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AVK's user avatar
AVK's user avatar
AVK
  • Member for 7 years, 9 months
  • Last seen this week
10 votes

Can a figure 8 be an orbit of $dx /dt =f(x,y)$, $dy/ dt =g(x,y)$ where $f$ and $g$ have continuous partial derivatives with respect to $x$ and $y$?

8 votes
Accepted

Does a symmetric matrix necessarily have a symmetric square root?

8 votes
Accepted

How to show that it is an invariant set?

8 votes
Accepted

Do chaos and/or limit cycles always require the existence of an unstable fixed point?

7 votes
Accepted

Problems finding a Lyapunov function

6 votes
Accepted

Find the closed path of given system of ordinary differential equation

5 votes
Accepted

Transform ODE system of first order into ODE of $n$-th order

5 votes
Accepted

Stability of a Degenerate Equilibrium Point in a Planar ODE

5 votes
Accepted

differential equations solve for exponents

5 votes
Accepted

$x''+(x^2+2x'^2-1)x'+x=0$ has a non trivial periodic solution.

4 votes

Meaning of Observability in LTI systems - how to actually find states.

4 votes

Show that the equilibrium point $(0,0)$ is asymptotically stable and an estimate of its basin of attraction

4 votes

Finding a Strict Lyapunov Function for $\ddot{x} + \dot{x} + x^3 = 0$

4 votes
Accepted

LaSalle for time varying systems

4 votes

Estimate blow-up time.

4 votes

Definition of the sinusoid in terms of differential equation

3 votes
Accepted

Does stability along axes imply stability of the fixed point?

3 votes

Determining stability of equilibrium point

3 votes

Show that the origin of the following system is stable (non-linear vs linear stability)

3 votes

Ask a problem of asymptotic solution of a system of nonlinear differential equations

3 votes
Accepted

Can conservative systems have unstable equilibrium points?

3 votes
Accepted

Derivative of a Lyapunov function for a nonlinear system

3 votes
Accepted

Find the Floquet multipliersfor the Markus & Yamabe system

3 votes
Accepted

Least Squares Solution of Minimal Norm when $A^{*}b = 0$

3 votes

Stability of the null solution of system of differential equations

3 votes
Accepted

Deriving inequality from a Lyapunov test of $x' = -x + y^3, \space y' = -y + ax^3$

3 votes

Find a matrix A such that $\operatorname{rank}{A} = \operatorname{rank}{A^2} \neq \operatorname{rank}{A^3}$

3 votes
Accepted

Show that the $\omega$-limit set of any orbit is on the set $K = \{(x,y) \in \mathbb{D} : x+y = 1\}$.

3 votes
Accepted

Hartman–Grobman theorem for a two-dimensional system

3 votes
Accepted

Exponential stability under global diffeomorphism

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