Questions tagged [delay-differential-equations]
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11 questions
2 votes
0 answers
67 views
Solution to delay differential equation with periodic modulation?
How to analytically solve the following delay differential equation with periodic modulation: $$\frac{d}{dt}f(t)=-i\cos(\Omega t)f(t)-\Gamma f(t-d)\Theta(t-d)+e^{ikt}.$$ The initial condition is $f(0)=...
- 21
2 votes
0 answers
148 views
When is a first-order proportional delay differential equation equivalent to a higher-order ordinary differential equation?
The proportional delay differential equation $$ xf'(x)+2xf'(x/2)+C+4f(x/2)-5f(x)=0 $$ with initial condition $f(0)=C$ expresses that Simpson's rule exactly integrates $f$ over any interval $[0,x]$ and ...
- 3,750
2 votes
1 answer
193 views
Looking for review of delay differential equations involving $f(x)$ and $f(x/k)$
A research problem unexpectedly leads me to a delay differential equation of the form $$ f(x)=\alpha(f(x),f(x/2))\,f'(x)+\beta(f(x),f(x/2))\,f'(x/2)+\gamma(f(x),f(x/2)) $$ For special cases of $\alpha,...
- 3,750
2 votes
0 answers
94 views
Where can I find resources for a paper "Stability analysis of a novel DDE of HIV CD4+ T-cells"?
I am currently working on a the paper [NND]: Question: On page 4, equation 6 introduces a concept related to the infection rate within the context of the HIV model. Unfortunately, the paper does not ...
- 248
0 votes
1 answer
316 views
How to force my differential equations give a bounded solution?
I have modeled the interaction of two physical quantities, $S$ and $B$, by the following differential equations (the second one is a delay differential equation): $$S'(t) = 0.31 S(t) \Big( 1 - \frac{S(...
user517860
1 vote
1 answer
149 views
Solving a particular delay PDE $\partial_q f(q,s-1) = -\sqrt{s(2+s)}f(q,s)$
I recently encountered a particular delay PDE in my work, the solution of which corresponds to the Laplace transform of some probability distribution. I'm having trouble to solve this equation. The ...
- 13
1 vote
1 answer
204 views
Solution to non-autonomous delay differential equation?
If you define a special function called the Lambert W function, you can explicitly solve the classic delay differential equation $x'(t) = x(t - a)$ by supposing the solution is some $\exp(\lambda t)$ ...
- 217
1 vote
0 answers
62 views
Help with a surface of delay differential equations
This question is difficult for me to phrase, as it's very much outside of my mathematical purview. This is a question which intersects directly with my research, but as I work predominantly in ...
- 398
1 vote
0 answers
155 views
Clarification on the proof of Lyapunov-Razumikhin asymptotic stability theorem for delayed differential equations
this is my first question here, hope I am in the right place :) Recently I have been looking at the proof of theorem 4.2 on Razumikhin stability for RFDEs in the book by Jack Hale and Lunel Verduyn: ...
- 11
0 votes
1 answer
460 views
How to solve this delay differential equation?
How to solve this DDE: \begin{align} \frac{1}{N_t} \frac{dN_t}{dt}=r\left(1-\frac{N_{t-\tau}}{K}\right) \end{align} where $N_0,K,r,\tau$ are constant? This differential equation is based on logistic ...
2 votes
2 answers
306 views
Asymptotics of a delay differential equation
Say we have the line segment $L(t) = [0,t]$, and randomly remove open intervals of length $1$ from $L(t)$ until no more open intervals of length $1$ remain. Define $u(t)$ as the expected measure of ...
