This is another example of how a system can change as a parameter is varied. Consider the...

This is another example of how a system can change as a parameter is varied. Consider the system

for a = 0, and a = ±0.1. Use the display rectangle − 1 ≤ x ≤ 1, and −1 ≤ y ≤ 1, and plot enough solutions in each case to describe behavior of the system. Describe what happens as the parameter a varies from negative values to positive values. (This is an example of a Hop bifurcation.) Hint: Look for something completely new, something other than an equilibrium point.