Question

 Consider the following differential equation system which describes the interaction between two species.

𝑥̇= 𝑥(−0.7 + 1.6𝑦)

𝑦̇ = 1.3𝑦(1 − 𝑦) − 0.5𝑥𝑦

a) What type of interaction is modeled by the system? What is the significance of the variables?

b) Find the equilibrium points and analyze their stability. 

Answer 1

The interaction type is a competing exception. Variables make sense as values of mutually exclusive goods, or goods.

$$\frac {\delta X}{\delta x}=-0.7+1.6y=0$$

$$\frac{\delta Y}{\delta y}=1.3-2.6y-0.5x=0$$

$$y=0.44$$

$$x=0.312$$