Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [ecology]

Questions about modeling biological populations, communities and ecosystems.

8
votes
1answer
258 views

Simulating a partial differential equation - reaction-diffusion systems and Turing patterns

I want simulate a reaction-diffusion system described by a PDE called the FitzHugh–Nagumo equation. The system that has been proposed by Alan Turing as a model of animal coat pattern formation and is ...
2
votes
0answers
114 views

Converting R code into Mathematica

I am trying rewrite R code in Mathematica. Since I am not an expert in R I am not getting ...
2
votes
2answers
239 views

Stochastic Lotka-Volterra Predator-Prey Model

I am struggling with writing a stochastic version of Lotka-Volterra predator-prey model. This is as far as I have gotten: ...
0
votes
1answer
134 views

How solve a PDE system with Specific Initial Condition?

I'm trying to solve a PDE system reaction-diffusion type (2D spatial + 1 temporal) coupled as described below. Another question of this same system was solved here: System of nonlinear PDE 2D (...
3
votes
1answer
289 views

System of nonlinear PDE 2D (Reaction-Diffusion type) with periodic boundary condition

I want to solve a system of Pde (2D) reaction diffusion type using NDSolve whose boundary conditions are and the initial conditions are or I thought of the following code ...
1
vote
0answers
71 views

Adding a perturbation to a dynamic 3-tier food chain model

I have a predator prey food chain model set up as follows, with x representing the resource, y the consumer, and z the predator: ...
9
votes
5answers
865 views

Simple Birth Death Process

I am trying to implement simple birth death process. Why my code does not work? Any suggestion. Thanks. Cross posted http://community.wolfram.com/groups/-/m/t/1205656 ...
0
votes
1answer
216 views

4-dimensional Lotka-Volterra plot

I was referring to the question I posted earlier in Mathematics forum, but then I came to see this example on Wikipedia. How did they plot the system in phase space? The closet relevant topic I have ...
0
votes
1answer
113 views

How to perform integration processes NDSOlve and show list of random variables used in this process?

I have an ODE system which solves of n variables, with initial conditions defined using the previous differential equation solution of n-1 variables and with an initial condition for the last variable ...
0
votes
2answers
197 views

How to solve an ODE system that periodically increases in size

I have an ODE system that increases in size according to the rules ...
6
votes
1answer
2k views

Rosenzweig-MacArthur predator-prey model [duplicate]

The predator-prey model is governed by the following system of ode's. \begin{eqnarray} &&\displaystyle{\frac{dx}{dt}=r x\left(1 - \frac{x}{K}\right) - \frac{s y x}{1 + s \tau x}},\\[0.1cm] &...
4
votes
0answers
148 views

Why is this non-vectorized NDSolve faster than vectorized?

I'm trying to get a feeling for stochastic population models. A simple starting place is a birth-death process whose deterministic limit is the logistic equation. The idea is to model the probability <...
23
votes
1answer
2k views

Gillespie Stochastic Simulation Algorithm

The Gillespie SSA is a Monte Carlo stochastic simulation algorithm to find the trajectory of a dynamic system described by a reaction (or interaction) network, e.g. chemical reactions or ecological ...
2
votes
1answer
168 views

how to write generic equation for Recurring differential equations?

Hi I am a biologist and I want to model some ecological data that I have. I am new to mathematics and to ODEs. I want to write generic equations for a multi-dimensional system of ODEs. So, I want to ...
5
votes
1answer
445 views

Stochastic Predator-Prey model using Gillespie's SSA

I'm trying to model the predator-prey situation using SSA. I am very new to Mathematica so my handling of matrices is probably terrible, and that's probably adding to my confusion: ...
4
votes
4answers
5k views

The Lotka-Volterra predator-prey model

I have a Mathematica assignment where we need to numerically solve a Lotka-Volterra predator-prey population equations. $$\frac{dx}{dt}=ax-bxy,\quad\frac{dy}{dt}=-cx+dxy,$$ where $a,b,c,d\in\mathbb{R}...
5
votes
2answers
1k views

Harvested prey–predator model incorporating a prey refuge

I want to plot the phase diagram of prey predator versus prey refuge to see how the prey refuge influences the population of prey and predator. And this is the system $x'=\alpha x(1-x/k)-\beta\frac{(...
1
vote
1answer
1k views

How to plot population growth model?

How would I draw the graph of a function $\frac{dy}{dt}=(Ry^2/T)-Ry$ in Mathematica? I have tried a few times but the constants are confusing me.