Question: equilibrium points of a nonlinear system, stability

Hi I am new to using Maple,

Mybe this is a very basic question.

I am trying to find solutions to the following nonlinear system of equations using fsolve.

This is the right hand side of a system of ODE.

I do get two solutions for the given parameter values. My question are:

1) How do I know that these are the only solutions within the given region?

2) How do I create a  loop to obtain the solutions for various values of myBeta?

3) How do I determine stability of each solution?

Many thanks in advance

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