Topic
Chaotic
About: Chaotic is a research topic. Over the lifetime, 28560 publications have been published within this topic receiving 483285 citations.
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01 Mar 2004TL;DR: In this article, a model of a single neuron with chaotic dynamics is proposed by considering the following properties of biological neurons: (1) graded responses, relative refractoriness and spatio-temporal summation of inputs.
Abstract: A model of a single neuron with chaotic dynamics is proposed by considering the following properties of biological neurons: (1) graded responses, (2) relative refractoriness and (3) spatio-temporal summation of inputs. The model includes some conventional models of a neuron as its special cases; namely, chaotic dynamics is introduced as a natural extension of the former models. Chaotic solutions of both the single chaotic neuron and the chaotic neural network composed of such neurons are numerically demonstrated.
1,166 citations
TL;DR: The historical timeline of this topic back to the earliest known paper is established and it is shown that building synchronizing systems leads naturally to engineering more complex systems whose constituents are chaotic, but which can be tuned to output various chaotic signals.
Abstract: We review some of the history and early work in the area of synchronization in chaotic systems. We start with our own discovery of the phenomenon, but go on to establish the historical timeline of this topic back to the earliest known paper. The topic of synchronization of chaotic systems has always been intriguing, since chaotic systems are known to resist synchronization because of their positive Lyapunov exponents. The convergence of the two systems to identical trajectories is a surprise. We show how people originally thought about this process and how the concept of synchronization changed over the years to a more geometric view using synchronization manifolds. We also show that building synchronizing systems leads naturally to engineering more complex systems whose constituents are chaotic, but which can be tuned to output various chaotic signals. We finally end up at a topic that is still in very active exploration today and that is synchronization of dynamical systems in networks of oscillators.
1,139 citations
TL;DR: In this article, the authors show that crisis events are prevalent in many circumstances and systems, and that, just past a crisis, certain characteristic statistical behavior (whose type depends on the type of crisis) occurs.
1,099 citations
TL;DR: In this article, an explanation is given for the exponential divergence of the orbits: it is due to the transition from libration to circulation of the critical argument of the secular resonance 2 (g4 − g3) − (s4 − s3) related to the motions of perihelions and nodes of Earth and Mars.
1,084 citations
01 Jan 2003
TL;DR: In this article, the basic principles of direct chaotic communications are presented for modeling diversity by chaos and classification by synchronization in high-dimensional dynamical systems, including cycled attractors of coupled cell systems and dynamics with symmetry.
Abstract: Cycling attractors of coupled cell systems and dynamics with symmetry- Modelling diversity by chaos and classification by synchronization- Basic Principles of Direct Chaotic Communications- Prevalence of Milnor Attractors and Chaotic Itinerancy in 'High'-dimensional Dynamical Systems- Generalization of the Feigenbaum-Kadanoff-Shenker Renormalization and Critical Phenomena Associated with the Golden Mean Quasiperiodicity- Synchronization and clustering in ensembles of coupled chaotic oscillators- Nonlinear Phenomena in Nephron-Nephron Interaction- Synchrony in Globally Coupled Chaotic, Periodic, and Mixed Ensembles of Dynamical Units- Phase synchronization of regular and chaotic self-sustained oscillators- Control of dynamical systems via time-delayed feedback and unstable controller
1,081 citations