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In mathematics, computer science and physics, a deterministic system is a system in which no randomness is involved in the development of future states of the system. [1] A deterministic model will thus always produce the same output from a given starting condition or initial state. [2]
In deterministic models (differential equations) each process (e.g. transcription, degradation) has a rate (which is typically a function of the state).! e.g. Rate of transcription = !! This gives a measure of how frequently each type of reaction is expected to occur (for a given state).! Alternatively, we can develop models centred on individual
Learning Goals # Apply physical laws to construct a deterministic model consisting of a system of differential equations. Apply nondimensionalization procedure to differential equations and interpret dimensionless parameters. Numerically approximate solutions of systems of differential equations.
Deterministic models are often described by systems of differential equations. Apply analytical methods to solve differential equations in special cases such as first order separable equations and second order constant coefficient equations .
The logistic equation is a deterministic model that predicts the population size at any future time point, given initial population size \( P(0) \). In summary, deterministic models are vital in applied mathematics for their ability to give precise and reliable descriptions of complex systems.
Deterministic models are based on the premise that the behavior of any grain in the assembly is dependent upon the behavior of all the other grains. From: Recrystallization and Related Annealing Phenomena (Third Edition) , 2017
A deterministic model is a type of model that assumes all input values are known and fixed, leading to a single outcome for a given set of inputs. In other words, the output of a deterministic model is entirely determined by its inputs, without any randomness or uncertainty involved.
