# Tag Info

2

If I understand your question correctly, you want to simplify the ODE system using your knowledge of the time scale difference associated to the processes described by the ODE system. In particular, I understand that you assume that the `internal' reaction dynamics $A + B \leftrightharpoons^{k_+}_{k_-} C$ in $\Omega$ occur on a much faster timescale than the ...

2

To make it simpler, think of it first in case of discrete time. You have a population of $x_k$, and on the next step each from these population produce on average $r$ kids, so if you don't allow deaths $$x_{k+1} = x_k + rx_k = (1+r)x_k = (1+r)^kx_0$$ which is obviously a growth function, exponential w.r.t time variable $k$. If you say that a production ...

2

The stochastic process model that you seem to have in mind can be rigorously formulated as follows. When you have a population of size $N$, each member of the population is independently waiting to make another member of the population. If you assume that the process is Markov, then these waiting times must be exponentially distributed. (Note that this ...

2

My recommendation would be Burgers equation. Don't know the specifics, but it arises in fluid mechanics. It is so called conservation law, and it means that for a invicid flow in fluid total energy of a flow is conserved. Fluid dynamics needs some learning, but much less than termodynamics, quantum mechanics etc In a inviscid case it looks like this (in one ...

2

I checked, your equations are correct for the system using mass-action kinetics. Write a matrix, rows corresponded to equations and columns related to your complexes, $\{se,c1,ep,sc1,c2\}$, then find it's row kernel space, column kernel of its transpose. Choose a basis for that and write equations arrived by the inner product of them and the vector ...

2

What I have read and seen myself before related to epidemiology and infectious diseases, you can take a look at section one of chapter 11 of the book Differential Equations, Dynamical Systems and an Introduction to Chaos written by Hirsch, Smale and Devaney. But in general there is a book from Springer called exactly Mathematical Epidemiology written by ...

2

According to a comment, you are multiplying the function $$f(x)=2\sin(22x)-0.4$$ by the function $g(x) = \cos(5x).$ The function $f(x)$ has a much longer period than $g(x)$, but it also has unequal amplitude above and below the axis. That is, the highest possible value of $f(x)$ is $$2-0.4 = 1.6$$ and the lowest possible value is $$-2-0.4 = -2.4$$ While ...

1

The Game of Life is but one example of: Cellular Automata, which are very useful for modelling complicated, non-linear, systems in physics, chemistry, biology, meteorology, cosmology, computational science, engineering, .... the whole gamut. Such stable patterns will arise, but are very difficult to predict from the basic laws. Cellular automata are ...

1

In think inequality is the social-economic concept, not a mathematical inequality as in "greater than". The left tail refers to the poorest part of the population, the right tail refers to the rich people. Roughly speaking, if we assume the existence of three social classes: poor, middle and rich, then left tail inequality refers to exactly how poor, and ...

1

The underlying problem is that the plate is subjected to distributed load with density $f$, and is fixed along the boundary in such a way that the boundary can neither mode nor rotate (clamping condition). The function $u$ represents vertical displacement of the plate when it has reached an equilibrium. Since an equilibrium is being studied, no time is ...

1

You appear to be considering something like: $$P\left ( x-\frac{\Delta x}{2} \leq X \leq x+\frac{\Delta x}{2} \right )$$ where $X$ is Gaussian with mean $\mu$ and standard deviation $\sigma$. This is exactly equal to $$\int_{x-\Delta x/2}^{x+\Delta x/2} \frac{1}{\sqrt{2 \pi} \sigma} e^{-(y-\mu)^2/(2\sigma^2)} dy$$ which can be straightforwardly ...

Only top voted, non community-wiki answers of a minimum length are eligible