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1. For each of the following systems, sketch the x- and y-nullclines and use this information to determine the nature o...
1. For each of the following systems, sketch the x- and y-nullclines and use this information to determine the nature of the phase portrait. You may assume that these systems are defined only for x,y 20. x' = x(y + 2x-2), y' = y(y-1 ) (a) 1. For each of the following systems, sketch the x- and y-nullclines and use this information to determine the nature of the phase portrait. You may assume that these systems are defined only for...
nullcline example: 1. For each of the following systems, sketch the x- and y-nullclines and use this information to determine the nature of the phase portrait. You may assume that these systems are defined only for x,y 20. (b) x' = x(y + 2x-2), y' = y(y + x-3) Figure 9.4 The (a) nullclines and (b) phase portrait for x'
For each of the following systems, sketch the x- and y-nullclines and use this information to determine the nature of the phase portrait. You may assume that these systems are defined only for x, y ≥ 0. (d) x' = x(2 – y – 2x), y' = y(3 – y – 4x)
1. (This is problem 5 from the second assignment sheet, reprinted here.) Consider the nonlinear system a. Sketch the ulllines and indicate in your sketch the direction of the vector field in each of the regions b. Linearize the system around the equilibrium point, and use your result to classify the type of the c. Use the information from parts a and b to sketch the phase portrait of the system. 2. Sketch the phase portraits for the following systems...
2. (28 marks) This questions is about the following system of equations x = (2-x)(y-1) (a) Find all equilibrium solutions and determine their type (e.g., spiral source, saddle) Hint: you should find three equilibria. b) For each of the equilibria you found in part (a), draw a phase portrait showing the behaviour of solutions near that equilibrium. -2 (c) Find the nullclines for the system and sketch them on the answer sheet provided. Show the direction of the vector field...
Please a- c for non linear system b 3. For each of the given non-linear systems, (a) find the equilibrium points, (b) near each equilibrium point, sketch the phase portrait of the linearized system, (c) use the information in (a) and (b) to sketch the phase portrait of the system: x' = - 4x + 4xy Sx = 2x – 2x² + 5xy ly=2y-y² – ry ly' = y - 2y2 + 2xy
Consider the non-linear system y-y(1-x-y). (a) Find equations for all of the x- and y-nullclines. (b) Find the coordinates of each equilibrium point of the system. (c) Sketch the nullclines in the phase plane. Clearly mark the equilibrium points. Also indicate the direction of flow on the nullclines. Consider the non-linear system y-y(1-x-y). (a) Find equations for all of the x- and y-nullclines. (b) Find the coordinates of each equilibrium point of the system. (c) Sketch the nullclines in the...
Exercise 3. (22 pts.) (Rabbits vs. Sheep) a)For each of the following ”rabbits vs. sheep” problems with x, y ≥ 0. Find the fixed points, classify them (type and stability), and find the eigenvalues and eigenvectors. Then sketch (by hand) a plausible phase portrait indicating nullclines, all relevant trajectories, and indicate all the different basins of attraction. Finally interpret the behavior of the population of the rabbits and sheep for the different systems (compare the three systems) • x˙ =...
1 Sec. 8.1 8.2 Homework For each of the following systems, find all critical points (b) find the linearization at each critical point and determine the type and stability of each critical point (c) draw a phase portrait confirming the type and stability of all critical points (1) / - (2+)(y-*) V = (4-1)y + r) (2) 1-1- (4) 2 - 1 - ry (5) x = (1-1-y) V-(3--20) Bonus computational work (use technology!) 1. Uee pplane to plot the...
Problem 1. For each of the following systems of autonomous differential equations, sketch the nullclines and find the equilibria da dy =y-x2 + 3x-2, a+ b 1000 ,2 1-7 a+b 1100 Problem 1. For each of the following systems of autonomous differential equations, sketch the nullclines and find the equilibria da dy =y-x2 + 3x-2, a+ b 1000 ,2 1-7 a+b 1100
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amrita jha Fri, Mar 25, 2022 6:57 PM