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.

learn more… | top users | synonyms

1
vote
1answer
38 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, ...
0
votes
1answer
44 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 ...
0
votes
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 ...
1
vote
1answer
30 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 ...
1
vote
1answer
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 ...
0
votes
0answers
16 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 ...
0
votes
2answers
33 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 ...
0
votes
1answer
30 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 ...
0
votes
0answers
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 ...
0
votes
0answers
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 ...
0
votes
1answer
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 ...
0
votes
0answers
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 ...
0
votes
0answers
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 ...
0
votes
0answers
14 views

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?
0
votes
0answers
6 views

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 ...
1
vote
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 ...
1
vote
1answer
36 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 ...
0
votes
0answers
18 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 ...
1
vote
1answer
34 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} = ...
1
vote
1answer
69 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} = ...
0
votes
1answer
34 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 ...
0
votes
0answers
19 views

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 ...
1
vote
0answers
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 ...
0
votes
1answer
19 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 ...
1
vote
0answers
32 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 ...
0
votes
1answer
19 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 ...
1
vote
0answers
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 ...
0
votes
1answer
26 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 ...
0
votes
0answers
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 ...
2
votes
3answers
230 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 ...
0
votes
0answers
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 ...
1
vote
0answers
29 views

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 ...
1
vote
0answers
16 views

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?
0
votes
1answer
53 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 ...
1
vote
0answers
83 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 ...
0
votes
2answers
39 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 ...
0
votes
0answers
19 views

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? ...
1
vote
1answer
45 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 ...
0
votes
1answer
40 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 ...
1
vote
2answers
45 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 ...
0
votes
2answers
21 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 ...
0
votes
1answer
41 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 $a$ ...
1
vote
0answers
12 views

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 ...
0
votes
1answer
31 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 ...
0
votes
0answers
19 views

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 + ...
0
votes
1answer
29 views

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, $$ ...
2
votes
2answers
38 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, ...
1
vote
0answers
21 views

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?
0
votes
0answers
19 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 ...
1
vote
0answers
35 views

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 ...