Consider the van der Pol system x? = y, y? = ?x + ?(1 ?
Question and Solution
Consider the van der Pol system x? = y, y? = ?x + ?(1 ? x2 )y, where we now allow the parameter ? to be any real number.
72 % (167 Review)
Consider the van der Pol system x? = y, y? = ?x + ?(1 ? x2 )y, where we now allow the parameter ? to be any real number. (a) Show that the origin is the only critical point. Determine its type and stability property, and how these depend on ?. (b) Let ? = ?1; draw a phase portrait and conclude that there is a periodic solution that surrounds the origin. Observe that this periodic solution is unstable. Compare your plot with Figure 7.5.4. (c) Draw a phase portrait for a few other negative values of ?. Describe how the shape of the periodic solution changes with ?. (d) Consider small positive or negative values of ?. By drawing phase portraits, determine how the periodic solution changes as ? ? 0. Compare the behavior of the van der Pol system as ? increases through zero with the behavior of the system in Problem 16. Problems 18 and 19 extend the consideration of the Rosenzweig
Your answer will be ready within 2-4 hrs. Meanwhile, check out other millions of Q&As and Solutions Manual we have in our catalog.
Get immediate access to 24/7 Homework Help, step-by-step solutions, instant homework answer to over 40 million Textbook solution and Q/A
Pay $7.00/month for Better Grades
Crazy for Study is a platform for the provision of academic help. It functions with the help of a team of ingenious subject matter experts and academic writers who provide textbook solutions to all your course-specific textbook problems, provide help with your assignments and solve all your academic queries in the minimum possible time.
Disclaimer: Crazy For Study provides academic assistance to students so that they can complete their college assignments and projects on time. We strictly do not deliver the reference papers. This is just to make you understand and used for the analysis and reference purposes only.