Chaos theory is an interdisciplinary area of scientific study and branch of mathematics. It focuses on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions. These 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 Brazil can cause a tornado in Texas.
Pink noise, 1⁄f noise, fractional noise or fractal noise is a signal or process with a frequency spectrum such that the power spectral density is inversely proportional to the frequency of the signal. In pink noise, each octave interval carries an equal amount of noise energy.
In the mathematical field of dynamical systems, an attractor is a set of states toward which a system tends to evolve, for a wide variety of starting conditions of the system. System values that get close enough to the attractor values remain close even if slightly disturbed.
Self-organized criticality (SOC) is a property of dynamical systems that have a critical point as an attractor. Their macroscopic behavior thus displays the spatial or temporal scale-invariance characteristic of the critical point of a phase transition, but without the need to tune control parameters to a precise value, because the system, effectively, tunes itself as it evolves towards criticality.
Stochastic resonance (SR) is a phenomenon in which a signal that is normally too weak to be detected by a sensor can be boosted by adding white noise to the signal, which contains a wide spectrum of frequencies. The frequencies in the white noise corresponding to the original signal's frequencies will resonate with each other, amplifying the original signal while not amplifying the rest of the white noise – thereby increasing the signal-to-noise ratio, which makes the original signal more prominent. Further, the added white noise can be enough to be detectable by the sensor, which can then filter it out to effectively detect the original, previously undetectable signal.
Mitchell Jay Feigenbaum was an American mathematical physicist whose pioneering studies in chaos theory led to the discovery of the Feigenbaum constants.
Klaus Ferdinand Hasselmann is a German oceanographer and climate modeller. He is Professor Emeritus at the University of Hamburg and former Director of the Max Planck Institute for Meteorology. He was awarded the 2021 Nobel Prize in Physics jointly with Syukuro Manabe and Giorgio Parisi.
Kurt Wiesenfeld is an American physicist working primarily on non-linear dynamics. His works primarily concern stochastic resonance, spontaneous synchronization of coupled oscillators, and non-linear laser dynamics. Since 1987, he has been professor of physics at the Georgia Institute of Technology.
Objective-collapse theories, also known spontaneous collapse models or dynamical reduction models, are proposed solutions to the measurement problem in quantum mechanics. As with other interpretations of quantum mechanics, they are possible explanations of why and how quantum measurements always give definite outcomes, not a superposition of them as predicted by the Schrödinger equation, and more generally how the classical world emerges from quantum theory. The fundamental idea is that the unitary evolution of the wave function describing the state of a quantum system is approximate. It works well for microscopic systems, but progressively loses its validity when the mass / complexity of the system increases.
Ardeshir "Adi" Ratan Bulsara is a scientist in the area nonlinear dynamics. The 2007 International Conference on Applied Nonlinear Dynamics (ICAND), held in Kauai, Hawaii, was a festschrift held in his honor of his 55th birthday.
Henry Emil Kandrup was an American astrophysicist and professor at the University of Florida, Gainesville. His major contributions were in the areas of galaxy dynamics and plasma physics.
Luca Gammaitoni is a scientist in the area of noise and nonlinear dynamics. He is currently the Director of the Noise in Physical System Laboratory at the Physics Department of the Università di Perugia, in Italy.
In mathematics, the Kardar–Parisi–Zhang (KPZ) equation is a non-linear stochastic partial differential equation, introduced by Mehran Kardar, Giorgio Parisi, and Yi-Cheng Zhang in 1986. It describes the temporal change of a height field with spatial coordinate and time coordinate :
Edward Ott is an American physicist most noted for his contributions to the development of chaos theory.
In mathematics, a continuous-time random walk (CTRW) is a generalization of a random walk where the wandering particle waits for a random time between jumps. It is a stochastic jump process with arbitrary distributions of jump lengths and waiting times. More generally it can be seen to be a special case of a Markov renewal process.
Roman Evsey Glazman was a Russian American physicist and oceanographer.
Peter David Drummond is a physicist and distinguished professor in the Centre for Quantum and Optical Science at Swinburne University of Technology.
Paul Brumer is a professor of chemistry at the University of Toronto in the field of chemical physics. He was elected a fellow of the American Physical Society in 1993 for "the development of quantum and classical dynamics of isolated molecules and the coherent control of chemical reactions."
Jay Fineberg is an Israeli physicist. He is a professor at The Racah Institute of Physics of the Hebrew University of Jerusalem. He is known for his work on various aspects of nonlinear physics, mainly in the fields of fracture and friction. He is an elected fellow of the American Physical Society and the Israel Physical Society.
JinqiaoDuan is a professor of mathematics at Illinois Institute of Technology, Chicago, USA.
