EvoLudoLab: Spatial Ecological PGG - Diffusion induced instability: Difference between revisions
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{{VirtualLab:EcoPGG| | {{VirtualLab:EcoPGG| | ||
options="--run --delay 100 --popsize 101x --popupdate D --geometry nf --intertype | options="--run --delay 100 --popsize 101x --popupdate D --geometry nf --intertype a --colors black:red:green --reportfreq 1 --diffusion 100:1 --inittype 2 --initfreqs 8:1:1 --basefit 1.0 --selection 1.0 --groupsize 8 --cost 1.0 --interest 2.5 --birthrate 1.0 --deathrate 1.2 --pdedt 0.05 --pdeL 256"| | ||
type=PDE| | type=PDE| | ||
title=Diffusion induced instability - Turing patterns| | title=Diffusion induced instability - Turing patterns| | ||
doc=The initial configuration is symmetric and the formation of Turing patterns through diffusion induced instability preserves this symmetry. Patterns emerge through the competing forces of cooperators (activtors) and defectors (inhibitors). In the absence of spatial extension, cooperators and defectors would co-exist in a stable equilibrium. In contrast to patterns emerging through diffusion induced co-existence, Turing patterns require a minimum difference between the diffusion rates of inhibitors (fast) and activators (slow). | doc=The initial configuration is symmetric and the formation of Turing patterns through diffusion induced instability preserves this symmetry. Patterns emerge through the competing forces of cooperators (activtors) and defectors (inhibitors). In the absence of spatial extension, cooperators and defectors would co-exist in a stable equilibrium. In contrast to patterns emerging through diffusion induced co-existence, Turing patterns require a minimum difference between the diffusion rates of inhibitors (fast) and activators (slow). | ||
The parameters are <math>r=2.5</math>, <math>N=8</math>, <math>c=1</math>, <math>b=1</math>, <math>d=1.2</math> using numerical integration of the partial differential equation with the diffusion constants <math>D_C=1</math>, <math>D_D= | The parameters are <math>r=2.5</math>, <math>N=8</math>, <math>c=1</math>, <math>b=1</math>, <math>d=1.2</math> using numerical integration of the partial differential equation with the diffusion constants <math>D_C=1</math>, <math>D_D=100</math>. The initial configuration is a circular disk of equal densities of cooperators and defectors (<math>0.1</math>) in the center of a square lattice with fixed (reflecting) boundary conditions.}} | ||
[[Category: Christoph Hauert]] | [[Category: Christoph Hauert]] | ||
