See Dynamical systems on networks, Epidemics on networks, Dynamical system, Chemical kinetics, Social dynamics

Often modelled by Continuous dynamical system, but sometimes by Discrete dynamical systems, like the Logistic map

Fundamental processes

Processes that affect number of individuals in a population.

• Death rate
• Birth rate
• Immigration rate
• Emigration rate

These processes show density dependence, that is dependence on the population size itself.

Logistic growth

$\frac{dx(t)}{dt}=bx(t)\left(1-\frac{x(t)}{K}\right)$

$K$ is the carrying capacity, which defines a stable Fixed point.

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Two species model

$\frac{dx_1}{dt}=bx_1-qx_2x_1$, $\frac{dx_2}{dt}=qx_2x_1-bx_1$

Mutualism (or Symbiosis)

$\frac{dx 1}{dt}= x 1 (r 1 -d_1x_1+ a 1 x 2 )$

$\frac{dx 2}{dt}= x 2 (r 2 -d_2x_2+ a 2 x 1 )$