Transcribed TextTranscribed Text

#1 Consider the system of planar nonlinear differential equations, x' = xy-x² y + y³ y'= x² + y ³ -xy² a) Convert the system to polar coordinates. b) Analyze the system and sketch a phase portrait. 2 Consider the predator prey model x' = ax - bxy y' = cxy-dy This system has an equilibrium at (x,y) = (2,a). Transform the equilibrium point to the origin and convert to polar coordinates. Compute G = so g(8)d0 and show that it is zero in this case. This proves 27 that the fixed point is a nonlinear center in this example (note that the system is not Hamiltonian) #3 Consider the system = - y' = x. Find a reversor S, identify Fix(S) and show that the origin is a nonlinear center.

Solution PreviewSolution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

    By purchasing this solution you'll be able to access the following files:

    50% discount

    $35.00 $17.50
    for this solution

    or FREE if you
    register a new account!

    PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

    Find A Tutor

    View available Differential Equations Tutors

    Get College Homework Help.

    Are you sure you don't want to upload any files?

    Fast tutor response requires as much info as possible.

    Upload a file
    Continue without uploading

    We couldn't find that subject.
    Please select the best match from the list below.

    We'll send you an email right away. If it's not in your inbox, check your spam folder.

    • 1
    • 2
    • 3
    Live Chats