In this program
- Autonomous ODEs
- Phase lines
- Bifurcations in one-dimensional systems (saddle-node, transcritical)
- Planar linear systems: classification via eigenvalues
- Phase plane analysis and nullclines
- Liapunov functions (introduction)
- Linearization
- Hartman–Grobman theorem (statement)
- See all →
First-order and planar systems
Bifurcations in one-dimensional systems (saddle-node, transcritical)
Dynamical systems · STEM / applied
Learning objective
Bifurcations in one-dimensional systems (saddle-node, transcritical)
Study materials
Study guide, practice problems, review, and practice test for this learning objective.
- Practice ProblemsComing soon
- Word ProblemsComing soon
- Mixed PracticeComing soon
- Multi-Step ProblemsComing soon
- Multi-Standard ProblemsComing soon
- Multi-Step Multi-StandardComing soon
- ReviewComing soon
- Practice TestComing soon
- Answer keyComing soon
Interactive practice
Quizzes, typed answers, and flashcards for this standard — coming soon.
- Coming soon
Quiz
Multiple-choice questions with instant feedback
- Coming soon
Typed practice
Type answers and check them
- Coming soon
Flashcards
Vocabulary and key facts
- Coming soon
Mixed quiz
Harder mixed review for this standard