All Questions
11
questions
0
votes
1
answer
41
views
How to solve an ODE where the rate is directly proportional to two amounts?
Two chemicals in solution react together to form a compound: one unit of compound is formed from $a$ units of chemical $A$ and $b$ units of chemical $B$, with $a + b = 1$. Assume the concentration ...
- 4,450
0
votes
1
answer
264
views
Mathematical expression for physical forces in pendulum ODE
A 16 lb weight is suspended from a spring having a spring constant of 5 lb/ft. Assume that an external force given by
24 sin (10t) and a damping force with damping constant 4, are acting on the spring....
- 612
4
votes
0
answers
121
views
Do repeated roots (and Real Jordan form) for ODE's come up in real world applications of ODE's
An equation like $y^{\prime \prime} + 2 y^{\prime} + y = 0$ has repeated roots: The characteristic polynomial is $r^2 + 2r + 1$ which has repeated roots $(-1,-1)$. Two basic solutions of the ODE are ...
- 705
1
vote
0
answers
45
views
Conceptual complex dynamics - Is it reasonable to perform bifurcation diagrams on PDE's?
I am working on a PDE model, the subject has been modeled with ODE's before. The articles usually have a bifurcation diagram, and to be able to validate my model, I want to compare my work with the ...
- 53
1
vote
1
answer
145
views
Basic ODE story - tank with pumps
Full tank has $500$ liter of water containing $0.2\%$ of salt. One pipe pumps clear water in ($100$ liters per minute) and the other gets the mixture from the tank ($100$ liters per minute too). ...
- 2,190
0
votes
1
answer
668
views
How to perform non dimensionalization on a population model with predation?
So this problem is from my homework and I've been having some trouble with it. We have the following model of population growth where a and b are positive constants and r is a positive growth rate:
$...
- 21
0
votes
1
answer
80
views
Equilibrium and Stability of Nonlinear Interactions
Examine the nonlinear model:
$$\triangle x_t = rx_t(1-\frac{x_t}{K})-sx_ty_t$$
$$\triangle y_t = -dy_t+\epsilon x_ty_t$$
Find the equilibrium and their stability. Here all the parameters are ...
- 594
1
vote
0
answers
97
views
Is Principal Component Analysis applicable to this type of situation?
I'm trying to model the response of ant populations to pheromones in this way:
The ants are simulated as Self Propelled Particles with internal energy. They undergo acceleration due to their internal ...
- 876
1
vote
1
answer
225
views
Analyzing the stability of equilibria
There's a model with a condition $r>\mu$:
$$\begin{align}
S'&=r(S+I)-\beta SI-\mu S \\
I'&=\beta SI-(\mu +\alpha)I
\end{align}$$
I can easily see that the equilibria of the second ...
- 963
1
vote
1
answer
359
views
Finding the basic reproduction number of a particular model
I have been reading a paper about a host-parasites models and for the model:
$$\begin{array}{rll}
\displaystyle{\frac{dx}{dt}}&=\lambda -dx -\beta v x & \text{Susceptible host} \\
\...
- 1,773
8
votes
2
answers
2k
views
Differential vs difference equations in mathematical modeling
I'm reading a little about mathematical modeling and I've seen some population models based on differential equations. I've also seen some (not many) that can support both difference and differential ...
- 1,773