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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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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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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26 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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8 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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1answer
390 views

How to model an aviation holding pattern mathematically?

A standard aviation holding pattern has four sections, each of which, in windless conditions, takes one minute to fly. The first is the inbound leg, which is the only one for which precise ...
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1answer
45 views

Mathematics of contamination [on hold]

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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1answer
23 views

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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2answers
74 views

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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23 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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1answer
16 views

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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11 views

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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1answer
42 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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2k views

Linear Programming: Three variable graphical solution

A small bank offers three type of loans: housing loans at $8.50$% interest, education loans at $13.75$% interest rates, and loans to senior citizens at $12.25$% interest. Further, it needs to ...
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1answer
406 views

Why does my Barabasi Albert model implementation doesn't produce a scale free network

I'm trying to implement the Barabasi Albert model to generate some scale free network matching a power law distribution of degree. I'm using a value $m = 2$ for the main parameter of the algorithm, ...
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1answer
48 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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1answer
34 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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1answer
31 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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2answers
34 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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20 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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18 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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1answer
31 views

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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18 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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22 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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35 views

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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34 views

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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17 views

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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Modulo 3 operation on days/seconds

Simple question.. I want to do a modulo 3 operation on the number of days in a month (28/30/31). and based on that i want to put my user into 3 different groups.. i am also willing to use seconds ...
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2answers
347 views

Phase Plane Analysis

Classify the fixed point at the origin and sketch an accurate phase portrait for the following system: $$\left\{\begin{matrix} \dfrac{dx}{dt}=36x-16y\\ \dfrac{dy}{dx}=-3x+28y \end{matrix}\right.$$ ...
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1answer
36 views

Working with mathematical models, HELP.

I'm currently doing a lot of self study with mathematics. I live in The Netherlands and hope to be admitted to Leiden University somewhere in 2016. Now, I have encountered a problem in my workbook ...
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2answers
97 views

Applied mathematics commonly needed in the following industries

I was just wondering if anyone could shed more light on specific topics in applied mathematics or other skills (programming, etc) commonly used in the following industries: oil and gas, ...
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1answer
40 views

Modeling a planes flight

my text book for differential equations has a nice applied 'project'/investigation that I have been working through over the weekend (this is not a homework question I just thought it may be ...
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1answer
72 views

Predator Prey Model

Consider the following system of equations, and assume that population of prey is measured in thousands, and that the population of predators is measured in hundreds. $$\frac{dx}{dt} = ...
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35 views

The Lotka-Volterra Model Continued

Consider the following system of equations, and assume that population of prey is measured in thousands, and that the population of predators is measured in hundreds. $$\frac{dx}{dt} = ...
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19 views

The correlation between alpha and beta

Consider the following 2-variable linear regression where error $e_i$'s are independently and identically distributed with mean 0 and variance 1; $$ y_i=\alpha + \beta (x_i - \bar {x}) + e_i$$ where ...
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11 views

reference for regime shifting models

I'm looking for a good introduction to regime shifting models. It would be nice to see things like simple example of regime shifting models, ways to detect a regime shift in data, fitting regime ...
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1answer
35 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 ...
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basic reproduction number of a simple SEIR-model

the normal SEIR-model is: $\begin{array}{rll} \displaystyle{\frac{dS}{dt}}&=\mu N -\mu S -\beta \frac{I}{N} S & \text{Susceptible} \\ \displaystyle{\frac{dE}{dt}}&= \beta \frac{I}{N} S ...
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1answer
21 views

Difference Between Lyapunov and Strong Lyapunov Function.

Good Day everyone. I was assigned to show that given an autonomous system of Differential Equations and a function $V$, I need to show that $V$ is Lyapunov function. To show that $V$ is Lyapunov. I ...
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34 views

Drawing a phase diagram

I am working through an example to draw a phase diagram the DE used is $\frac{dx}{dt}=xy(x-1)(x-y)$ In the first step I have to identify the isoclines by setting $\frac{dx}{dt}=0$ having done this I ...
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1answer
20 views

Method for determining the average deviation of data values over time?

I've recorded my weight every day since 1 January 2012 and plotted the data in an Excel spreadsheet. For convenience, I've set the minimum and maximum values on the y-axis to the weights that ...
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17 views

How to model a coding problem with Poisson Distribution

I've met a problem in information theory that deals with probability and number of occurrence. It states that: The probability of a single bit being corrupted is p. Now I have an error-correction ...
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3answers
242 views

Is it possible to solve the Zebra Puzzle/Einstein's Riddle using pure math?

A coworker of mine posted a problem in our local communication software that seems to be a simpler variation of the Zebra Puzzle/Einstein's Riddle. I know how to solve it intuitively, by using ...
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1answer
27 views

What is a convex model?

I know what is a convex function. Wikipedia says: In mathematics, a real-valued function f(x) defined on an interval is called convex (or convex downward or concave upward) if the line segment ...
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25 views

Approach on solving limit equation systems and finding some f given assymptotes?

This is a "reverse" question of finding the asymptote of a function Recently, I am interested in doing some sort of modelling which involve equations of the form $$@(t)=1-f(t)$$ where $f(t)$ is ...
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17 views

How do you determine if its an improper node of a proper node?

This is my example but your welcome to elaborate if you have better examples. Suppose we have a system of differential equations $$\frac{dR}{dt}=aJ \\ \frac{dJ}{dt}=bR$$ s.t. $a,b \gt 0$. I've ...
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What is a bifurcation point?

Given a density dependent difference equation, $N_{n+1}=N_{n}e^{r[1-(N_{n}/K)]}=f(N_{n})$, with $r > 0$ and $K > 0$. I've found that the equilibria are at $N^*=K$ or $0$. Discussing their linear ...
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Discrete logistic model

Given a difference equation such as N_{n+1}=N_{n}exp^{r[1-(N_{n}/K]=f(N_{n}). What does it mean when they say density-dependent difference equation?
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87 views

Study the stability of the following ODE: $u'=u(1-u)-\alpha$

Given that $\alpha$ is real, I'm being asked to give a basic analysis for this nonlinear ODE. However the problem is that I'm having trouble understanding how to pick the conditions we need to study ...
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57 views

How do we plot nonlinear differential equations

If this is not nonlinear I apologize, I'm still learning differential equations. I am attempting to make a stream plot of a predator-prey model of eccentric closed curves by using the following ...