Complexity Measurement and Bifurcation Analysis of a New Lake Model: Coincidence with the Hénon Map

This study presents a novel lake ecosystem model that captures the intricate dynamics of nutrient cycling through nonlinear interactions. The model incorporates external phosphorus loading and internal recycling rates to explore a range of ecological outcomes, from stable equilibria to chaotic oscillations. We investigate the bifurcation phenomena within this model, revealing how changes in parameters can lead to significant shifts in ecosystem behavior. Our analysis demonstrates that the model can replicate behaviors similar to the Hénon map under specific parameter settings. Through numerical simulations, we examine the system's sensitivity to variations in nutrient parameters, uncovering the potential for unpredictable dynamics and chaos as the recycling rate increases. The emergence of chaotic behavior is further supported by entropy analysis, highlighting the model's complexity and its implications for real-world ecosystems. Notably, our findings resonate with the work of Tay et al., demonstrating that increased nutrient recycling can lead to bistability and abrupt shifts in ecosystem stability, emphasizing the critical importance of effective nutrient management to avert detrimental ecological consequences. This research contributes valuable insights into the dynamics of freshwater ecosystems, underscoring the intricate interplay between nutrient inflow, recycling, and bifurcation in maintaining ecological balance.