All the necessary information is provided. What is missing? 4. Existence of periodic solutions...
80.2K
Verified Solution
Link Copied!
Question
Accounting
All the necessary information is provided. What is missing?
4. Existence of periodic solutions (a) Briefly explain the conditions under which the Poincar-Bendixson theorem for two-dimensional dynamical systems guarantees the existence of a periodic orbit. (b) Use the Poincar-Bendixson theorem to discuss the existence of a limitcycle for the system d r (1 12) + ur? cos (20) dt exp (r) + sin (20) dt For which values of u do you expect that a limit cycle exists? Do you expect it to be stable? (c) Show that the system d = -2-y+cY d = y + 2x3 - 2.4 has no periodic solutions. Hint: show that V 20M + ay" is a Lyapunov function for suitable m, n, a. 2 4. Existence of periodic solutions (a) Briefly explain the conditions under which the Poincar-Bendixson theorem for two-dimensional dynamical systems guarantees the existence of a periodic orbit. (b) Use the Poincar-Bendixson theorem to discuss the existence of a limitcycle for the system d r (1 12) + ur? cos (20) dt exp (r) + sin (20) dt For which values of u do you expect that a limit cycle exists? Do you expect it to be stable? (c) Show that the system d = -2-y+cY d = y + 2x3 - 2.4 has no periodic solutions. Hint: show that V 20M + ay" is a Lyapunov function for suitable m, n, a. 2
Answer & Explanation
Solved by verified expert
Get Answers to Unlimited Questions
Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!
Membership Benefits:
Unlimited Question Access with detailed Answers
Zin AI - 3 Million Words
10 Dall-E 3 Images
20 Plot Generations
Conversation with Dialogue Memory
No Ads, Ever!
Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
