A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modelling.

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Predator and prey model: non-dimensionalization

I've been trying to non-dimensionalize the differential equations for the predator and prey model. I've written down the procedure below which I was using for non-dimensionalizing the differential ...
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2answers
66 views

Product of two sinusoidal functions model

I'm trying to make a model of the rise and fall of sea levels. According to this explanation and image in the textbook, the product of two sinusoidal functions should look something like this: ...
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40 views

what are the practical uses of “game of life” or “langton's Ant”

A few questions: Besides looking really cool, what are the practical uses of "game of life" or "langton's Ant"? I understand how agent-based modeling itself is a potentially useful methodoly, not ...
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1answer
45 views

Bifurcation - first-order ODEs

Construct a first-order ODE with one critical point if $\left\lvert \mu \right\rvert \ge 1$ and three critical points if $\left\lvert \mu \right\rvert \lt 1$ and draw a bifurcation diagram. ...
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50 views

How to reduce the chemical reaction system $A+B \rightleftharpoons^{k_+}_{k_-} C$ with transfer using the quasi steady state assumption

Suppose we have the reaction $$A+B \rightleftharpoons^{k_+}_{k_-} C$$ within some reaction $\Omega\subset\mathbb{R}^3$, we assume this region to be well mixed and we denote the concentration of $A$ as ...
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16 views

Parametrize a sigmoid function given, $(0,a)$, $(b,a/2)$, $f'(b)=c$ and $\lim_{x \rightarrow \infty}f(x)=0$

I want to write a sigmoid function with the following properties $f(0)=a$, for some specified $a>0$ $f(b)=a/2$, for some specified $b>0$ $f'(b)=c$, for some specified $c<0$ $\lim_{x ...
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1answer
14 views

adding error terms to a mathematical model

I am reading a heuristic model of a herding activity of some animals. The mathematical (heuristic) model that was developed understandably includes an error term to account for a little ...
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70 views

Advice on Mathematical Modeling with Differential Equations

I am on my fourth year studying in a bachelor program in applied mathematics and computer science and plan to write a term paper on mathematical modeling using differential equations. This will be the ...
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45 views

Finding bifurcation values of one-parameter families of first-order differential equations

Consider the following one-parameter families of first-order differential equations defined on the reals: $$ \dot x = \mu - x - e^{-x} $$ $$ \dot x = x(\mu + e^x) $$ $$ \dot x = x - \frac{\mu ...
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16 views

Mathematic modelisation of a gym members

i'm working on a business case, where i should run a gym (gym club/fitness club). I want to know if there's some well know mathematic modelisations ready made for that kind of cases. For instance, ...
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1answer
30 views

How do I compute a realization of h(x) given its PDF and covariance?

Desription of problem I've added a picture of what I want to compute. In the nomenclature of the picture, I want to compute a realization of y(x) given the known distributions and constants. Let's ...
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34 views

Population Growth; Differential Equations

The population of a certain community is known to increase at a rate proportional to the number of people present at time $t$. Suppose it is known that the population of the community is $10,000$ ...
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17 views

How to find mean and covariance for a multivariate Gaussian under a linear transformation W?

While there is a related question on here and it is very informative, my case has some additional conditions. We have a likelihood function and want to find its distribution, $$ p(Y|X,W) = ...
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9 views

Estimate function given PDF and covariance

Let's say $h(x)$, random variable, represents the height of a surface, with x being the usual x-axis. The probability distribution function is: $P(h) = Ke^{-\frac{h^2}{2s^2}}$ is Gaussian, where $K$ ...
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1answer
36 views

Bilaplacian - Explanation of the (Clamped) Plate Problem

I am studying the numerical aspects of fourth-order elliptic problems now, and I came across the plate problem: Let $\Omega\subset\mathbb{R}^n$ bounded domain with Lipschitz-Boundary. Find $u$ s.t. ...
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2answers
51 views

Theoretical justification of exponential growth differential equation

Consider a number of $x_0$ reproducing individuals and ignore death and limiting environmental factors. I've heard that the growth of such a population (of bacteria, insects, humans, etc...) can be ...
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16 views

If then condition on mixed linear integer programming

My English is not as good as yours, sorry for that. I hope you understand me. Here is the question:
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1answer
42 views

Mathematical Epidemiology Reference Request

I'm looking for a good Textbook for learning Mathematical Epidemiology. Something that I could read through and use as a future reference book. Thanks for the advice!
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41 views

Evaluating integral with respect to brownian motion

I am attempting to integrate $$ \int _{0}^{t} \sin(s) dW_s $$ whereas $W_s$ is brownian motion, in some sense a normal random variable with mean 0 and variance $s$. I looked around in stack ...
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38 views

Conditional expectation and Variance

I have the interest rate model: $r(t)= x(t)+y(t)+\phi(t) $ $r(0)=0 $ $dx(t)⁼-ax(t)dt+\sigma dW_1(t) $ $x(0)=0$ $dy(t)⁼-bx(t)dt+\nu dW_2(t) $ $y(0)=0$ $(W_1,W_2) $Brownian (2 dimensions) ...
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23 views

Modify Nicholson-Bailey mdoel

Suppose that we modify the assumptions of the Nicholson-Bailey model in the following way: if a host has one encounter with parasitoid it gives rise to c parasitoid progeny, but if it has two or more ...
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20 views

Modeling Gaussian components with standard vs exact functions

I'm studying a paper on modeling DNA histograms. It presents two alternative formulas for modeling Gaussian components: Standard form: $G(x) = ...
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16 views

Can sombody give me an ntuitive explanation about regression estimates as weighted averages?

I am trying to study weighted least square and found one article that sounds like it is explaining what I am trying to study. But I want to get some intuitive explanation about each calculation and ...
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38 views

Self learning complex systems modeling

I am currently a senior studying mathematics. My program is heavily focused on pure maths, however, my interests lie in the area of applied mathematics. Specifically, I am interested in the study of ...
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9 views

converting GA's fitnessfunction to mathematical expression

As part of my final report I have to explain my fitness function method using in mathematical form. However I am not very good at this. I have came up with something that I will share with you here. I ...
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24 views

Composite sinusoidal functions

Let' say you have a graph as such: !(http://blogs.scientificamerican.com/roots-of-unity/files/2014/12/sinxsin2x.jpg) ! (Black one) And you know that it's function is in the general form of ...
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53 views

Formulation for solving puzzle game mathematically

I'm developing a solver for a simple constraint-based puzzle game. Here is an example of the puzzle: $$\begin{align} - \;6\; -\\ - - -\\ - \;3\; - \end{align} $$ The given 3$\times$3 grid of "clues" ...
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1answer
69 views

An algorithmic method to simplify the mathematical modeling of a reaction network using conservation laws

Consider the reaction scheme. where $S$ is the substrate, $E$ is the enzyme, $P$ is the product, $C_1$ and $C_2$ are enzyme substrate complexes. Let $[S] = s$, $[E] = e$, $[C_1] = c_1$, $[C_2] = ...
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1answer
49 views

When fitting a polynomial to data points, how to determine the reasonable degree to use?

I have wondered the following: Suppose that there is a set of data points $(x_i,y_i)$. Then I would like to know if it is more reasonable to assume if there is a polynomial relation of degree $m$ ...
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1answer
18 views

How to nondimenzionalize concerning the arc lenght

My question is a general one concerning mathematical modeling and the calculation of the arc lenght. There is a function $ f\colon [a, b]\to\mathbb {R} $, where $ f (x) $ includes a lot of parameters. ...
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57 views

what does it mean by this mathematical modeling

This is a mathematical model: $$ Z_{i} = \sum_{S \epsilon S'} P_{i} (S=S') $$ where set $$\ S'= \left\{ (X_0,X_1,..., X_{k-1}) | X_i \epsilon S, \forall 0≤i ≤k-1,X_i ≤X_j, \forall i ≤ j ...
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42 views

Natural Transformation Inductively defined?

So, I'm working on this project and I'm having some trouble with a definition. Maybe some more educated Category Theorists can help me. The context is actually not very relevant, as I just need to ...
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8 views

Distribute individuals to relevant mentors as evenly as possible

I'm working on a site that needs a matching feature, but I'm wondering if there's a mathematical model that already tackles what I'm trying to do. Users belong to Mentors, but they can choose their ...
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44 views

Mathematical Modeling

If the number of possible routes is less than 4, probability (a) will be used. All the routes will be considered and the travel time for each route will be calculated. However, if there are more or ...
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16 views

Determining relative weights of input variables

For $Q = f(a, b, c, d)$, what is a statistical test to determine the relative weight of how these variables contribute to $Q$? Better yet, how do I come up with a function for it? To put into ...
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1answer
100 views

Mathematical Modeling of Route Optimization

Do any of you know how to come up with equations or mathematical way of representing these problems? 1) Finding probability of choosing number of routes (i) If n of routes less than 4, consider ...
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1answer
19 views

Time Series with increasing dimension

I am stuck with the following problem from research. I am not sure how to model this situation. I have a vector time series whose dimension increases with time, $t$. Specifically, let ...
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17 views

Symmetric discrete catenary

I have to solve a problem of "Symmetric discrete catenary with odd number of particles". I've been told that knowing it has odd number of particles means that you can adjust the solution of ...
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16 views

How to calculate the cross-correlation of a halfwave?

I'm trying working on a vehicle modle and testing it with steering maneuvres standardised by the ISO. When it comes to data analysis the ISO standard says the following: 6.4 Time lag and Sine Time ...
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1answer
28 views

Discrete version of continuous SIR model

I'm working with a SIR infection model, which is $$\begin{array}{rcl} \frac{dS}{dt} & = & -\beta IS\\ \frac{dI}{dt} & = & \beta IS-\gamma I\\ \frac{dR}{dt} & = & \gamma I ...
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12 views

The interim equilibrium levels

supposed I have a function as $$ Y_i=(p_i-c+x_i)(1-b(p_i-p_j)+g(k_i-k_j))-hk_i^2-mx_i^2 $$ The interim equilibrium levels is $$ p_i=\frac{1}{b}+c+\frac{g(k_i-k_j)}{3b}-\frac{2x_i+x_j}{3} $$ I have ...
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28 views

How to use the Monte Carlo method with curve fitting

I have an assignment in which I need to choose statistical data from the Australian Bureau of Statistics and fit a curve to it. I've chosen the slaughtering of bulls in NSW (first Excel file, ...
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1answer
14 views

A function to return 1 if and only if two strings match in a certain number of characters

I want to formulate equation for comparing two strings $A$, and $B$ each of length $x$. The function should be $1$ if they are matching in at least $x-l$ characters. Otherwise the function should be ...
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1answer
31 views

Find RHS from LHS.

$A=\left[ \begin{array}{cc} 0 & 1 \\ 1 & 0 \\ \end{array} \right]<==>\left[\begin{array}{cccc} 0 & 0 & 1 & 1 \\ 0 & 0 & 1 & 1 \\ 1 & 1 & 0 & 0 \\ ...
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1answer
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Damped Driven Oscillator Dimensional Analysis

So, I am studying the damped driven oscillator with the following drive force: \begin{equation} M\ddot{x}+\gamma \dot{x}+kx=F_0 \cos({\omega t}) \end{equation} where $M$ is the mass, $\gamma$ is the ...
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1answer
17 views

Is there any tool that could turn a Petri Net into system of math equations?

I have a colored, descrete Petri Net. I have a picture. How to get a math (ODE\DE\system of equations) representation of it?
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22 views

AHP (Analytical Hierarchical Process) for individual selection decision with equally important objectives

How can I apply AHP for individual selection decision when all the objectives are important? For example, I want to select a car. The car needs to have all the characteristics (all the components). In ...
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32 views

Adding two sinusoidal functions together (i.e $10\sin x+\cos x$ or $5\sin x+\sin x$)

I'm doing my math exploration on modeling tide levels and wanted to know if it was possible to find a function by just looking at a graph, and knowing their points that looks like (see image on ...
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2answers
57 views

Trying to model an equation for this problem:

A drug is administered once every four hours. Let Dt be the amount the drug in blood system at t-th interval. The body eliminates a certain fraction p of the drug during each time interval. If the ...
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27 views

How to iterate a function 8 times about a given interval of x in a Discrete Dynamical System

This is Dynamical Systems, specifically a discrete system. We are using L and R as in Left and Right such as: L=[0,0.5] R=(0.5,1] and LL=[0,0.25] LR=(0.25,0.5] and so on like that. We keep ...