Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

Can anyone help me please to solve these two questions? (3) Consider the system a: = siny, y = sins. (a) Find and classify the

Can anyone help me please to solve these two questions?

image text in transcribedimage text in transcribed
(3) Consider the system a: = siny, y = sins. (a) Find and classify the critical points of the system (b) Show that it is reversible (c) Show that there are therefore closed orbits around the xed point at (11', D) (Hint: write the system in terms of if: = :1: 7r and y and show that this new system is reversible). ((1) Show that the lines 3; = is are invariant, meaning any initial condition on the line has a trajectory on the line. (e) Sketch the phase portrait of the system. 1 (6) [bompare Strogatz, 6.8.7) Conaiderlthe DS r = (2301 y we, 3} = y(2: 1). (a) Plot the vector eld to help your intuition. (1)) Find the xed points (c) Plot the phase portrait (d) Argue using index theory why there can't be any closed orbits

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

Statistical Inference

Authors: George Casella, Roger L. Berger

2nd edition

0534243126, 978-0534243128

More Books

Students also viewed these Mathematics questions