That the Lotka-Voltera system has critical points ( 0 , 0 ) , ( 0 , K ) , ( x ^ , y ^ ) where y ^ = a b , c x ^ = r K ( K − y ^ ) .

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Answer 1

Question

Chapter 10.4, Problem 20E

(a)

To determine

To show: That the Lotka-Voltera system has critical points (0,0),(0,K),(x^,y^) where y^=ab,cx^=rK(K−y^).

(b)

To determine

To show: The critical points (0,0) and (0,K) are saddle points and the critical point (x^,y^) is either stable node or stable spiral point.

(c)

To determine

To show: That if y^<4bK2r+4bK then critical point (x^,y^) is a stable spiral point.

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Answer 2

Question

Chapter 10.4, Problem 20E

(a)

To determine

To show: That the Lotka-Voltera system has critical points (0,0),(0,K),(x^,y^) where y^=ab,cx^=rK(K−y^).

(b)

To determine

To show: The critical points (0,0) and (0,K) are saddle points and the critical point (x^,y^) is either stable node or stable spiral point.

(c)

To determine

To show: That if y^<4bK2r+4bK then critical point (x^,y^) is a stable spiral point.

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Answer 3

Question

Chapter 10.4, Problem 20E

(a)

To determine

To show: That the Lotka-Voltera system has critical points (0,0),(0,K),(x^,y^) where y^=ab,cx^=rK(K−y^).

(b)

To determine

To show: The critical points (0,0) and (0,K) are saddle points and the critical point (x^,y^) is either stable node or stable spiral point.

(c)

To determine

To show: That if y^<4bK2r+4bK then critical point (x^,y^) is a stable spiral point.

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Answer 4

Question

Chapter 10.4, Problem 20E

(a)

To determine

To show: That the Lotka-Voltera system has critical points (0,0),(0,K),(x^,y^) where y^=ab,cx^=rK(K−y^).

(b)

To determine

To show: The critical points (0,0) and (0,K) are saddle points and the critical point (x^,y^) is either stable node or stable spiral point.

(c)

To determine

To show: That if y^<4bK2r+4bK then critical point (x^,y^) is a stable spiral point.

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Answer 5

Chapter 10.4, Problem 20E

(a)

To determine

To show: That the Lotka-Voltera system has critical points (0,0),(0,K),(x^,y^) where y^=ab,cx^=rK(K−y^).

(b)

To determine

To show: The critical points (0,0) and (0,K) are saddle points and the critical point (x^,y^) is either stable node or stable spiral point.

(c)

To determine

To show: That if y^<4bK2r+4bK then critical point (x^,y^) is a stable spiral point.

Answer 6

Chapter 10.4, Problem 20E

(a)

To determine

To show: That the Lotka-Voltera system has critical points (0,0),(0,K),(x^,y^) where y^=ab,cx^=rK(K−y^).

Answer 7

Chapter 10.4, Problem 20E

(a)

To determine

To show: That the Lotka-Voltera system has critical points (0,0),(0,K),(x^,y^) where y^=ab,cx^=rK(K−y^).

Answer 8

(b)

To determine

To show: The critical points (0,0) and (0,K) are saddle points and the critical point (x^,y^) is either stable node or stable spiral point.

Answer 9

(b)

To determine

To show: The critical points (0,0) and (0,K) are saddle points and the critical point (x^,y^) is either stable node or stable spiral point.

Answer 10

(c)

To determine

To show: That if y^<4bK2r+4bK then critical point (x^,y^) is a stable spiral point.

Answer 11

(c)

To determine

To show: That if y^<4bK2r+4bK then critical point (x^,y^) is a stable spiral point.

Answer 12

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Answer 13

Expert Solution & Answer

Answer 14

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Answer 15

Ch. 10.1 - In Problems 16 write the given nonlinear...Ch. 10.1 - Prob. 2E Ch. 10.1 - In Problems 16 write the given nonlinear...Ch. 10.1 - Prob. 4E Ch. 10.1 - In Problems 16 write the given nonlinear...Ch. 10.1 - In Problems 16 write the given nonlinear...Ch. 10.1 - Prob. 7E Ch. 10.1 - Prob. 8E Ch. 10.1 - Prob. 9E Ch. 10.1 - Prob. 10E

That the Lotka-Voltera system has critical points ( 0 , 0 ) , ( 0 , K ) , ( x ^ , y ^ ) where y ^ = a b , c x ^ = r K ( K − y ^ ) .

Solution Summary: The author explains that the Lotka-Voltera system has critical points: (0,0),

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To show: That the Lotka-Voltera system has critical points (0,0),(0,K),(x^,y^) where y^=ab,cx^=rK(K−y^).

To show: The critical points (0,0) and (0,K) are saddle points and the critical point (x^,y^) is either stable node or stable spiral point.

To show: That if y^<4bK2r+4bK then critical point (x^,y^) is a stable spiral point.

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