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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Modelling the Möbius strip using implicit functions

While researching on Möbius strips I found its parametric representation on a lot of websites claiming it is easier. Can someone please explain what problems appear when modelling the Möbius strip ...
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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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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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27 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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18 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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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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21 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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32 views

Rate at which an element (oxygen) changes temperature [closed]

I'm going to start off by introducing myself & the question. My name is Ryan, I'm only a high school graduate & a very big thinker, I love to know whats going on in the world & how it ...
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15 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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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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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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38 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 ...
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79 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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2answers
36 views

is there any mathematical model how the guitar strings are related?

I'm just curious to know the mathematical relationship between guitar strings and how their frequency changes with the variation of guitar's string length and thickness. Say, I'm vibrating some node ...
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A model for melting and for weaving or interweaving?

I would like to know whether there are mathematical models for the processes of melting (like an ice-cream melting on the biscuit rather than snow) and weaving (or interweaving). If so, of what kind? ...
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29 views

First Order ODE – A skydiver weighing 180 lb falls vertically downward

...from an altitude of 5000ft and opens the parachute after 10s of free fall. Assume that the force of air resistance, which is directed opposite velocity, is of magnitude 0.75|v| when the parachute ...
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36 views

Continuous Annuity Question

I need to calculate the present value of a level continuous annuity which pays $1000/mo. for 10 years. The force of interest is 5/(3+2t). I tried taking the integral of e^(integral of force of ...
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44 views

N2 diffusion through a vertical fluid column

Trying to figure out the mathematical model that might correlate to laboratory results. I have a cylindrical pressure vessel (picture a can) with height, h, and radius, r. It is filled with distilled ...
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20 views

Differential Equation Modeling

Quick disclaimer: This is not graded homework - all homework is assigned but not turned in. There is no assigned book, and hence no answers to given problems. These questions are for the purpose ...
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39 views

How to solve a system of linear equations exactly?

Given a system of equations, $$\frac{dR}{dt}=-aR+bJ, \quad \frac{dJ}{dt}=-aJ+bR,$$ I have to discuss what happens to their love(Romeo and Juliet mathematical modeling exercise) is their caution $a$ ...
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Calculate the time taken, in seconds, for the water in the cup to cool to a drinkable temperature of 45 °C?

This problem concerns the cooling of water in a well-insulated, cylindrical cup that is opened at the top. 0.368 kg of water at 81 °C is poured into the cup which is left to stand on a table at an ...
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From kinetics rate to individual probabilities

I'm building an agent-based model for convection-reaction simulations. Basically my particles are moving at a certain speed in their environment and when they encounter receptors they can bind to them ...
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29 views

How should I go about obtaining the explicit solution to this logistic first-order nonlinear ordinary differential equation?

I have to find the explicit solution to this harvesting problem in a population model where $\frac{dN}{dt}=rN(1-\frac{N}{K})-H(N)$ such that $H=qEN$, subject to initial condition $N(0)=N_0$. Here ...
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multivariable linearization

I have been asked to linearise the fallowing equilibrium points are phy=theta yaw=0 x,y,z=0 The idea I have using V'z as a model: -g+(kcm/m)(cos(phy)cos(thata)*voltages + ...
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Using Phase planes, how do I find graphically the equilibria and their stability of a logistic growth model??

I'm having trouble understanding the concept of phase portrait which I never learned in my applied differential equations class. The question is asking to study the logistic growth model, $$ ...
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2answers
35 views

I have an equation I would like solving.

I need to solve the following problem Decorator A is painting a large wall. At her current rate, she will complete the wall in 1 hour and 40 minutes. Decorator B is painting a similar wall, ...
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Regression analysis model vs mathematical model

Can anyone explain the difference between the equation generated from a regression analysis as opposed to a mathematical model such as $E = m \cdot {c^2}$ type models?
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17 views

Conditions for always positive gradient of heat field in evolutionary thermo-elastic system

I am investigating stability and convergence of series of approximations for coupled thermoelasticity problem yielded by one-step recurrent time-integration scheme. I've managed to show that the ...
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Forming a differential equation from game

I was wondering if someone could help me form a differential equation from the following game: A population consists of two types of diets, fish and veg. People play a with every other person and the ...
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28 views

Linear model, Newton's Cooling law

A thermometer is removed from a room where the temperature is 70 and is taken outside, where the air temperature is 10. After half a minute the thermometer reads 50. What is the reading of the ...
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Websites or books on modelling

I have some operational data that I'm looking to model. However I'm a bit lost as to where to start. I'm looking for some websites or books on modelling data. Can anyone provide some advice?
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Trajectory Code Problem

Problem 2. “Pumpkin chucking” is a competition event to see which team can shoot a pumpkin as far as possible, usually with a pneumatic cannon. In this problem we’re going to write a computer program ...
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Help needed for a step by step calculation

I hope I can get some help to understand step by step calculations for formulas below. If I have a weighted distance formula like below: $d(O, P) = \sqrt{\frac{\hat{x_1^2}}{\hat{s_{11}}} + ...
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Question about problem linear programming math modeling

Consider points $A(4.7,−4.1,−1.5)$,$B(−0.4,−2.4,1.9)$,$C(−0.3,−2.1,−6.5)$ and $D(2.7,−3.6,4.0)$. How to discover if segment $AB$ has intersection different of zero with the segment $CD$? Formulate ...
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I'm having trouble finding the right direction to take in this HIV modeling exercise

Cells that are susceptible to HIV infection are called T (target) cells. Let $T(t)$ be the population of uninfected T-cells, $T*(t)$ that of the infected T-cells, and $V(t)$ the population of the HIV ...
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88 views

Notions of consistency / heterogeneity in sets of vector values

The problem Let us consider a row vector u of size $n\in\mathbb{N}$, containing only binary values (0,1): $$u=(u_1 \cdots u_n), n\in\mathbb{N}$$ $$\forall i \in \{1\ldots n\}, u_i \in\{0,1\}$$ I ...
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38 views

Modelling a continious-time queue which behaves differently when there are more or less people being served.

For my research I am trying to model a continuous-time queue which behaves differently when there are more or less people being served. The arrival rate in the queue is constant, however the departure ...
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47 views

After how many bounces is the ball subsequently always less than 5cm from the ground?

a). A ball is thrown vertically upwards with a speed of 20 metres per second from a point 3 metres above the ground. Find the speed with which it hits the ground. b). If the ball rebounds with a ...
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26 views

Stability of a function with logaritms

I am trying to proof that the following equation is stable if $|1-ln(\alpha)|<1$; $$f(x)=\alpha x e^{- \beta x}$$ So the equilibrity points would be $x=0$ and $x=\frac{ln\alpha}{\beta}$, the ...
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Learning to Apply Mathematical Concepts ( i.e. function modelling, etc.)

Firsty, I want to state my situation clearly. I am one of those students who are incredibly good at absorbing mathematical concepts but without knowing how to apply them. I get A's but it is growing ...
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Formulating equation for distances between atoms

I'm trying to formulate notation to describe code that calculates the distances between protein atoms (represented as points in 3D space). Fragments consist of residues (amino acids) and each residue ...
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21 views

Best method for assessing repeatability between year 1 and year 2

I have a data set of values for a particular measured metric for employees for the year 2013, and a set of values for the same measured metric for the year 2014. I am looking to assess the ...
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Competition Model - System of differential equations

Two plants are feeding off the same substrate, whose weight at time t is S(t). One of the plants began to feed off the substrate 20 days earlier than the other. Devise a system of differential ...
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Differential Equation of a Probability Density Function

I have a deterministic rule of my variable (ODE model), $\frac{dY}{dt} = at$, in which $a$ is a parameter in my deterministic model (let's say growth rate) and $t$ is the time. I know that on every ...
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How does one solve ODE with some domain constraints?

So far I have no clue, how to go about this .. in school we did not go over constraint based ODES. So let's say we have $\ x'' = -ax' $ $\ y'' = -ay' - b $ Note: a,b are constant and x(t), y(t). ...
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Question about noise term in SDEs

Do any properties/assumptions of SDEs prevent the noise term from being extremely large? Using a simple population growth model as an example, $\frac{dNt}{dt} = (r_{t} + W_{t})Nt , N0$ given, ...
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Finding the correction factor of a model

If I have a model, and data against that model. The model says that it should be linear, and the data begins linear and drops away from the line as x decreases. Is there some function I can multiply ...