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Results tagged with differential-equations
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user 15570
Ordinary or partial differential equations. Delay differential equations, neutral equations, integro-differential equations. Well-posedness, asymptotic behavior, and related questions.
4
votes
Accepted
Can a periodically additively perturbed sinusoidal vector field on the circle have a stable ...
The claim is true. (As proved here, it is quite unique to sinusoidal vector fields. The same reference also mentions, in its introduction, existing applications of equation (1) with $g$ taking the par …
- 708
7
votes
2
answers
257
views
Can a periodically additively perturbed sinusoidal vector field on the circle have a stable ...
I have heard that differential equations on $\mathbb{S}^1$ of the form
\begin{equation} \hspace{40mm} \dot{\theta}(t) \ = \ A\sin(\theta(t)) + g(t) \hspace{4mm} \mathrm{mod} \ 2\pi, \hspace{40mm} (1) …
- 708
10
votes
2
answers
341
views
Is this Riccati equation ("Josephson junction") always phase-locked at integer rotation numb...
Given parameters $(a,k,A) \in \mathbb{R}^3$, we consider on $\mathbb{S}^1$ the $2\pi$-periodic ODE
$$ \dot{\theta} \ = \ - a\sin(\theta) + k + A\cos(t) \hspace{4mm} \mathrm{mod} \ 2\pi. $$
Identifying …
- 708