3. Consider the competition system (x for coyotes and y for foxes)x' = 3x - 2xy - x², y'= 3y - 2xy - y².Find all fixed points. Denote by R the unique fixed point (ro, yo) with ro> 0 and yo > 0. Is itstable (co-existence) or unstable (one species extinction)?

The given system of differential equations is x'=3x-2xy-x2y'=3y-2xy-y2 The fixed point of a…

Answered: 3. Consider the competition system (r…

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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5. Let h Ah x = [h₁ + ²√5 h = √5], where h is a real parameter. (a) Find all values of h for which the system X' = AX has either a center, a spiral sink, or a spiral source. (b) Find all values of h for which X' = AX has a sink or a source.
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3. Consider the competition system (r for coyotes and y for foxes) x' = 3x - 2xy - x², y'=3y - 2xy-y². Find all fixed points. Denote by R the unique fixed point (ro, yo) with o> 0 and yo > 0. Is it stable (co-existence) or unstable (one species extinction)?