Biology Reference
In-Depth Information
simulate discrete stochastic models. A prominent example is Brownian
agents.
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4.2. Methods for Discrete Deterministic Models
Simulations of discrete deterministic models are frequently implemented
using methods from the class of finite automata. The most prominent
examples are cellular
a
automata
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and agent-based simulations.
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In
finite automata, spatially distributed computational cells (or agents) with
certain attributed properties interact according to sets of deterministic
rules. These interaction rules map the state (the values of the attributed
properties) of the interacting cells to certain actions, which in turn
change the states of the cells. Finite automata are powerful and fascinat-
ing tools, as already small sets of simple rules can give rise to very com-
plex nonlinear model behavior. They can be used for diverse purposes
such as studying behavioral aspects of interacting individuals in ecosys-
tems, studying artificial life, simulating interacting neurons,
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simulating
social interactions,
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or simulating pattern-forming mechanisms in mor-
phogenesis.
5
Another important class of discrete deterministic simula-
tions is found in MD.
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Here, the atomistic behavior of molecules is
simulated by explicitly tracking the dynamics and positions of all atoms.
Atoms in classical MD are modeled as discrete particles that interact
according to deterministic mechanisms such as interatomic bonds, van
der Waals forces, or electrostatics.
4.3. Methods for Continuous Stochastic Models
Continuous stochastic models formulated as SDEs can be numerically
simulated using a variety of stochastic integration methods,
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most
notably Euler-Maruyama or Milstein's higher-order method.
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It is,
however, important to keep in mind that each simulation represents just
one possible realization of the stochastic process. In order to estimate
means and variances, many independent simulations need to be performed
a
The word “cellular” refers to computational cells in the algorithm and does not
imply any connection with biological cells.
