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8. 7. 2026.
Global Dynamics of a Darwinian Food-Limited Evolutionary Model
We investigate the asymptotic behavior of the solutions of the evolutionary version of the food-limited equation dxdt=xrK−xK+Crx where r, growth rate, K, carrying capacity, and 1C, the rate of replacement of a species at saturation, are positive. We assume that growth rate r and the carrying capacity K are functions of some trait that evolve over time. Using previously established methodologies, we investigate the effects of parameters dependent on a trait evolving over time with respect to a trait and describe the global behavior of the solutions and give biological interpretations. Additionally, we give simulations of particular examples with biological relevance.