Chaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions, and were once thought to have completely random states of disorder and irregularities. Chaos theory states that within the apparent randomness of chaotic complex systems, there are underlying patterns, interconnection, constant feedback loops, repetition, self-similarity, fractals, and self-organization. The butterfly effect, an underlying principle of chaos, describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state. A metaphor for this behavior is that a butterfly flapping its wings in Texas can cause a tornado in Brazil.
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, an ecosystem, a living cell, and ultimately the entire universe.
A power outage is the loss of the electrical power network supply to an end user.
The Santa Fe Institute (SFI) is an independent, nonprofit theoretical research institute located in Santa Fe, New Mexico, United States and dedicated to the multidisciplinary study of the fundamental principles of complex adaptive systems, including physical, computational, biological, and social systems. The institute is ranked 24th among the world's "Top Science and Technology Think Tanks" and 24th among the world's "Best Transdisciplinary Research Think Tanks" according to the 2020 edition of the Global Go To Think Tank Index Reports, published annually by the University of Pennsylvania.
Dynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical systems. From a physical point of view, continuous dynamical systems is a generalization of classical mechanics, a generalization where the equations of motion are postulated directly and are not constrained to be Euler–Lagrange equations of a least action principle. When difference equations are employed, the theory is called discrete dynamical systems. When the time variable runs over a set that is discrete over some intervals and continuous over other intervals or is any arbitrary time-set such as a Cantor set, one gets dynamic equations on time scales. Some situations may also be modeled by mixed operators, such as differential-difference equations.
In the context of network theory, a complex network is a graph (network) with non-trivial topological features—features that do not occur in simple networks such as lattices or random graphs but often occur in networks representing real systems. The study of complex networks is a young and active area of scientific research inspired largely by empirical findings of real-world networks such as computer networks, biological networks, technological networks, brain networks, climate networks and social networks.
Steven Henry Strogatz, born August 13, 1959, is an American mathematician and the Susan and Barton Winokur Distinguished Professor for the Public Understanding of Science and Mathematics at Cornell University. He is known for his work on nonlinear systems, including contributions to the study of synchronization in dynamical systems, and for his research in a variety of areas of applied mathematics, including mathematical biology and complex network theory.
Douglas R. White was an American complexity researcher, social anthropologist, sociologist, and social network researcher at the University of California, Irvine.
Yoshiki Kuramoto is a Japanese physicist in the Nonlinear Dynamics group at Kyoto University who formulated the Kuramoto model and is also known for the Kuramoto–Sivashinsky equation. He is also the discoverer of so-called chimera states in networks of coupled oscillators.
Adilson E. Motter is the Charles E. and Emma H. Morrison Professor of Physics at Northwestern University, where he has helped develop the concept of synthetic rescue in network biology as well as methods to control the nonlinear dynamics of complex networks. In joint work with Takashi Nishikawa, he discovered the phenomenon of converse symmetry breaking. Motter's research is focused on complex systems and nonlinear phenomena, primarily involving complex networks, systems biology, chaos and statistical physics.
Cristopher David Moore, known as Cris Moore, is an American computer scientist, mathematician, and physicist. He is resident faculty at the Santa Fe Institute, and was formerly a full professor at the University of New Mexico.
Jürgen Kurths is a German physicist and mathematician. He is senior advisor in the research department Complexity Sciences of the Potsdam Institute for Climate Impact Research, a Professor of Nonlinear Dynamics at the Institute of Physics at the Humboldt University, Berlin, and a 6th-century chair for Complex Systems Biology at the Institute for Complex Systems and Mathematical Biology at Kings College, Aberdeen University (UK). His research is mainly concerned with nonlinear physics and complex systems sciences and their applications to challenging problems in Earth system, physiology, systems biology and engineering.
Edward Ott is an American physicist most noted for his contributions to the development of chaos theory.
In network science, the efficiency of a network is a measure of how efficiently it exchanges information and it is also called communication efficiency. The underlying idea is that the more distant two nodes are in the network, the less efficient their communication will be. The concept of efficiency can be applied to both local and global scales in a network. On a global scale, efficiency quantifies the exchange of information across the whole network where information is concurrently exchanged. The local efficiency quantifies a network's resistance to failure on a small scale. That is the local efficiency of a node characterizes how well information is exchanged by its neighbors when it is removed.
Eckehard Schöll is a German physicist and mathematician as well as a Professor of theoretical physics at the Technical University of Berlin. He is an expert in the field of nonlinear dynamics and head of the group Nonlinear dynamics and control. His work pertains to research in the fields of mathematics and physics, particularly semiconductor physics, neurodynamics and bifurcation theory. His latest research is also related to topics in biology and the social sciences, e.g. simulation of the dynamics in socioeconomic or neuronal networks. He is one of the forerunners into the research of chimera states.
Yamir Moreno is a professor of Physics at the Department of Theoretical Physics of the University of Zaragoza and Director of the Institute for Biocomputation and Physics of Complex Systems at the same institution.
Stefano Boccaletti is an Italian physicist. He is senior researcher at the CNR's Institute for Complex Systems in Florence, Italy. His research is mainly concerned with nonlinear and statistical physics, and complex systems sciences with applications to systems biology and systems medicine, data and networks sciences, social science and engineering, among others.
Jesús Gómez-Gardeñes is a Spanish physicist, currently Full Professor in Condensed Matter Physics at the University of Zaragoza (Spain). He is known for his works on complex systems, in particular on the structure and dynamics of complex networks.
Manlio De Domenico is an Italian physicist and complex systems scientist, currently Professor of Physics at the University of Padua and previously at the Fondazione Bruno Kessler in Trento (Italy). In 2014 he has co-founded the Mediterranean School of Complex Networks, and in 2019 he has contributed to found the Italian Chapter of the Complex Systems Society.
Roberta Sinatra is an Italian scientist and associate professor at the IT University of Copenhagen. She is known for her work in network science and conducts research on quantifying success in science.
