Mathematical model for diffusion of the rhizosphere microbial degradation with impulsive feedback control

Continuous and Discrete Dynamical Models of Total Nitrogen Transformation in a Constructed Wetland: Sensitivity and Bifurcation Analysis

In this research, we study a dynamical system of total nitrogen transformation in a mangrove-filled constructed wetland. The system’s variables are the mangrove biomass concentration and total nitrogen concentration in wastewater and in soil solution. We investigate the system’s dynamics by examining the local stability of the equilibriums, simulating the phase portrait and solutions and providing time-dependent parameter sensitivity analyses. The analysis shows that the level of garbage acts as the parameter for when mangrove biomass will disappear. Both the graphs of the system solutions and the sensitivity function in the case of biomass concentration and total nitrogen concentration in soil solution versus time show symmetrical features at specific time intervals. According to the sensitivity index when reaching equilibrium, the level of garbage is the most sensitive parameter to the system. In addition, we explore the model’s discrete form by investigating the conditions for the equilibrium’s local stability and presenting bifurcation diagrams for each parameter. The symmetrical aspects are visible in the visualization of the bifurcation diagram and the solutions’ chaotic behavior.