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

Question

Want to see the full answer?

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.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Students have asked these similar questions

For the following function f and real number a, a. find the slope of the tangent line mtan = f' (a), and b. find the equation of the tangent line to f at x = a. f(x) = 2x² + 3x; a = 2 a. Slope: b. Equation of tangent line: y

For the following function f and real number a, find f' (a). f(x) = = √x+4; a = 0 f' (a)

Find the slope of the secant line between the values x₁ and x2 for the function y = f (x). Answer exactly or round to 2 decimal places. f(x) = √√x x7; x₁ = 11, x2 = 23 Slope:

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.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

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.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

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.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

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

Expert Solution & Answer

Answer 13

Expert Solution & Answer

Answer 14

Want to see the full answer?

Check out a sample textbook solution

See solution

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),

Videos

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.

Want to see the full answer?

Chapter 10 Solutions