Question

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

 _Ẋ = 0.2x − 0.0002x² − 0.006𝑥𝑦

𝑦̇ = 0.015𝑦 + 0.0008𝑥𝑦

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 type of behavior is competing for exclusion. Variables have the value of quantitative values of two independent factors.

$$\frac{\delta X}{\delta x}=0.2-0.0004x-0.006y=0$$

$$\frac{\delta Y}{\delta y}=0.015+0.0008y=0$$

$$x=18.75$$

$$y=32$$