7.3.2 in Strogatz "Using numerical integration, compute the limit cycle of Exercise 7.3.1 and verify that...

7.3.2 in Strogatz

"Using numerical integration, compute the limit cycle of Exercise 7.3.1 and verify that it lies in the trapping region you constructed."

Exercise 7.3.1 refers to the system "x'=x-y-x(x^2+5y^2), y'=x+y-y(x^2+y^2)"

Expert Solution

7.3.2 A limit cycle is a closed solution curve which is the limit set of nearby solution curves. If the solution curves spiral into the limit cycle as t → ∞, it is a attracting limit cycle. If they spiral into the limit cycle as t → −∞, it is a repelling limit cycle.

Colby Messinger answered 2 years ago

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