# Questions tagged [ecology]

Questions about modeling biological populations, communities and ecosystems.

32 questions
Filter by
Sorted by
Tagged with
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 $$\dfrac{dx}{dt} = ax(1 - x) - h (1 + \sin{... • 173 4 votes 1 answer 155 views ### Steady state solution (1D) of nonlinear dispersal equation Now I'm interested in the equation$$\frac{\partial }{\partial x}\Bigl(\text{sgn}(x) u \Big) +\frac{\partial}{\partial x} \Bigl[ u^2 \frac{\partial u}{\partial x} \Bigr] =0$$with boundary conditions ... • 401 12 votes 2 answers 495 views ### 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 15 votes 3 answers 424 views ### 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 ... • 17.8k 7 votes 1 answer 215 views ### Sensitivity analysis of parameter on eigenvalues of predator-prey model I am trying to do a sensitivity analysis of the parameter g on the eigenvalues of this simple predator-prey Lotka Volterra model. I know that this code is entirely ... • 71 2 votes 1 answer 117 views ### 1-D prey-predator system with diffusion and time-dependent parameters in Mathematica 12 Please you find attached a Mathematica program for the existence of almost periodic solutions for a class of Lotka-Volterra prey-predators systems with diffusion and time-dependent parameters in ... • 121 2 votes 1 answer 81 views ### ParametricNDSolve with a delay differential equation I have a set of delay differential equations that I solve numerically from 0 < t < T. y[T] is then used as the initial ... 4 votes 1 answer 80 views ### Trying to recreate a plot which tracks the age of individuals inside a compartment model I am using a compartment model from this paper. I am trying to recreate Figure 6. I will be honest, I have no clue how to approach this. The paper doesn't give information on how to achieve the ... • 57 4 votes 1 answer 116 views ### How can I speed up NDSolve I have written a simulation that solve a pde, I used a method I found on this site to speed up the calculation but it is still slow. Is there any way to speed up the prosses? ... • 99 1 vote 0 answers 67 views ### Simulating a partial differential equation, uniform vegetation and bare soil system (2 species) I want to simulate a system of two plants ,woody and herbaceous species; with starting condition that half of the grid (square grid) is filled with woody specie, the herbaceous specie exist on the ... • 99 3 votes 1 answer 844 views ### Bifurcation diagram for ODEs I have a system of ODEs ... • 89 5 votes 1 answer 618 views ### Mathematica code for bifurcation diagram in 3D Good day. I need help with the code in mathematica to plot the bifurcation diagram (e vs z*) or (e vs x*), for the system ... • 89 25 votes 2 answers 4k views ### 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 ... • 353 0 votes 1 answer 156 views ### Numerically solve delay ODE I am trying to numerically solve a simple delay ODE in mma for the first time. I think this is likely a simple fix. I first tried to solve system as ordinary differential equation system for up to 𝑡... 2 votes 1 answer 251 views ### Parametric plot of the critical points of an ODE I have a single ODE of the form x'[t] = -(y*n*n + z*n) x[t] + w (1-x[t]) x[t] where the second part of the ODE is the logistic growth with the maximum allowed ... • 135 17 votes 1 answer 2k 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 ... • 1,100 2 votes 2 answers 648 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: ... • 31 0 votes 1 answer 208 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 (... • 1,100 3 votes 1 answer 641 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 ... • 1,100 1 vote 0 answers 96 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 5 answers 1k 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 1 answer 362 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 ... • 113 0 votes 1 answer 166 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 ... • 1,100 0 votes 2 answers 235 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 ... • 1,100 8 votes 1 answer 4k 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 0 answers 208 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 <... • 17.5k 28 votes 1 answer 3k 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 ... • 45.3k 2 votes 1 answer 267 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 1 answer 618 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: ... • 51 6 votes 4 answers 9k 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 $a,b,c,d\in\mathbb{R}... • 173 6 votes 2 answers 1k views ### Harvested prey–predator model incorporating a prey refuge I want to plot the phase diagram of prey predator versus prey refuge to see how the prey refuge influences the population of prey and predator. And this is the system$x'=\alpha x(1-x/k)-\beta\frac{(...
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.