(b)A dynamical system is governed by two equations:(a)Find critical points of this system.|x=y,[y=In(x² + y)-3y.Here a dot on the top of a symbol stands for the derivative with respect to t.(c)Using linearisation of the system in the neighbourhood of each critical point,determine the nature of the critical points.Draw qualitatively but neatly these critical points and corresponding trajectorydiagrams.

The given system of differential equations are:We need to identify the critical points.We know that…

Answered: A dynamical system is governed by two…

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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Related questions

Question

(b)
A dynamical system is governed by two equations:
(a)
Find critical points of this system.
|x=y,
[y=In(x² + y)-3y.
Here a dot on the top of a symbol stands for the derivative with respect to t.
(c)
Using linearisation of the system in the neighbourhood of each critical point,
determine the nature of the critical points.
Draw qualitatively but neatly these critical points and corresponding trajectory
diagrams.

Expert Solution

Step 1: Introduction

The given system of differential equations are:

$table row cell x with dot on top end cell equals y row cell y with dot on top end cell equals cell ln open parentheses x cubed plus y close parentheses minus 3 y end cell end table$

We need to identify the critical points.

We know that a point $open parentheses a comma b close parentheses$ is said to be critical point of the system $x with dot on top equals f open parentheses x comma y close parentheses comma space y with dot on top equals g open parentheses x comma y close parentheses$ if $f open parentheses a comma b close parentheses equals 0$ and $g open parentheses a comma b close parentheses equals 0$ .