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Biological Growth models as modifications of the exponential

Exponential growth [1]

Logistic Model

Classical form

Logistic Model of population growth :[2]

Or autocompetition for the substrate

Logistic may be also autocompetion : [3]

Or exponential with explicit braking

Explicit braking function in logistic model : [4]

Properties

3 solutions differing by initial conditions : [5]

A simple 2 populations competing for the substrate

2 populations (logistic) and one substrate : [6]

Monod's Model

Classical

Monod's growth model of bacteria classical equation: [7]

Explicit braking function on the exponential growth

The braking function is an hyberbol : [8]

Monod's Model with acceleration and other complications

And now an acceleration at the beginning : [9]
With a delayed growth and mortality : [10]
Monod's Chemostat model : [11]

Monod's relatives

The closely-related Contois'Model : [12]

Exponential growth with other braking functions

Allee's model : [13]
Monomolecular:[14]
Gompertz's Model :[15]
Growth of individuals and Gompertz's Model : [16]
Von Bertalanffy's model :[17]

Another approach :Simply Diffusing

Three compartiments 1 :[18]
Three compartiments 2 :[19]
Excretion of fibroin from sericigen glands :[20]

Interactions

Interactions of populations

Lotka-Volterra

Interaction between preys and predator (Lotka-Volterra) :[21]
Interaction between preys and predator with logistic growth :[22]
Bacteria and ameoba :[23]

Holling-Tanner

Holling-Tanner :[24]
Holling-Tanner with instability :[25]
Holling's Model : [26]
Substrate diffusion growth and grazing (unrealist) : [27]

Interactions of biology and chemistry

Nitrogen fixation in soil by bacteria : [28]

Epidemiology

SIR Model :[29]
Simplistic AIDS Model : [30]
A (better) model of AIDS epidemics :[31]

Others

Sinus : a way to schematize regular variations : [32]
Lorentz chaotic model (not biologic) :[33]

Of course here is your sandbox for you to test directly your owns models (we provide a simple exponential as backbone)

DynW Sandbox is at [34]

Sun Aug 17 11:33:56 2008