Introduction to Complex Systems in Biology (and Beyond)

A course by Dirk Brockmann

Tutorials

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Random Walks & Stochastic Processes

This tutorial provides as brief overview of random walks and stochastic processes, stochastic differential equations, the central limit theorem and some other basic stuff.
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Bifurcation Analysis of One-Dimensional Dynamical Systems

This tutorial introduces the concept of bifurcation analysis in one-dimensional dynamical systems, focusing on the bifurcation diagram and the stability of fixed points.
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The Kuramoto model of coupled oscillators

This tutorial explores the Kuramoto model, a mathematical model of coupled oscillators, focusing on synchronization phenomena and the emergence of collective behavior in complex systems.
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The logistic map

This tutorial explores the properties of the logistic map, a classic example of a one-dimensional dynamical system, focusing on its bifurcation diagram and chaotic behavior.
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Random Variables & Probability Distributions

This tutorial captures the basics of random variables and probability theory. It is really very basic and only explores the very fundamental aspects one should know.
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One-dimensional dynamical systems

This tutorial introduces one-dimensional dynamical systems, focusing on the stability of fixed points and the behavior of trajectories in phase space.