Question

blot aston. a To explore the concepts just introduced, investigate the Verhulst model in your report. This is a model of population growth first published by Pierre Verhulst (1845, 1847) to model the development of a population in a limited environment. The continuous ver- sion of the model is described by the differential equation: = = = rx (1-3 i = 1 (5) K is a parameter called the carrying capacity of the system, i.e. is it the maximum popu- lation that can be sustained with the available resources (e.g. food). The rate at which the population is growing or dying out is described by the parameter r. This is a very simple model of population growth. dx dt (a). What are the fixed points of this equation? (Set i = 0 to find them). Ploti versus x * for chosen values of r and K to graphically see where the fixed points are. Use the flow-on-a-line analysis described above to determine which fixed points are stable and which are unstable.​

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