A MODEL OF PHYSIOLOGICALLY STRUCTURED POPULATION-DYNAMICS WITH A NONLINEAR INDIVIDUAL GROWTH-RATE

In this article we consider a size structured population model with a nonlinear growth rate depending on the individual's size and on the to tal population. Our purpose is to take into account the competition fo r a resource (as it can be light or nutrients in a forest) in the grow th of the individuals and study the influence of this nonlinear growth in the population dynamics. We study the existence and uniqueness of solutions for the model equations, and also prove the existence of a ( compact) global attractor for the trajectories of the dynamical system defined by the solutions of the model. Finally, we obtain sufficient conditions for the convergence to a stationary size distribution when the total population tends to a constant value, and consider some simp le examples that allow us to know something about their global dynamic s.