08.08.2015 Views

Unexpected Behaviors in Higher- Order Positive Feedback Loops

Order Positive Feedback Loops - Creative Learning Exchange

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12 D-4455-22.001: a 2: b2b(0)=10.001a(0)=-121 2 1 21-2.000.00 1.50 3.00 4.50 6.00TimeFigure 5: Convergent behavior from <strong>in</strong>itial conditions a(0) = -1, b(0) = 1(second-order positive feedback loop).2.001: a 2: b0.002b(0)=12 211a(0)=-0.99121-2.000.00 1.50 3.00 4.50 6.00TimeFigure 6: Unstable convergence perturbed to exponential growth(second-order positive feedback loop).Independent Exploration:Make a comparative scatter graph of a vs. b, and try many <strong>in</strong>itial values of a andb. This is done <strong>in</strong> the Graph Pad Dialog box. First, select Scatter under Graph Type.Then double click a and b under Allowable to be Selected, as normally done. To plot

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