Unstable, spiral point Asymp. stable, spiral point Stable center A= p2 - 4q = 0 Proper or improper nodes Unstable node Asymp. stable node A=p2 - 4g <0 Unstable, saddle point A = p2 – 4q >0 Proper or improper nades
Unstable, spiral point Asymp. stable, spiral point Stable center A= p2 - 4q = 0 Proper or improper nodes Unstable node Asymp. stable node A=p2 - 4g <0 Unstable, saddle point A = p2 – 4q >0 Proper or improper nades
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
18.Continuing Problem 17, show that the critical point (0, 0) is
a.Asymptotically stable if q > 0 and p < 0;
b.Stable if q > 0 and p = 0;
c.Unstable if q < 0 or p > 0.
The results of Problems 17 and 18 are summarized visually in Figure 9.1.8
FIGURE 9.1.8 Stability and classification of critical point (0, 0) as a function of p = a11 + a22 and q = a11a22 − a12a21.
Transcribed Image Text:Unstable, spiral point
Asymp. stable, spiral point
Stable
center
A= p2 - 4q = 0
Proper or improper nodes
Unstable
node
Asymp. stable
node
A=p2 - 4g <0
Unstable, saddle point
A = p2 – 4q >0
Proper or improper nades
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