Chapter 7.6, Problem 4E

To determine

To Find: The reason to use the plus and the minus sign.

Answer to Problem 4E

The minus sign shows that the population of the crocodile should decrease the population of the frogs.

Explanation of Solution

Given:

The population of flies, frogs and the crocodiles coexist in the environment and the population for these three in function is $P\left(t\right),Q\left(t\right),R\left(t\right)$ .

Calculation:

Consider the pollution of the flies in the absence of the frog is,

  $\frac{dP}{dt}=a\cdot P$

Here, a is the positive constant.

The interaction between the flies and the frogs population will hurt the population of the number of flies therefore,

  $\frac{dP}{dt}=a\cdot P-lQ$

Consider the population of the frogs in the absence of the flies is,

  $\frac{dQ}{dt}=-bQ+mP$

The interaction between the frog and the crocodile population will hurt the population of the frogs that is,

  $\frac{dQ}{dt}=-bQ+mP-nR$

Consider that the population of the crocodiles in the absence of the frog is,

  $\frac{dR}{dt}=-cR$

Consider that the minus sign shows that the population of the crocodile should decrease the population of the frogs.

The interaction between the crocodiles and the population of the frog help in the population of the crocodiles that is,

  $\frac{dR}{dt}=-cR+kQ$ .