Let Nn be the population at time n of a species following th

Let N_n be the population at time n of a species following the discrete logistic growth equation. That is. N_n+1 - N_n/delta t = r N_n (1 - N_n/K), Show that N_n has upper bound.

Solution

Solution:-1.In logistic growth , a population \'s per capita growth rate gets smaller and smaller as population size approaches a maximum imposed by limited resources in the environment, known as the carrying capacity K.

2.Logistic growth produces S-shaped curve.

3. Per Capita growth r gets smaller as population approches its maximum size.

4.The population will grow slowly at first , but it will grow faster and faster atleast for a while.At some point, however , population growth wil began to slow because of the term (1-Nn/k ) is getting smaller and smaller as N_n gets larger and close to K.

The discrete equation shows that the behaviour of population is jointly determined by r and K.

From the above four points we can conclude that, N_n ,which is the population at time n of a species approches to maximum limit ,hence N_n has an upper bound.