Regulating spatiotemporal dynamics of tussock-sedge coupled map lattices model via PD control

Abstract

The tussock sedge, a plant widely distributed in freshwater wetlands across North America, plays a vital role in wetland ecosystems by reinforcing embankments, stabilizing slopes, and preventing soil erosion. However, the aging of sedges leads to the accumulation of significant amounts of plant wracks, which inhibits nutrient replenishment and hinders growth. Therefore, maintaining stable population densities and uniform growth of sedges is no time to delay. In this study, we develop a spatiotemporally discrete coupled map lattices (CMLs) model for the tussock-sedge system. By conducting a linear stability analysis, the stability conditions for the steady state are derived. Then the Flip bifurcation, Neimark–Sacker bifurcation, and Turing bifurcation of the CMLs model are investigated using bifurcation theory and the center manifold theorem. Notably, a proportional–derivative (PD) controller is designed and incorporated into the CMLs model, which can delay the occurrence of Flip bifurcation and Neimark–Sacker bifurcation, thereby preventing the oscillation and chaotic behavior of tussock population density. Additionally, the incorporation of the PD controller broadens the threshold for Turing instability, modifies the types of Turing patterns, and ensures uniform plant growth. Finally, numerical simulations are performed to illustrate the dynamical behaviors of the CMLs model, demonstrating the effectiveness of the PD control implementation.