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Date
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Technique Narrative
373
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192
downloads
0
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1-030-RandomPerturbation-TechniqueNarrative
After a brief historical view of this problem, we will demonstrate the derivation of first order linear differential equations with random perturbations.
random perturbation
Brownian motion
Langevin equation
Riemann-Steiltjes integral
Wiener process
Ito's calculus
Modeling Scenario
453
views
180
downloads
0
comments
1-039-StochasticPopModels-ModelingScenario
We develop strategies for creating a population model using some simple probabilistic assumptions. These assumptions lead to a system of differential equations for the probability that a system is in state (or population size) n at time t.
Probability
population dynamics
Variance
Mean
stochastic
deterministic
Modeling Scenario
306
views
227
downloads
0
comments
1-027-StochasticProcesses-ModelingScenario
We build the infinite set of first order differential equations for modeling a stochastic process, the so-called birth and death equations. We will only need to use integrating factor solution strategy or DSolve in Mathematica for success.
Variance
Mean
stochastic
random
operations research
industrial engineering
Poisson process
traffic
Free Online Textbook
210
views
83
downloads
0
comments
2018-Eduardo-Sontag-Lecture_Notes_on_Mathematical_Systems_Biology
I am often asked if it is OK to use these notes in courses at other universities. The answer is “of course!” though I strongly suggest that a link to my website be provided, so that students can always access the current version.
biology
textbook
systems
dyanmical system
Free Online Textbook
464
views
94
downloads
0
comments
2012-Brian_Ingalls-Mathematical Modelling in Systems Biology An Introduction
This is a comprehensive text with much biology background to motivate the mathematical modeling, exercises and answers, and many rich examples.
spatial
sensitivity analysis
gene regulatory networks
stochastic
bifurcation
metabolic networks
electrophysiology
transduction
rate laws
biochemical reactions
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