Mathematical modeling | Complex systems theory | Complex dynamics
A complex system is a system composed of many components which may interact with each other. Examples of complex systems are Earth's global climate, organisms, the human brain, infrastructure such as power grid, transportation or communication systems, complex software and electronic systems, social and economic organizations (like cities), an ecosystem, a living cell, and ultimately the entire universe. Complex systems are systems whose behavior is intrinsically difficult to model due to the dependencies, competitions, relationships, or other types of interactions between their parts or between a given system and its environment. Systems that are "complex" have distinct properties that arise from these relationships, such as nonlinearity, emergence, spontaneous order, adaptation, and feedback loops, among others. Because such systems appear in a wide variety of fields, the commonalities among them have become the topic of their independent area of research. In many cases, it is useful to represent such a system as a network where the nodes represent the components and links to their interactions. The term complex systems often refers to the study of complex systems, which is an approach to science that investigates how relationships between a system's parts give rise to its collective behaviors and how the system interacts and forms relationships with its environment. The study of complex systems regards collective, or system-wide, behaviors as the fundamental object of study; for this reason, complex systems can be understood as an alternative paradigm to reductionism, which attempts to explain systems in terms of their constituent parts and the individual interactions between them. As an interdisciplinary domain, complex systems draws contributions from many different fields, such as the study of self-organization and critical phenomena from physics, that of spontaneous order from the social sciences, chaos from mathematics, adaptation from biology, and many others. Complex systems is therefore often used as a broad term encompassing a research approach to problems in many diverse disciplines, including statistical physics, information theory, nonlinear dynamics, anthropology, computer science, meteorology, sociology, economics, psychology, and biology. (Wikipedia).
Mathematical modeling of evolving systems
Discover the multidisciplinary nature of the dynamical principles at the core of complexity science. COURSE NUMBER: CAS 522 COURSE TITLE: Dynamical Systems LEVEL: Graduate SCHOOL: School of Complex Adaptive Systems INSTRUCTOR: Enrico Borriello MODE: Online SEMESTER: Fall 2021 SESSION:
From playlist What is complex systems science?
Swarms, Societies, and Superorganisms
How do we decompose the drivers of success and failure in complex living groups? COURSE NUMBER: CAS 503 COURSE TITLE: Fundamentals of Complex Systems Science: Collectives LEVEL: Graduate SCHOOL: School of Complex Adaptive Systems INSTRUCTOR: Bryan Daniels MODE: Online SEMESTER: Fall 202
From playlist What is complex systems science?
Discrete-Time Dynamical Systems
This video shows how discrete-time dynamical systems may be induced from continuous-time systems. https://www.eigensteve.com/
From playlist Data-Driven Dynamical Systems
Intro to Linear Systems: 2 Equations, 2 Unknowns - Dr Chris Tisdell Live Stream
Free ebook http://tinyurl.com/EngMathYT Basic introduction to linear systems. We discuss the case with 2 equations and 2 unknowns. A linear system is a mathematical model of a system based on the use of a linear operator. Linear systems typically exhibit features and properties that ar
From playlist Intro to Linear Systems
System of Equations with Three Equations and Three Variables
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From playlist Systems of Equations
Reactive Systems use a high-performance software architecture. They are resilient under stress, and their reactive design allows them to scale elastically to meet demand. The reactive design approach allows the creation of more complex, more flexible systems and forms the basis for some of
From playlist Software Engineering
The Anatomy of a Dynamical System
Dynamical systems are how we model the changing world around us. This video explores the components that make up a dynamical system. Follow updates on Twitter @eigensteve website: eigensteve.com
From playlist Research Abstracts from Brunton Lab
From playlist Complex Multiplication
Sebastián Donoso: Recent developments in finite rank systems
I will comment on recent results concerning the topological properties of finite rank Cantor minimal systems. I will mention some ideas to estimate their word complexity and ask a few open problems. CIRM HYBRID EVENT Recorded during the meeting "Algebraic and Combinatorial Invariants
From playlist Virtual Conference
MIT 6.001 Structure and Interpretation of Computer Programs, Spring 2005 Instructor: Harold Abelson, Gerald Jay Sussman, Julie Sussman View the complete course: https://ocw.mit.edu/6-001S05 YouTube Playlist: https://www.youtube.com/playlist?list=PLE18841CABEA24090 Generic Operators Despi
From playlist MIT 6.001 Structure and Interpretation, 1986
DevOpsDays Boston 2017 - There is No Root Cause... by Matthew Boeckman
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From playlist DevOpsDays Boston 2017
Events are our industry’s near and dear. All technological conferences are full of talks on event sourcing, event driven architectures, or event driven integrations. So hey, why not make another one? …But a bit different: Let’s talk about the dark side of this pattern. Events, as any tool,
From playlist Microservices
Jacob Lurie: A Riemann-Hilbert Correspondence in p-adic Geometry Part 1
At the start of the 20th century, David Hilbert asked which representations can arise by studying the monodromy of Fuchsian equations. This question was the starting point for a beautiful circle of ideas relating the topology of a complex algebraic variety X to the study of algebraic diffe
From playlist Felix Klein Lectures 2022
Bosonic Complex Quantum Networks: What, when and why - S. Maniscalco - Workshop 1 - CEB T2 2018
Sabrina Maniscalco (Univ. Turku) / 17.05.2018 Bosonic Complex Quantum Networks: What, when and why. In this talk I will present some perspectives on these questions by looking at Hamiltonian models describing complex networks of quantum harmonic oscillators. I will first show that such
From playlist 2018 - T2 - Measurement and Control of Quantum Systems: Theory and Experiments
DevOpsDays Philadelphia 2019 - We Have a Complex Systems Problem… by Jon Moore
DevOpsDays Philadelphia 2019 - We Have a Complex Systems Problem…and We Need to Talk About It by Jon Moore Software used to be something that you walked into a Babbage’s store in the mall and bought in a box. That’s clearly no longer the case. The tech industry’s products and services hav
From playlist DevOpsDays Philadelphia 2019
DevOpsDays Philadelphia 2019 - We Have a Complex Systems Problem…and We Need to... by Jon Moore
DevOpsDays Philadelphia 2019 - We Have a Complex Systems Problem…and We Need to Talk About It by Jon Moore Software used to be something that you walked into a Babbage’s store in the mall and bought in a box. That’s clearly no longer the case. The tech industry’s products and services hav
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Systems of Equations Two Variables Two Equations Infinitely Many Solutions
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Systems of Equations Two Variables Two Equations Infinitely Many Solutions
From playlist Systems of Equations
Lecture 4B | MIT 6.001 Structure and Interpretation, 1986
Generic Operators Despite the copyright notice on the screen, this course is now offered under a Creative Commons license: BY-NC-SA. Details at http://ocw.mit.edu/terms Subtitles for this course are provided through the generous assistance of Henry Baker, Hoofar Pourzand, Heather Woo
From playlist MIT 6.001 Structure and Interpretation, 1986