2. For the following coupled systemx=yy = x(1-x²)+yfind all equilibrium points and determine the nature of the linear system around each of theequilibrium points. Draw the null-clines, directions of the trajectories on each null-clines andhence draw the approximate phase plots the the system.

Let x'=f(x,y), y'=g(x,y) be a system of differential equations,then the equilibrium points occur at…

Answered: For the following coupled system x=y y…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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3. Consider the nonlinear system S a' = y y = 4 – a2 + 2y %3D a) Find all critical points. b) For each critical point find the linearized system and determine its type and stability. Then determine type and stability of each critical point for the nonlinear system. c) Sketch the phase portrait near each critical point. Carefully mark sketched solutions with arrows.
|cco ) Imagine the system of nonlinear ODE's below represents a population of hawks and crows, respectively: dt 1-y = x² - y² = a.) Find the equilibrium points for this system. If necessary, round to two decimal places (e.g. 150.156 rounds to 150.16). b.) Use the Linearization Theorem to classify each equilibrium point. Show all necessary work, as we did throughout the lessons. Be sure to fully verify the validity of each classification by checking conditions of the theorem. c.) Are there any equilibrium points to which hawks and crows can converge, assuming the initial population sizes are not equal to any of the equilibrium points? Explain based on your understanding of your classifications.
For each of the nonlinear systems below, use technology to draw phase portraits (attach to the solution), determine equillibrium solutions and visually estimate whether they are stable or unstable. (a) x' = In(y + 2) x² + y (b) I' y' = y-x² - 8y² X-
Solve the following system: -y+t. = dt du = x-t dt
8. For the system below, find all the critical points, find the linearization at each crit- ical point and classify it. Also indicate if they are stable, asymptotically stable, or unstable. a' = (0.6 – 0.01y)x, y = (0.002r – 0.4)y
Use the method of undetermined coefficients to solve the given nonhomogeneous system." dx 2x + Зу - 8 dt %3D dy = -X - 2y + 6 dt X(t) = %3D
Consider a disease that propagates according to the system dx 357 — Зху — 3х dt dy = X dt х?у — 13ху — 68у where X represents susceptible individuals and y represents infected individuals. (a) Find all biologically meaningful equilibria.
Please do a,c,d

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For the following coupled system x=y y = x(1-x²)+y find all equilibrium points and determine the nature of the linear system around each of the equilibrium points. Draw the null-clines, directions of the trajectories on each null-clines and hence draw the approximate phase plots the the system.