Spatio-temporal population control applied to management of aquatic plants

Optimal control for the nonlinear Fisher-Kolmogorov system with applications to aquatic plant management

“…We can also observe that the equation system (12) have an exact analytic solution in each instant t, taken into account an initial condition w j (0) = (w 0 ) j . In the works of [4] and [5] it may be seen the application of such a system to the population of some plant species.…”

“…The initial and boundary conditions depend on the specificity of each application. For example, in an application of an aquatic plant system [5] the initial conditions may be given by:…”

“…The initial and boundary conditions have been taken as in ( 17) and ( 18), respectively. The plant considered in this application is the Eichhornia crassipes and the related coefficients values have been taken from the works [4,5,12,20]. The coefficients values are: K = 700.68, a = 0.103, b = 0.000147, D = 1.33 and τ = 1.…”

“…The works [4,21] solve optimization problems to find the optimal population level which keeps a best performance of the concerning system, taking into account only a temporal evolution. Spatiotemporal control has been proposed in the recent works [5], used as an application to a water hyacinths population.…”

“…Based on [4,5,21] this work proposes a new formulation for the control problem of aquatic plants in stabilization ponds. Initially, a temporal optimization problem is solved, using a general Lotka-Volterra model.…”