Consider the system x'=xy+y2 and y'=x2 -3y-4. Find all four equilibrium points and linearize the system...
Consider the system x'=xy+y2 and y'=x2 -3y-4. Find all four equilibrium points and linearize the system around each equilibrium point identifying it as a source, sink, saddle, spiral source or sink, center, or other. Find and sketch all nullclines and sketch the phase portrait. Show that the solution (x(t),y(t)) with initial conditions (x(0),y(0))=(-2.1,0) converges to an equilibrium point below the x axis and sketch the graphs of x(t) and y(t) on separate axes.
Please write the answer on white paper using black and orient it properly so that it can be easily read.
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Consider the system x'=xy+y2 and y'=x2
-3y-4. Find all four equilibrium points and linearize the system...
Consider the system: x' = y(1 + 2x) y' = x + x2 - y2 a. Find all the equilibrium points, and lin...
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Please show work!!
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Consider the spring model
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problem. Linearize the first-order system that you obtained there
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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...
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3) Given the systemxx2-x,y'-2y, find all fixed points. For each fixed point linearize the system near the fixed point, shift the...
Please show work!!
(1 point) Take the system x' = 4x – xy, y = 5y + x2. How many critical points are there? What is the critical point with the largest x-coordinate? ( The linearization at this point is | tion at this point is [*] =A (Where A is where A is ul A = At this point the behavior is For behavior write one of "saddle", "source", "sink", "spiral sink", "spiral source", "center".
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...
1. (20 marks) This question is about the system of differential equations dY (3 1 (a) Consider the case k 0 i. Determine the type of equilibrium at (0,0) (e.g., sink, spiral source). i. Write down the general solution. ili Sketch a phase portrait for the system. (b) Now consider the case k -3. (-1+iv ) i. In this case, the matrix has an eigenvalue 2+i/2 with eigenvector and an eigenvalue 2-W2 with eigenvector Determine the type of equilibrium at...
Consider the spring model
x″−8x+2x3=0, x ″ − 8 x + 2 x 3 = 0 , we looked at in the previous
problem. Linearize the first-order system that you obtained there
at the third of the critical points you found. [x′y′]=A[xy] [ x ′ y
′ ] = A [ x y ] , where
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