Questions tagged [ecology]

Questions about modeling biological populations, communities and ecosystems.

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2 votes
2 answers
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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{...
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  • 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 $...
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  • 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 ...
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  • 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 ...
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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 ...
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  • 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 ...
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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 ...
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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 ...
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  • 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? ...
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  • 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 ...
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  • 99
3 votes
1 answer
844 views

Bifurcation diagram for ODEs

I have a system of ODEs ...
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  • 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 ...
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  • 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 ...
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  • 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...
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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 ...
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  • 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 ...
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  • 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: ...
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  • 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 (...
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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 ...
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  • 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: ...
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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 ...
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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 ...
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  • 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 ...
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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 ...
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  • 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] &...
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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 <...
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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 ...
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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 ...
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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: ...
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  • 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}...
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  • 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{(...
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1 vote
1 answer
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.
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