Consider the differential equation u' = F (u) where u = [ay] and the function on the right hand side is F (u) = [ -x+ 2xy y - xy (1) The Jacobian of F (u) has entries (3) Classify the behavior at the origin: Attractor Repellor Saddle Center J₁1 J21 (2) The origin is an equilibrium point. Evaluated at the origin, the Jacobian has entries J11 (5) At this equilibrium point, the Jacobian is J21 Spiral attractor Spiral repellor (4) The differential equation has another equilibrium point at = J₁1 J21 = = x= || || = ⒸJ12 = J22 J12 J22 y = || J12 || = J22 ||

Consider the differential equation u' = F (u) where u = [ay] and the function on the right hand side is F (u) = [ -x+ 2xy y - xy (1) The Jacobian of F (u) has entries (3) Classify the behavior at the origin: Attractor Repellor Saddle Center J₁1 J21 (2) The origin is an equilibrium point. Evaluated at the origin, the Jacobian has entries J11 (5) At this equilibrium point, the Jacobian is J21 Spiral attractor Spiral repellor (4) The differential equation has another equilibrium point at = J₁1 J21 = = x= || || = ⒸJ12 = J22 J12 J22 y = || J12 || = J22 ||

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.1: Solutions Of Elementary And Separable Differential Equations

Problem 54E: Plant Growth Researchers have found that the probability P that a plant will grow to radius R can be...

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