[47] Each of the following problems can be interpreted as describing the interaction of two competing species with populations z₁(t) and ₂(t). In each of these problems, find the equilibrium of co-existence, give the linear approximating system near this equilibrium, and determine whether this equilibrium is stable, asymptotically stable, or unstable with respect to the nonlinear system. (b) {12=7₂2(9-5₁-27₂) x₂ = x₂(9-2x1 - 5x2) [47] (a) The equilibrium of co-existence is (1,2)= (2, 1). The linear approximating system near (2, 1) is -2 -8 #D][2][3] -2 -5 X2 d dt The equilibrium (2, 1) is unstable. (b) The equilibrium of co-existence is (₁,2)= (1, 2). The linear approximating system near (1, 2) is The equilibrium (1,2) is asymptotically stable. #Q-³63] -10 d dt 2 2-2
[47] Each of the following problems can be interpreted as describing the interaction of two competing species with populations z₁(t) and ₂(t). In each of these problems, find the equilibrium of co-existence, give the linear approximating system near this equilibrium, and determine whether this equilibrium is stable, asymptotically stable, or unstable with respect to the nonlinear system. (b) {12=7₂2(9-5₁-27₂) x₂ = x₂(9-2x1 - 5x2) [47] (a) The equilibrium of co-existence is (1,2)= (2, 1). The linear approximating system near (2, 1) is -2 -8 #D][2][3] -2 -5 X2 d dt The equilibrium (2, 1) is unstable. (b) The equilibrium of co-existence is (₁,2)= (1, 2). The linear approximating system near (1, 2) is The equilibrium (1,2) is asymptotically stable. #Q-³63] -10 d dt 2 2-2
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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Question
47 solution provided by instructor for practice therefore not graded work
![[47] Each of the following problems can be interpreted as describing the interaction of two
competing species with populations x₁(t) and x₂(t). In each of these problems, find the
equilibrium of co-existence, give the linear approximating system near this equilibrium,
and determine whether this equilibrium is stable, asymptotically stable, or unstable with
respect to the nonlinear system.
x₁ = x₁(6— ₁ — 4x2)
(b)
S x₁ = x₁(6 — 4x₁ – T2)
-
-
=
-
[47] (a) The equilibrium of co-existence is (₁, 2) = (2, 1).
-2 -8
The linear approximating system near (2, 1) is #0-1333
-2
-5
d
dt I2
The equilibrium (2,1) is unstable.
(b) The equilibrium of co-existence is (₁, ₂) = (1,2).
The linear approximating system near (1,2) is
The equilibrium (1,2) is asymptotically stable.
d
=
-4
#0333]
-10
dt 12
X2
=
2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8c89c353-252e-4eca-b673-064be33ffdb0%2F7138dc6c-817e-4524-8ceb-e6d590dc32ac%2Flyyrnwc_processed.png&w=3840&q=75)
Transcribed Image Text:[47] Each of the following problems can be interpreted as describing the interaction of two
competing species with populations x₁(t) and x₂(t). In each of these problems, find the
equilibrium of co-existence, give the linear approximating system near this equilibrium,
and determine whether this equilibrium is stable, asymptotically stable, or unstable with
respect to the nonlinear system.
x₁ = x₁(6— ₁ — 4x2)
(b)
S x₁ = x₁(6 — 4x₁ – T2)
-
-
=
-
[47] (a) The equilibrium of co-existence is (₁, 2) = (2, 1).
-2 -8
The linear approximating system near (2, 1) is #0-1333
-2
-5
d
dt I2
The equilibrium (2,1) is unstable.
(b) The equilibrium of co-existence is (₁, ₂) = (1,2).
The linear approximating system near (1,2) is
The equilibrium (1,2) is asymptotically stable.
d
=
-4
#0333]
-10
dt 12
X2
=
2
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