A system of non-linear differential equations has anequilibrium point at the origin with the Jacobian matrixAJJSelect the option that gives the classification of thelinearised system of equations at this equilibriumpoint.Select one:O Star sinkO Spiral sinkO SinkO SourceO Centre

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Answered: A system of non-linear differential…

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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The function of 2 variables: f (x,y) = (5/2)x2 + 2xy - 12x + (3/2)y2 - 7y + (31/2) Has a stationary point at (2,1). At this stationary point, the Hessian matrix for f is: H = [5 2] [2 3] Which one of these options best describes the stationary point? A. The stationary point is a saddle point B. The stationary point is a local minimum C. The stationary point is a local maximum D. The nature of the stationary point cannot be determined by the Hessian matrix
H.W_2: Consider the characteristic equation of a system: S6 + 55-254 - 35³ - 7S² - 4S-4 = 0 Use Routh- Hurwitz criterion, determine the number of roots with positive real parts. Comment on the stability of the system.
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1-4d)
THE USE OF ARTIFICIAL INTELLIGENCE IS PROHIBITED
The function of two variables ƒ(x, y) = 3x² – 2xy − 10x + y² + 2y +9 has a stationary point at (2, 1). At this stationary point, the Hessian matrix for fis H=[6₂ -2 Select the option that describes this stationary point. Select one: 2]. -2 The stationary point is a saddle point. The nature of the stationary point cannot be determined from the Hessian matrix. The stationary point is a local maximum. The stationary point is a local minimum.
1-4c)
a) Show that the nonlinear dynamical system ý = 1 – x² – y? ,2 i = 2y – x* + 1, - has two equilibrium points and find their locations. b) Use the linearisation theorem to classify the nature of the equilibrium points and give two separate sketches showing phase portraits of the linearised systems. Your sketches should include isoclines (of the linearised systems) and all the straight line phase paths of the linearised systems (if any exist). c) Sketch the phase portrait of the nonlinear dynamical system indicating directions of the trajectories and the horizontal and vertical isoclines.

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A system of non-linear differential equations has an equilibrium point at the origin with the Jacobian matrix [3] J Select the option that gives the classification of the linearised system of equations at this equilibrium point. Select one: O Star sink O Spiral sink O Sink O Source O Centre