Questions tagged [ecology]

Questions about modeling biological populations, communities and ecosystems.

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31 votes
1 answer

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 ...
12 votes
2 answers

Nonlinear dispersal equation modeling insect aggregation

I'm a newbie with Mathematica, I know it's a basic answer, but I can't solve the problem on my own. I have the following equation reflecting insect aggregation at low population densities (taken from ...
  • 401
8 votes
1 answer

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] &...
3 votes
1 answer

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 ...
  • 1,238
17 votes
1 answer

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 ...
  • 1,238
15 votes
3 answers

Solving the Lotka-McKendrick model with NDSolve

The Lotka-McKendrick model is a demographic model that represents the way a population changes over time due to fertility and mortality. For an age-specific population density $ u(a, t) $, and a total ...
  • 18k
6 votes
2 answers

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{(...
6 votes
4 answers

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}...
  • 173
26 votes
2 answers

Turing patterns

I am new in learning Turing patterns. Is there any sample code available to generate such patterns in ecology model (Lotka–Volterra model)? The above figure is taken from this paper, and is based on ...
  • 363
10 votes
5 answers

Simple Birth Death Process

I am trying to implement simple birth death process. Why my code does not work? Any suggestion. Thanks. Cross posted ...
2 votes
2 answers

Poincaré section for non-autonomous logistic equation with periodic harvesting

I'd like to plot the Poincaré section based on the problem from here: see exercise 8.1 Given that the standard logistic equation with harvesting function is $$\dfrac{dx}{dt} = ax(1 - x) - h (1 + \sin{...
  • 173
0 votes
1 answer

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 ...
  • 113