CONTROL OF PARAMETERS OF A DELAYED DIFFUSIVE AUTOTROPH HERBIVORE SYSTEM

Abstract

This paper deals with the eco-biological dynamics of a delayed diffusive autotroph-herbivore population ecosystem with nutrient recycling. The real situation is represented by a set of two-dimensional nonlinear ordinary differential equations involving autotroph-herbivore biomass. Plant populations undergo critical changes with different amplitude in plant ecology. We propose a description of plant communities as interesting systems which resembles to the behavior of real media. The delay and diffusion parameter have a great role to shape the dynamical features of the system. We have studied the growth of an autotroph and herbivore population depending on the limiting nutrient which is partially recycled through bacterial decomposition. We have analyzed the asymptotic stability and switching to instability with bifurcation of the model system with delay and diffusion where diffusion controls directly the delay parameters of our system. All the analytical results are interpreted ecologically and compared with the simulated computer results.