Chaos at fifty

  title={Chaos at fifty},
  author={Adilson E. Motter and David K. Campbell},
  journal={Physics Today},
In 1963 an MIT meteorologist revealed deterministic predictability to be an illusion and gave birth to a field that still thrives. 

Figures from this paper

Applied mathematics: How chaos forgets and remembers
A study of the dynamics of chaotic systems in the context of information theory adds a twist to this saying that makes predictions about the future more difficult.
Relativistic quantum chaos in graphene
Classical chaos gains some additional degrees of freedom in materials with excitations described by the Dirac equation.
Ed Lorenz: Father of the ‘Butterfly Effect’
Ed Lorenz, rightfully acclaimed as the father of the ‘Butterfly Effect’, was an American mathematician and meteorologist whose early work on weather prediction convinced the world at large about the
Method to Sense Changes in Network Parameters with High-Speed, Nonlinear Dynamical Nodes
A method to Sense Changes in Network Parameters with High-Speed, Nonlinear Dynamical Nodes by using high-speed, nonlinear dynamical nodes to sense changes in network parameters.
The chaotic dynamics of drilling
In the study of drilling dynamics, many investigations are limited to laboratory systems and simple mathematical models. Using field measurement data and a new dynamical model in a rotary steerable
Slim Fractals: The Geometry of Doubly Transient Chaos
Traditional studies of chaos in conservative and driven dissipative systems have established a correspondence between sensitive dependence on initial conditions and fractal basin boundaries, but much
Introduction to Supersymmetric Theory of Stochastics
The possibility of constructing a unified theory of DLRO has emerged recently within the approximation-free supersymmetric theory of stochastics (STS), which may be interesting to researchers with very different backgrounds because the ubiquitous DLRO is a truly interdisciplinary entity.
Natural Dynamics for Combinatorial Optimization
Stochastic and or natural dynamical systems (DSs) are dominated by sudden nonlinear processes such as neuroavalanches, gamma-ray bursts, solar flares, earthquakes etc. that exhibit scale-free
Chaos, patterns, coherent structures, and turbulence: Reflections on nonlinear science.
The paradigms of nonlinear science were succinctly articulated over 25 years ago as deterministic chaos, pattern formation, coherent structures, and adaptation/evolution/learning, which hoped to provide the tools and concepts for the understanding and characterization of the strongly nonlinear problem of fluid turbulence.
Conservative chaos in a simple oscillatory system with non-smooth nonlinearity
In this paper, we consider some unusual features of dynamical regimes in the non-smooth potential $$V(x)=|x|$$ which is a piece-wise linear function. Also, we consider the dynamics in more


The essence of chaos
Glimpses of chaos a journey into chaos our chaotic weather encounters with chaos what else is chaos?
Chaos in dynamical systems
Preface 1. Introduction and overview 2. One-dimensional maps 3. Strange attractors and fractal dimensions 4. Dynamical properties of chaotic systems 5. Nonattracting chaotic sets 6. Quasiperiodicity
Fractal Geometry of Nature
This book is a blend of erudition, popularization, and exposition, and the illustrations include many superb examples of computer graphics that are works of art in their own right.
Chaos in Conservative Systems
By Liouville’s Theorem, the solution flow for a conservative Hamiltonian system preserves volumes in phase space. Poincare’s Recurrence Theorem then shows that most solution curves in phase space
Introduction to the focus issue: fifty years of chaos: applied and theoretical.
This Focus Issue collects 13 papers, from authors and research groups representing the mathematical, physical, and biological sciences, that were presented at a symposium held at Kyoto University from November 28 to December 2, 2011, and identifies some common themes that appear in them and in the theory of dynamical systems.
Synchronization in chaotic systems.
This chapter describes the linking of two chaotic systems with a common signal or signals and highlights that when the signs of the Lyapunov exponents for the subsystems are all negative the systems are synchronized.
Chaotic flow: the physics of species coexistence.
It is argued that a peculiar small-scale, spatial heterogeneity generated by chaotic advection can lead to coexistence and sheds light on the enrichment of phytoplankton and the information integration in early macromolecule evolution.
Deterministic nonperiodic flow
Finite systems of deterministic ordinary nonlinear differential equations may be designed to represent forced dissipative hydrodynamic flow. Solutions of these equations can be identified with
A Philosophical Essay On Probabilities
Pierre-Simon Laplace (1749-1827) is remembered amoung probabilitists today particularly for his "Theorie analytique des probabilites", published in 1812. The "Essai philosophique dur les
The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors
1. Introduction and Simple Properties.- 1.1. Introduction.- 1.2. Chaotic Ordinary Differential Equations.- 1.3. Our Approach to the Lorenz Equations.- 1.4. Simple Properties of the Lorenz Equations.-