Journal ArticleDOI
Letters: Chaos and transient chaos in simple Hopfield neural networks
Xiao-Song Yang,Quan Yuan +1 more
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A class of simple chaotic Hopfield neural networks is presented, and a bifurcation from transient chaos to chaos is discussed.About:
This article is published in Neurocomputing.The article was published on 2005-12-01. It has received 106 citations till now. The article focuses on the topics: Synchronization of chaos & Hopfield network.read more
Citations
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Hidden extreme multistability with hyperchaos and transient chaos in a Hopfield neural network affected by electromagnetic radiation
TL;DR: In this paper, the chaotic dynamics in a three-neuron-based Hopfield neural network (HNN) with stimulation of electromagnetic radiation is investigated, where the neural network is modeled by utilizing a flux-controlled memristor to describe the effects of electromagnetic field on neurons.
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H∞ synchronization of chaotic systems using output feedback control design
TL;DR: Based on Lyapunov theory, linear matrix inequality (LMI) and linear matrix equality (LME) formulation, the output feedback controller is established to not only guarantee stable synchronization of both master and slave systems but also reduce the effect of external disturbance to an H∞-norm constraint.
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Coexistence of Chaos with Hyperchaos, Period-3 Doubling Bifurcation, and Transient Chaos in the Hyperchaotic Oscillator with Gyrators
TL;DR: A new (smooth) mathematical model based on the Shockley diode equation is derived to explore the dynamics of the hyperchaotic oscillator with gyrators introduced by Tamasevicius and co-workers, suitable for integrated circuit implementation.
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Initial offset boosting coexisting attractors in memristive multi-double-scroll Hopfield neural network
TL;DR: This paper introduces a non-ideal flux-controlled memristor model into a Hopfield neural network (HNN), a novel memristive HNN model with multi-double-scroll attractors that has excellent randomness and is suitable for image encryption application.
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Influences of electromagnetic radiation distribution on chaotic dynamics of a neural network
Hairong Lin,Chunhua Wang +1 more
TL;DR: With the increasing of the number of neurons stimulated by electromagnetic radiation, the dynamics behaviors of the neural network gradually change from period moving to chaos, transient chaos and intricate hyperchaos, which could give new insights to understand the occurrence mechanism of some neuronal diseases.
References
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Book
Neurons with graded response have collective computational properties like those of two-state neurons
TL;DR: In this article, a model for a large network of "neurons" with a graded response (or sigmoid input-output relation) is studied, which has collective properties in very close correspondence with the earlier stochastic model based on McCulloch--Pitts neurons.
Book
Introduction to Applied Nonlinear Dynamical Systems and Chaos
TL;DR: The Poincare-Bendixson Theorem as mentioned in this paper describes the existence, uniqueness, differentiability, and flow properties of vector fields, and is used to prove that a dynamical system is Chaotic.
Journal ArticleDOI
Ergodic theory of chaos and strange attractors
Jean-Pierre Eckmann,David Ruelle +1 more
TL;DR: A review of the main mathematical ideas and their concrete implementation in analyzing experiments can be found in this paper, where the main subjects are the theory of dimensions (number of excited degrees of freedom), entropy (production of information), and characteristic exponents (describing sensitivity to initial conditions).
Book
Chaos in dynamical systems
TL;DR: In the new edition of this classic textbook, the most important change is the addition of a completely new chapter on control and synchronization of chaos as mentioned in this paper, which will be of interest to advanced undergraduates and graduate students in science, engineering and mathematics taking courses in chaotic dynamics, as well as to researchers in the subject.
Chaos in dynamical systems
TL;DR: In the new edition of this classic textbook, the most important change is the addition of a completely new chapter on control and synchronization of chaos as discussed by the authors, which will be of interest to advanced undergraduates and graduate students in science, engineering and mathematics taking courses in chaotic dynamics, as well as to researchers in the subject.