48 solution provided by instructor therefore not graded work, please explain why the graph looks like that as well [48] In the predator-prey system= x(1-2y),{} y = y(-1+x),sketch the phase portrait in the first quadrant {r > 0, y ≥ 0}, and determine whethereach equilibrium is stable, asymptotically stable, or unstable.[48] (0,0) is unstable. (1,1/2) is stable but not asymptotically stable.1.50.5of3

Answered: Image /qna-images/answer/8ec14557-9c69-45b6-a91e-005cb0c461b6.jpg

[48] In the predator-prey system sketch the phase portrait in the first quadrant {x ≥ 0, y ≥ 0}, and determine whether each equilibrium is stable, asymptotically stable, or unstable. [48] (0,0) is unstable. (1,1/2) is stable but not asymptotically stable. 1.5 y l I' = x(1-2y), y = y(-1+x), 0.5 01

[48] In the predator-prey system sketch the phase portrait in the first quadrant {x ≥ 0, y ≥ 0}, and determine whether each equilibrium is stable, asymptotically stable, or unstable. [48] (0,0) is unstable. (1,1/2) is stable but not asymptotically stable. 1.5 y l I' = x(1-2y), y = y(-1+x), 0.5 01

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter14: Discrete Dynamical Systems

Section14.3: Determining Stability

Problem 1YT

See similar textbooks

Similar questions

x' = 1 х. Construct the phase plane for the points (2,2), (2,0), (2,-2), (0,2), (0,-2), (-2,2), (-2,0) and (-2,-2). 2.5 1.5 1 0.5 -0.5 -1 -1.5 -2 -2.5 3 -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2.5
6. State whether the equation is ordinary or partial, linear or nonlinear, and give its order. * (x + y) dx + (3x² – 1) dy = 0 ordinary, linear in x, order 1 ordinary, linear in y, order 1
For the phase portrait shown below 1 -1 -2 -3 -4 -5 Classify the equilibrium point (0,0). Give type, and indicate whether it is stable or unstable.
Solve the DE. (x³ + xy²-y)dx + (y³ + x²y + x) dy = 0 O arctan(;)=C - ng? (²) = C - x² - y² O 2arctan(;)=C - - O 2arctan O arctan (²) = C - x² - y²
nt) Consider the discrete-time dynamical system x+1 = 0.57x, +0. What is the equilibrium for this system? What is the updating function rule f(x)? What is the derivative of the updating function? Is the equilibrium stable, unstable, or neither? 1.4
Consider the discrete-time dynamical system xt+1 = 5xt(1-xt).If xt = 4/5, xt +1 = _____Is x1 = 4/5 an equilibrium for this system? ______Write the updating function rule as f(x) = 5x(1-x).Compute the derivative: f'(x) = ______Evaluate the derivative at the equilibrium: ___________Is the equilibrium stable, unstable or neither? ________
Asap
Find the 2nd partial derivatives of : = 3xy+y -4x+7
Consider the autonomous system y' = y (y – 3) (a) Write a phase portrait for the above equation. (b) Identify any stable equilibrium solutions. (c) Identify any unstable equilibrium solutions.
x'(t) = - (; ) * Draw a phase portrait for the system. Classify the equilibrium point (0,0) and identify its stability
Assume that dx1/dt= x1(2-x1)-x1x2 dx2/dt= x1x2-x2 a) Graph the zero isoclines. b) Show that (1, 1) is an equilibrium, and use the graphical approach to determine its stability.
Find the solution. (D3 - 3D - 2)y =0; when x =0, y=0, y' = 9, y" = 0. A y = (-1+ 2x)e-2*+ e 2* B y = (-2 + x)e-+2e* C y = (-1+ 2x)e2 + 2e -* D y = (-2 + 3x)e+2e2x Question 2 Find the solution. (D5 - D³ly = 0