1,511 research outputs found
Robust stability for stochastic Hopfield neural networks with time delays
This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2006 Elsevier Ltd.In this paper, the asymptotic stability analysis problem is considered for a class of uncertain stochastic neural networks with time delays and parameter uncertainties. The delays are time-invariant, and the uncertainties are norm-bounded that enter into all the network parameters. The aim of this paper is to establish easily verifiable conditions under which the delayed neural network is robustly asymptotically stable in the mean square for all admissible parameter uncertainties. By employing a Lyapunov–Krasovskii functional and conducting the stochastic analysis, a linear matrix inequality (LMI) approach is developed to derive the stability criteria. The proposed criteria can be checked readily by using some standard numerical packages, and no tuning of parameters is required. Examples are provided to demonstrate the effectiveness and applicability of the proposed criteria.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Nuffield Foundation of the UK under Grant NAL/00630/G, and the Alexander von Humboldt Foundation of German
Chaotic image encryption using hopfield and hindmarsh–rose neurons implemented on FPGA
Chaotic systems implemented by artificial neural networks are good candidates for data encryption. In this manner, this paper introduces the cryptographic application of the Hopfield and the Hindmarsh–Rose neurons. The contribution is focused on finding suitable coefficient values of the neurons to generate robust random binary sequences that can be used in image encryption. This task is performed by evaluating the bifurcation diagrams from which one chooses appropriate coefficient values of the mathematical models that produce high positive Lyapunov exponent and Kaplan–Yorke dimension values, which are computed using TISEAN. The randomness of both the Hopfield and the Hindmarsh–Rose neurons is evaluated from chaotic time series data by performing National Institute of Standard and Technology (NIST) tests. The implementation of both neurons is done using field-programmable gate arrays whose architectures are used to develop an encryption system for RGB images. The success of the encryption system is confirmed by performing correlation, histogram, variance, entropy, and Number of Pixel Change Rate (NPCR) tests
A "Cellular Neuronal" Approach to Optimization Problems
The Hopfield-Tank (1985) recurrent neural network architecture for the
Traveling Salesman Problem is generalized to a fully interconnected "cellular"
neural network of regular oscillators. Tours are defined by synchronization
patterns, allowing the simultaneous representation of all cyclic permutations
of a given tour. The network converges to local optima some of which correspond
to shortest-distance tours, as can be shown analytically in a stationary phase
approximation. Simulated annealing is required for global optimization, but the
stochastic element might be replaced by chaotic intermittency in a further
generalization of the architecture to a network of chaotic oscillators.Comment: -2nd revised version submitted to Chaos (original version submitted
6/07
A Survey on Continuous Time Computations
We provide an overview of theories of continuous time computation. These
theories allow us to understand both the hardness of questions related to
continuous time dynamical systems and the computational power of continuous
time analog models. We survey the existing models, summarizing results, and
point to relevant references in the literature
Unstable Dynamics, Nonequilibrium Phases and Criticality in Networked Excitable Media
Here we numerically study a model of excitable media, namely, a network with
occasionally quiet nodes and connection weights that vary with activity on a
short-time scale. Even in the absence of stimuli, this exhibits unstable
dynamics, nonequilibrium phases -including one in which the global activity
wanders irregularly among attractors- and 1/f noise while the system falls into
the most irregular behavior. A net result is resilience which results in an
efficient search in the model attractors space that can explain the origin of
certain phenomenology in neural, genetic and ill-condensed matter systems. By
extensive computer simulation we also address a relation previously conjectured
between observed power-law distributions and the occurrence of a "critical
state" during functionality of (e.g.) cortical networks, and describe the
precise nature of such criticality in the model.Comment: 18 pages, 9 figure
Delay-independent stability in bidirectional associative memory networks
It is shown that if the neuronal gains are small compared with the synaptic connection weights, then a bidirectional associative memory network with axonal signal transmission delays converges to the equilibria associated with exogenous inputs to the network. Both discrete and continuously distributed delays are considered; the asymptotic stability is global in the state space of neuronal activations and also is independent of the delays
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