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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Spring-mass System Phase Plane

If a spring-mass system has a friction force proportional to the cube of velocity, then $$m\frac{d^2x}{dt^2} + a\left(\frac{dx}{dt}\right)^3 + kx = 0$$ (a) Derive a first-order differential ...
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28 views

How to transform one polynomial curve into another

I have a problem: I have two polynomial splines: For red curve I have used Rational fraction function with p=3/q=2 and for blue curve I have also used rational fraction function with p=1/q=3 It ...
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48 views

Differential equations, chemical reactions

A chemical substance A changes into substance B at rate $\alpha$ times the amount of A present. Substance B changes into C at rate $\beta$ times the amount of B present. If initially only substance A ...
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29 views

Failed to understand basic approach of mathematical modeling in research ideas [on hold]

I am very new to mathematical modeling. I study different probabilistic approaches but fail to understand how it can be implemented over any research activity. Is there any set of rules to apply for ...
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18 views

Random walk problems [on hold]

What is the difference between restricted and unrestricted random walk in gamblers terminology?
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23 views

ordinary differential equations-morphogen gradient

I am reading a paper by Merkin and Sleeman (2005) Find the approximation solution of $(u')^2=\frac{2}{k}(u-\frac{1}{k}\ln(1+ku)); ~~u(0)=1$ for $k$ sufficiently small. they gave the following ...
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57 views

Can car traffic be managed by mathematical formula? [on hold]

How car traffic is managed? Is it managed by mathematical algorithm? Or by human(operator)? If it's by operator, can it be managed mathematically? Or is it by physics? By what theories/formula? ...
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15 views

System of separable diff. eqns, explicit solution and curves, Lotka-Volterra model

In the book on p.68 is a system of differential equations for a Predator-Prey model (Lotka-Volterra) given as: $$ \dot x=x(\alpha-c\gamma) \\ \dot y=y(\gamma x -\delta) $$ On the next page, it is ...
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+50

Modeling, Measuring, and Maximizing “Mixedness”

Background: My class has $10$ students and $3$ tables; naturally, the students are distributed with $3, 3,$ and $4$ seated at the individual tables. On the second day of class, students sat in the ...
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23 views

Choose Scaling for t

My question is the last part of the d) part of the exercise 1.17 in Mark Holms' Introduction to Applied Mathematics. The exercise is given below, where I have emphasized the part of it that is my ...
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29 views

linear or bilinear interpolation

I want to know how to use linear and bilinear interpolation in 2D. Specifically the pairs $(x_1,y_1)$, $(x_2,y_2)$, $(x_3,y_3)$, and $(x_4,y_4)$ are given in a quadrilateral. In this case how to ...
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32 views

Rain forecast model and least squares

Good evening everyone, I'm trying to create a rain forecast model, I have about 720 data, which correspond to monthly rainfall in 60 years during the 12 months of the year. I have a matrix ...
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28 views

Probability of agreeing to do some work depending on the payment

I am looking for several options of modeling the probability of people agreeing to do some work depending on the price/payment. The payment can only range between $p_1$ and $p_2$, $(p_1 < p_2)$. I ...
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13 views

Modeling reasons for minimizing the distance between parameters

In system identification, when new parameters are calculated, is there any reason for the parameters to be close to the original parameters ?
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17 views

reformulating an integer quadratic problem into a linear integer problem

I am trying to solve an optimization problem, in order to find an optimal runtime schedule for a machine. It involves one boolean variable $x_{t} \in \mathbb{\{0,1\}}$, that describes whetever the ...
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23 views

Calculating weighs in a model

I am creating an index related to walkability. For this I have sevaral factors like length of sidewalk available, user perception rating on various measures of performance, and many other factors. My ...
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15 views

Concatenated model for 2D?

I am looking for a way to perform 2D convolution through a concatenated model. I am not looking for a faster way of doing 2D convolution. My objective is to find a scheme where I can perform it in ...
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2answers
41 views

Laplace Transform of derivative squared

I'm trying to solve a problem while I'm studying Control Theory and I came up with a difficult question. $ \mathcal{L}\left[y'(t)^2 \right] $ Basically I need to find the Laplace Transform of this ...
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17 views

Finding ratio of four value factors

Before reading this i know the question i asked can be answered based on our strategies, but i'd like to know the methods of quantifying these strategies into numbers. I'm doing subscriber profiling ...
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29 views

How can I show that $x'(t) = - (1-x(t))'$ from $x(t)$'s functional form?

I have a differential equation modelling the concentration of vaccinators in a population. Here are a few assumptions. Assume we can write the concentration of vaccinators as $x$, and that we can ...
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5 views

Conversion of cylindrical harmonic field into space-harmonic field for plane waves

It is well known that a plane wave can be represented by an infinite sum of cylindrical wave function of the form $\varphi^i(\rho,\phi)=e^{\left(-j\beta \rho ...
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17 views

“Damping factor” for a set of non-linear ODEs

I am not sure if this question is on-topic here I have a set of four non-linear ODEs representing a negative feedback. I have done parameter variation by random sampling to study the sensitivity of ...
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39 views

Modelling a warehouse in optimization?

I am trying to model the following rather general optimization problem. Let $p_{t}$ be a given non time series of product prices. These are fixed points $p_{t}$ is not described as a random variable. ...
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33 views

nondimensionalisation for an ODE

I need help to understand 'nondimensionalisation' for ODEs better. I stacked how to deal with a constant input in a prey-predator model. I reproduced the following ODE system ...
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27 views

At time $t=0$, the traffic pattern on a long highway consists of two sections

At time $t=0$, the traffic pattern on a long highway consists of two sections of constant density joined by a shock located to the left of $x=0$ and moving in the positive direction. If the traffic ...
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19 views

Averaging Models in Excel

I am working in Excel and have two sets of data points that come up with a percentage for the likelihood of a recession. I am wondering what the best strategy would be to combine these data points? ...
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what is the influence of the specific statistical model selection in a practical project

I hope this is the right place to ask this question. But if it is not, please feel free to migrate. There is a famous quote, which is like "all models are wrong, but a few are useful". So, I was just ...
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22 views

Discrete sinusoidal to state space

I'm looking to apply an optimal LQR filter to a discrete signal of the form $x[n]=Asin(ω_0n+ϕ)+v[n]$ The amplitude $A$ and the phase $ϕ$ are unknown variables I want to estimate using the filter, ...
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33 views

modelling the behavior of a particle

I want to study the evolution of a particle as a function of time, then in dynamical systems, the usual thing to do would be to define the state of the particle. Usually we are able to do this by ...
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11 views

Methods for Extrapolating Data Close To Observations

I am aware of many different ways to go about interpolating between the values of known data points. However, whenever I come upon (I work in Quantitative Finance) the need to extrapolate data I find ...
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48 views

Mathematics of contamination [closed]

I want to know the distribution of residual material (contamination) in subsequent refills. For example, suppose a cup normally used for transferring salt is used, without cleaning, for transferring ...
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28 views

Solving 2nd order ODE with 2 independent parameters(over finite intervals), with bounds on solution

I have a 2nd order ODE of the form: $\ddot {x} + 2c \dot {x} + 39Ex = 0 $ $Initial$ conditions being: x(0) = 0 and $\dot {x}(0)$=0.1 Where c is in the interval [1,5] and E is in the interval ...
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Light attenuation through water at an angle

I know that light intensity decreases exponentially governed by \begin{equation*} \frac{dy}{dx} = -ky \end{equation*} where $y$ is the intensity and $x$ is the distance. Now what happens when light ...
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what is the meaning of Ricker model?

How can I interpret Ricker model? It is about population model but it has the term $e^{1-x}$ see: $$a_{t+1} = a_t e^{r\left(1-\frac{a_t}{k}\right)}.$$ http://www.dma.uvigo.es/~eliz/pdf/oman.pdf ...
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formula to establish correlation between multiple library functions

I am trying to predict the change in timeliness of holds delivery relative to number of owned Bestsellers, number of holds and the checkout window. (yes, it really is a library question). To do this ...
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44 views

Relatively simple system of nonlinear ODEs

There are a lot of questions like this on MSE as well as online resources on the subject, but a) the MSE questions are either unanswered or correspond to systems substantially different from this one, ...
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two objects moving in opposite directions.

I don't need a specific answer for this question, and would rather prefer to know how to solve questions like this one. So far I've tried using the $v=d/t$ formula to form equations, but haven't ...
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51 views

Are my results realistic or is there an error somewhere?

The background is that I'm solving a problem in Numerical Analysis which I asked about here: Is my derivate correctly programmed? Now if I use the new code, then I get a result that is along the ...
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39 views

fourth order runge-kutta method and heavyside step function.

So I'm trying to model a hydrodynamic system that introduces a sudden "jump" in the value of a function at a specific time. The system is solved with a Runge-Kutta fourth order method. I have a ...
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1answer
41 views

Approximate model of a convex/concave surface

I have a set of measurements in 3d that yields a concave surface of a function $f(x,y)$ that I don't know its expression. I am thinking to approximate the function to a model where any point from the ...
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22 views

Why are porous medium equations posed on connected domains? Shouldn't it be done on a domain with holes (or pores)?

The porous medium equation is supposed to model gas flow through porous media (i.e. some object with holes in it). Why then, in theory of weak solutions, do people study the equation on a sufficiently ...
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25 views

5-dimensional First Order Nonlinear ODE stability analysis

I have a system of 5 first order nonlinear ODEs, with 2 nonzero equilibria. Is it possible to perform a stability/ bifurcation analysis with 10 unknown parameters? Is it possible to fix 8 parameters ...
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37 views

Rumour/Gossip theory problem to simulate fire propagation.

I have a set of planar graphs I am using to model a landscape. I am trying to model fire propagation. So if say fire starts at node A, there is a chance that fire can propagate to all of A's adjacent ...
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How do I determine the critical number that would the eradicate pests and that it is less than a quarter of the environment carrying capacity

The sterile insect release method for pest control releases a number of sterile insects into a population. If a population n of sterile insects is maintained in a population, a possible simple model ...
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19 views

Finding the values of a that will cause the population to become extinct

Given the finite difference equation $x_{n+1}=ax_{n}exp(−x_{n})$ for $x_{n}≥0$, where a is a positive constant, describing the population of a species. I've determined the fixed points to be ...
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23 views

How do you find the values of a that will cause a period-doubling bifurcation?

Given the finite difference equation $x_{n+1}=ax_{n}exp(-x_{n})$ for $x_{n}\geq0$, where a is a positive constant. I've determined the fixed points to be $x^*=ln(a),0$. How do I determine the values ...
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How can I mathematically model the combinatory problem?

I have the following problem, and I would like to model it using a mathematical formula, for a purpose of optimization problem: let's say that I have two tasks $[T_1, T_2]$, and $3$ resources ...
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Graph modeling using calculus

The question asks of a function $f(x)$ in the domain $[0,9]$ whose graph has the following properties. $1)$ Local minimum at $(3,1)$ only in the domain $(0,9)$. $2)$ Local maximum at $(5,5)$ only in ...
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Can Poisson distribution be used in my example?

Lets say that I have an infinite population of individuals of finite density. The aim of the individuals is to find shelter. Density of individuals is $x$ and density of shelters is $y$. In a given ...
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How do you find the fixed points for the system of equation containing variables y, e, and z?

For part d, I have the obvious (0,0) but how do you find the second fixed point?