A predator-prey interaction is described by the Lotka-Volterra model x'= -0.3x + 0.04xy y' = 0.4y0.04xy. (a) Find the critical point in the first quadrant. (x, y) = =([ Use a numerical solver to sketch some population cycles. (Choose x(0) = 9 and y(0) = 6.) 14 14 12 x(t) 12 x(t) 10 10 8 ~~ 4 y(t) 5 100 20 40 60 O 0 80 100 20 40 60 80 12 x(t) 10 10 wwwwww 4y(t) 4-y(t) 20 40 80 60 100 00 20 100 00 40 60 80 (b) Estimate the period of the periodic solutions that are close to the critical point in part (a). (Choose x(0) = 9 and y(0) = 6. Use a CAS to estimate the period and round your answer to two decimal places.) 8 4 y(t) O ⁰
A predator-prey interaction is described by the Lotka-Volterra model x'= -0.3x + 0.04xy y' = 0.4y0.04xy. (a) Find the critical point in the first quadrant. (x, y) = =([ Use a numerical solver to sketch some population cycles. (Choose x(0) = 9 and y(0) = 6.) 14 14 12 x(t) 12 x(t) 10 10 8 ~~ 4 y(t) 5 100 20 40 60 O 0 80 100 20 40 60 80 12 x(t) 10 10 wwwwww 4y(t) 4-y(t) 20 40 80 60 100 00 20 100 00 40 60 80 (b) Estimate the period of the periodic solutions that are close to the critical point in part (a). (Choose x(0) = 9 and y(0) = 6. Use a CAS to estimate the period and round your answer to two decimal places.) 8 4 y(t) O ⁰
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Transcribed Image Text:A predator-prey interaction is described by the Lotka-Volterra model
x' = -0.3x + 0.04xy
y' = 0.4y = 0.04xy.
(a) Find the critical point in the first quadrant.
(x, y)
=
Use a numerical solver to sketch some population cycles. (Choose x(0)
14
12 EX(t)
10
8
6
4 y(t)
2F
20
40
60
80
60
80
100
12 Ex(f
10
www
8
6
4Fy(t)
4-y(t)
2
2
20
40
60
80
100
20
40
60
80
100
(b) Estimate the period of the periodic solutions that are close to the critical point in part (a). (Choose x(0) = 9 and y(0) = 6. Use a CAS to estimate the period and round your answer to two decimal places.)
t
100
= 9 and y(0) = 6.)
14
12 FX(t)
10
8
4Fy(t)
2
12 Ex(t)
10-
8
20
40
t
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman