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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TL;DR: The authors describe the conditions necessary for synchronizing a subsystem of one chaotic system with a separate chaotic system by sending a signal from the chaotic system to the subsystem by sending signals from the Chaos Junction.
Abstract: The authors describe the conditions necessary for synchronizing a subsystem of one chaotic system with a separate chaotic system by sending a signal from the chaotic system to the subsystem. The general scheme for creating synchronizing systems is to take a nonlinear system, duplicate some subsystem of this system, and drive the duplicate and the original subsystem with signals from the unduplicated part. This is a generalization of driving or forcing a system. The process can be visualized with ordinary differential equations. The authors have build a simple circuit based on chaotic circuits described by R. W. Newcomb et al. (1983, 1986), and they use this circuit to demonstrate this chaotic synchronization. >
1,234 citations
TL;DR: In this paper, the generalized stability theory of the synchronized motions of the coupled oscillator systems was developed with the use of the extended Lyapunov matrix approach, and the explicit formula for a stability parameter was given.
Abstract: The general stability theory of the synchronized motions of the coupled· oscillator systems is developed with the use of the extended Lyapunov matrix approach. We give the explicit formula for a stability parameter of the synchronized state W unlfWhen the coupling strength is weakened, the coupled system may exhibit several types of non· synchronized motion. In particular, if W Unlf is chaotic, we always get a transition from chaotic Wunlf to a certain non· uniform state and finally the non·uniform chaos. Details associated with such transition are investigated for the coupled Lorenz model. As an application of the theory, we propose a new experimental method to directly measure the positive Lyapunov exponent of intrinsic chaos in reaction systems.
1,167 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