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When having a differential equations set, are there rules to know about the stability of the equilibrium points? If its stable, unstable or semi stable? What do you look for? for example the differential equations set : with equilibrium points: E0 = (0, 0), E1 = (1, 1), E2 = (1, −1), E3 = (−1, −1), E4 = (−1, 1).

When having a differential equations set, are there rules to know about the stability of the equilibrium points? If its stable, unstable or semi stable? What do you look for? for example the differential equations set : with equilibrium points: E0 = (0, 0), E1 = (1, 1), E2 = (1, −1), E3 = (−1, −1), E4 = (−1, 1).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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When having a differential equations set, are there rules to know about the stability of the equilibrium points? If its stable, unstable or semi stable? What do you look for?

for example the differential equations set :

with equilibrium points: E0 = (0, 0), E1 = (1, 1), E2 = (1, −1), E3 = (−1, −1), E4 = (−1, 1). 

q p p(1 – q²), -q(1 - p²).
Transcribed Image Text:q p p(1 – q²), -q(1 - p²).
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