In each of Problems
(a) Determine all critical points of the given system of equations.
(b) Find the corresponding linear system near each critical point.
(c) Find the eigenvalues of each linear system. What conclusions can you then draw about the nonlinear system?
(d) Draw a phase portrait of the nonlinear system to confirm your conclusions, or to extend them in those cases where the linear system does not provide definite information about the nonlinear system.
(e) Draw a sketch of, or describe in words, the basin of attraction of each asymptotically stable critical point.
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
A Problem Solving Approach to Mathematics for Elementary School Teachers (12th Edition)
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
The Heart of Mathematics: An Invitation to Effective Thinking
Finite Mathematics & Its Applications (12th Edition)
Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)
Mathematical Methods in the Physical Sciences
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,