Lyapuniv-functions
We have the system of ODEs
$y_1'= y_2$
$y_2'=-y_2-\sin(y_1)$.
Decide for each of the following functions whether it is a Lyapunov-function of $(0,0)$ or not:
$V(y_1,y_2)= y_1^2+y_2^2$.
$V(y_1,y_2)= \frac{y_2^2}{2}+(1- \cos(y_1))$.
$V(y_1,y_2)= \frac{(y_1+y_2)^2}{2} + y_1^2 + \frac{y_2^2}{2}$.
Ichbinanonym
116
Answer
Answers can only be viewed under the following conditions:
- The questioner was satisfied with and accepted the answer, or
- The answer was evaluated as being 100% correct by the judge.
1 Attachment
Mathe
3.6K
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
- answered
- 796 views
- $13.00
Related Questions
- Laplace transforms / ODE / process model
- How does the traffic flow model arrive at the scaled equation?
- Laplace transforms and initial value problems.
- Suppose $u \in C^2(\R^n)$ is a harmonic function. Prove that $v=|\nabla u|^2$ is subharmonic, i.e. $-\Delta v \leq 0$
- Ordinary Differential Equations Integrating Factors Assignment
- Differential Equations (2nd-order, general solution, staionary solution, saddle point, stable branch)
- Calculus - 2nd order differential equations and partial derivatives
- A linear ODE
