Effect of noisy environment and evidence of chaos in aquatic snail-epiphyte-submerged macrophyte interactions

Submerged macrophytes are crucial in aquatic ecosystem as they enhance the apparent clarity of lakes and rivers by absorbing significant amount of nutrients and control eutrophication. Epiphytic species create shading effect that inhibits the growth of submerged macrophytes and they generally sensitive to allelopathically active substances produced by submerged plants. Both submerged macrophytes and epiphytes are impacted significantly by selective predation of snails. A mathematical model involving snails, epiphytes, and submerged macrophytes characterized by SI-type disease in submerged macrophytes is proposed and examined in this article. Hopf and transcritical bifurcations are explored comprehensively in order to demonstrate the one parametric bifurcations in the deterministic model. Additionally, the model undergoes quasiperiodic and chaotic dynamics through period doubling and Neimark-Sacker bifurcations. Under chaotic conditions, the detrimental allelopathic effect of the submerged macrophytes on epiphytes may prevent epiphyte growth, helping the system to recover from chaos and retain stability. The suggested model system also shows bi-parametric bifurcations including generalized Hopf, double Hopf, and Chenciner bifurcations. The deterministic model is extended by including environmental white noise. At low white noise strength, we found that the stochastic system oscillates around the solutions of the equivalent deterministic system, but at high intensity, the populations are driven to extinction. Crucially, the elimination of infection from aquatic ecosystems can be achieved with high white noise levels and low infection rate. This comprehensive investigation of the interactions involving snails, submerged macrophytes, and epiphytes offers significant new knowledge of the intricate dynamics of aquatic environments.