation analyses. The bifurcation results revealed that rising temperatures would lead to an abrupt increase in algae concentration, shifting the lake to eutrophic state. Regime shift thresholds of external phosphorus loading are identified at various temperatures. A higher flushing rate is required to restore the lake when the temperature increases. Variation in algae mortality rate at different temperatures would lead to the occurrence of bistability and Hopf bifurcations. In two-parameter space of external phosphorus loading and algae mortality rates, variation in temperature causes various model dynamics, including saddle-node bifurcation, Bogdanov-Takens bifurcation and Hopf bifurcation. The complex dynamics and regime shift thresholds simulated from the model can guide early interventions to prevent irreversible degradation.