2,870 research outputs found
Modelling and control of chaotic processes through their Bifurcation Diagrams generated with the help of Recurrent Neural Network models: Part 1—simulation studies
Many real-world processes tend to be chaotic and also do not lead to satisfactory analytical modelling. It has been shown here that for such chaotic processes represented through short chaotic noisy time-series, a multi-input and multi-output recurrent neural networks model can be built which is capable of capturing the process trends and predicting the future values from any given starting condition. It is further shown that this capability can be achieved by the Recurrent Neural Network model when it is trained to very low value of mean squared error. Such a model can then be used for constructing the Bifurcation Diagram of the process leading to determination of desirable operating conditions. Further, this multi-input and multi-output model makes the process accessible for control using open-loop/closed-loop approaches or bifurcation control etc. All these studies have been carried out using a low dimensional discrete chaotic system of Hénon Map as a representative of some real-world processes
Stability analysis of impulsive stochastic Cohen–Grossberg neural networks with mixed time delays
This is the post print version of the article. The official published version can be obtained from the link - Copyright 2008 Elsevier LtdIn this paper, the problem of stability analysis for a class of impulsive stochastic Cohen–Grossberg neural networks with mixed delays is considered. The mixed time delays comprise both the time-varying and infinite distributed delays. By employing a combination of the M-matrix theory and stochastic analysis technique, a sufficient condition is obtained to ensure the existence, uniqueness, and exponential p-stability of the equilibrium point for the addressed impulsive stochastic Cohen–Grossberg neural network with mixed delays. The proposed method, which does not make use of the Lyapunov functional, is shown to be simple yet effective for analyzing the stability of impulsive or stochastic neural networks with variable and/or distributed delays. We then extend our main results to the case where the parameters contain interval uncertainties. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. An example is given to show the effectiveness of the obtained results.This work was supported by the Natural Science Foundation of CQ CSTC under grant 2007BB0430, the Scientific Research Fund of Chongqing Municipal Education Commission under Grant KJ070401, an International Joint Project sponsored by the Royal Society of the UK and the National Natural Science Foundation of China, and the Alexander von Humboldt Foundation of Germany
Regular graphs maximize the variability of random neural networks
In this work we study the dynamics of systems composed of numerous
interacting elements interconnected through a random weighted directed graph,
such as models of random neural networks. We develop an original theoretical
approach based on a combination of a classical mean-field theory originally
developed in the context of dynamical spin-glass models, and the heterogeneous
mean-field theory developed to study epidemic propagation on graphs. Our main
result is that, surprisingly, increasing the variance of the in-degree
distribution does not result in a more variable dynamical behavior, but on the
contrary that the most variable behaviors are obtained in the regular graph
setting. We further study how the dynamical complexity of the attractors is
influenced by the statistical properties of the in-degree distribution
Almost periodic solutions of retarded SICNNs with functional response on piecewise constant argument
We consider a new model for shunting inhibitory cellular neural networks,
retarded functional differential equations with piecewise constant argument.
The existence and exponential stability of almost periodic solutions are
investigated. An illustrative example is provided.Comment: 24 pages, 1 figur
pth moment exponential stability of stochastic fuzzy Cohen–Grossberg neural networks with discrete and distributed delays
In this paper, stochastic fuzzy Cohen–Grossberg neural networks with discrete and distributed delays are investigated. By using Lyapunov function and the Ito differential formula, some sufficient conditions for the pth moment exponential stability of such stochastic fuzzy Cohen–Grossberg neural networks with discrete and distributed delays are established. An example is given to illustrate the feasibility of our main theoretical findings. Finally, the paper ends with a brief conclusion. Methodology and achieved results is to be presented
Toward a dynamical systems analysis of neuromodulation
This work presents some first steps toward a
more thorough understanding of the control systems
employed in evolutionary robotics. In order
to choose an appropriate architecture or to construct
an effective novel control system we need
insights into what makes control systems successful,
robust, evolvable, etc. Here we present analysis
intended to shed light on this type of question
as it applies to a novel class of artificial neural
networks that include a neuromodulatory mechanism:
GasNets.
We begin by instantiating a particular GasNet
subcircuit responsible for tuneable pattern generation
and thought to underpin the attractive
property of “temporal adaptivity”. Rather than
work within the GasNet formalism, we develop an
extension of the well-known FitzHugh-Nagumo
equations. The continuous nature of our model
allows us to conduct a thorough dynamical systems
analysis and to draw parallels between this
subcircuit and beating/bursting phenomena reported
in the neuroscience literature.
We then proceed to explore the effects of different
types of parameter modulation on the system
dynamics. We conclude that while there are
key differences between the gain modulation used
in the GasNet and alternative schemes (including
threshold modulation of more traditional synaptic
input), both approaches are able to produce
tuneable pattern generation. While it appears, at
least in this study, that the GasNet’s gain modulation
may not be crucial to pattern generation ,
we go on to suggest some possible advantages it
could confer
- …