1. Grass lives independently, and the law of independent existence follows the law of Logistic;

2. There are no other herbivores except deer on the grassland;

Deer can't live independently. Without grass, the annual mortality rate of deer is certain;

4. Assume that the compensation rate of grass to deer is a linear function of grassland density;

5. The annual herbivorous ability of each deer is a linear function of grassland density.

Establishment of model and its solution

Remember that the inherent growth rate of grass is r, the maximum density of grass is n, the annual mortality rate of deer living independently is d, the herbivorous ability of deer is a when grass is the most flourishing, and the annual compensation effect of grass on deer is b; K+ 1 year, the density of grass is, and the number of deer is. In k years, the density of grass is 0, and the number of deer is 0.

When grass lives independently and grows according to Logistic law, the differential model of grass growth at this time is, but the number of grass will be reduced due to deer's predation on grass, satisfying the following equation:

( ) ( 1)

Deer can't live independently without grass, so the model of deer's independent life is, but the existence of grass will compensate the deer's mortality, so the following difference equation is satisfied:

( ) (2)

In addition, the number of deer in the initial state is 0, and the initial value of grassland density is 0.

The value of each parameter is:

, , , ,