Bifurcation points. Consider the system
Where
determine the x and y nullclines, respectively. Any point where an
In each of Problem 11 through 14:
a) Sketch the nullcelines and describe how the critical points move as
b) Find the critical points.
c) Let
d) Find the bifurcation point
e) For
Want to see the full answer?
Check out a sample textbook solutionChapter 7 Solutions
Differential Equations: An Introduction to Modern Methods and Applications
Additional Math Textbook Solutions
Mathematics for Elementary Teachers with Activities (5th Edition)
Introductory Mathematics for Engineering Applications
Mathematical Methods in the Physical Sciences
Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)
Calculus Volume 1
Excursions in Modern Mathematics (9th Edition)
- Find a system of two equations in two variables, x1 and x2, that has the solution set given by the parametric representation x1=t and x2=3t4, where t is any real number. Then show that the solutions to the system can also be written as x1=43+t3 and x2=t.arrow_forwardApplying variation of parameters to the DE: " – y = et + e-*, we get the following system of equations: uj e + uze- = 0 uj e* – uze- = e* + e¬* What are uj and u2? (u1 and uz are functions of x.) 2x O u - u1 = -e*; u2 e +e-2; uz = - te 2a: = In. 8 8. = In O In sin a (e"); u2 = sec a (e-*)arrow_forwardApplying variation of parameters to the DE: y"-y= e" +eª,we get the following system of equations: u e" + u, e- = 0 || u e" – uze- = e® + e=® What are u1 and u2? (u1 and u2 are functions of x.) O u %3D %3D | O u1 = -e"; uz = -e * %3D O u1 = In sin x (e"); u2 = sec x (e) %3D O u1 =+e-2; u2 %3D 1/2arrow_forward
- Applying variation of parameters to the DE: " – y = e* + e-*, we get the following system of equations: uj eº + u,e-² = 0 u e" – u,e-* = eª + e¬* What are u1 and u2? (U1 and uz are functions of x.) u1 = -e"; u2 %3D O u1 = ;a – ÷e-2*; u2 = = -e2 - æ 2 O uj = In sin a (e*) ; u2 = sec x (e") i+e ; uz = - fee 1 -2r 1 O uj = 4 2r 8 8arrow_forwardFind Duf at P. = f(x, y, z) = 6x³y³z³; P(2, -2, 2); u Duf = i i + 2 - 2 karrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,