Interpretation:
For the system
All the bifurcations that occur as
Concept Introduction:
Fixed points are the points where
The graph of the vector field for different values of
The saddle-node bifurcation is the basic mechanism by which fixed points are created and destroyed. As a parameter is varied, two fixed points move toward each other, collide, andmutually annihilate.
A subcritical pitchfork bifurcation occurs when there is a single unstable fixed point present, which after the change of parameters becomes unstable, and two new symmetric unstable fixed points appear.
Want to see the full answer?
Check out a sample textbook solutionChapter 3 Solutions
Nonlinear Dynamics and Chaos
- Prove that in a given vector space V, the zero vector is unique.arrow_forwardWrite a formula for a two-dimensional vector field which has all vectors of length 7 and perpendicular to the position vector at that point. V=?arrow_forwardIn maths ,what is the relationship between the degree of a field extension and the dimension of its vector space?arrow_forward
- Find a field F = M(x, y)i + N(x, y)j in the xy-plane with the property that at each point (x, y) ≠ (0, 0), F is a unit vector pointing toward the origin. (The field is undefined at (0, 0).)arrow_forwardConsider the vector field F = ⟨ax + by, cx + dy⟩. Show that F has zero circulation on any oriented circle centered at the origin, for any a, b, c, and d, provided b = c.arrow_forwardUse the Stoke’s theorem to show that: for any closed curve" C "and differentiable scalar fields "f" and "g"arrow_forward
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning