A Novel Chaotic Neural Network Architecture (original) (raw)

Attractor Switching by Neural Control of Chaotic Neurodynamics

Network: Computation in Neural Systems, 9, 1998

Chaotic attractors of discrete-time neural networks include infinitely many unstable periodic orbits, which can be stabilized by small parameter changes in a feedback control. Here we explore the control of unstable peri- odic orbits in a chaotic neural network with only two neurons. Analytically a local control algorithm is derived on the basis of least squares minimiza- tion of the future deviations between actual system states and the desired orbit. This delayed control allows a consistent neural implementation, i.e. the same types of neurons are used for chaotic and controlling modules. The control signal is realized with one layer of neurons, allowing selective switching between different stabilized periodic orbits. For chaotic modules with noise random switching between different periodic orbits is observed.

Control of chaos in delay differential equations, in a network of oscillators and in model cortex

Physica D-nonlinear Phenomena, 1995

We extend the Ott-Grebogi-Yorke method to the stabilization of unstable orbits in a network of oscillators exhibiting spatiotemporal chaotic activity, wherein the perturbation is applied to the variables of the system. With the help of numerical simulations we show that a method developed by Pyragas can stabilize unstable orbits in a one variable delay differential equation and in a model cortical network with delay. We discuss the relevance of these results in the physiological processes of the brain. 0167-2789/95/$09.50 (~) 1995 Elsevier Science B.V. All rights reserved SSD1 0167-2789(95) 00108-5

An adaptive chaotic neural network

2002

Abstract The non-linear dynamics of a chaotic attractor offer a number of useful features to the developer of neuromorphic systems. Included in these is the ability for efficient memory storage and recall. A chaotic attractor has a potentially infinite number of unstable periodic orbits (UPO) embedded within it. These orbits can be stabilised with the application of delayed feedback inhibition. This research investigates the possibility of using such delayed feedback in a network to stabilise different UPOs in response to disparate input stimuli.

Adaptive targeting of chaotic response in periodically stimulated neural systems

Chaos: An Interdisciplinary Journal of Nonlinear Science, 2006

We demonstrate a technique for the enhancement of chaos in a computational model of a periodically stimulated excitable neuron. "Anticontrol" of chaos is achieved through intermittent adaptive intervention, which is based on finite-time Lyapunov exponents measured from the time series. Our results suggest that an adaptive strategy for chaos anticontrol is viable for increasing the complexity in physiological systems that are typically both noisy and nonstationary.

Control of Chaos in Networks with Delay: A Model for Synchronization of Cortical Tissue

Neural Computation, 1994

The unstable periodic orbits of chaotic dynamics in systems described by delay differential equations are considered. An orbit is stabilized successfully, using a method proposed by Pyragas. The system under investigation is a network of excitatory and inhibitory neurons of moderate size, describing cortical activity. The relevance of the results for synchronized cortical activity is discussed.

Controlling Chaos using adaptive weights in an Oscillatory Neural Network

The complex Hopfield neural network (CHNN)[1,2], which is an extension of the Hopfield Neural Network from real number domain to complex number domain, exhibits both fixed point and oscillatory behavior. It may be used as an associative memory in which patterns are stored as stable oscillations. Perfect retrieval is observed when only a single pattern is stored. However, when multiple patterns are stored, the network often wanders from one stored pattern to another without settling on any single pattern. This chaotic behavior, characteristic of a large network of nonlinear oscillators, results in unacceptably low storage capacity. We found that using weights that adapt even during retrieval can alleviate this problem. Simulations show that using adaptive weights dramatically enhances network capacity. This goes against the fundamental tenet of connectionism according to which weights are supposed to encode the information contained in the network, and must be held constant once training/storage is completed. The work gives rise to a novel view of the weights as transient, intermediate variables -the information which is traditionally supposed to be held in the weights is now imagined to be held in a longer-term memory store. Implications of the current work to neurophysiology are briefly considered.

Dynamics of neural systems with time delays

2017

Complex networks are ubiquitous in nature. Numerous neurological diseases, such as Alzheimer's, Parkinson's, epilepsy are caused by the abnormal collective behaviour of neurons in the brain. In particular, there is a strong evidence that Parkinson's disease is caused by the synchronisation of neurons, and understanding how and why such synchronisation occurs will bring scientists closer to the design and implementation of appropriate control to support desynchronisation required for the normal functioning of the brain. In order to study the emergence of (de)synchronisation, it is necessary first to understand how the dynamical behaviour of the system under consideration depends on the changes in systems parameters. This can be done using a powerful mathematical method, called bifurcation analysis, which allows one to identify and classify different dynamical regimes, such as, for example, stable/unstable steady states, Hopf and fold bifurcations, and find periodic soluti...

Time-Delayed Feedback in a Net of Neural Elements: Transition from Oscillatory to Excitable Dynamics

Fluctuation and Noise Letters, 2007

The influence of time-delayed feedback on the dynamics of a net of oscillatory FitzHugh-Nagumo elements is investigated. We show that the global oscillation of the net can be suppressed (amplitude death) via time-delayed feedback for properly chosen delay time and feedback strength. The result of a linear stability analysis fits very well to the simulations. In the amplitude death regime, weak additive noise can induce excitation waves (noise-induced pattern formation), a fingerprint of excitable network dynamics.

Feedback Control Tames Disorder in Attractor Neural Networks

Proceedings of the International Joint Conference on Computational Intelligence, 2009

Typical attractor neural networks (ANN) used to model associative memories behave like disordered systems, as the asymptotic state of their dynamics depends in a crucial (and often unpredictable) way on the chosen initial state. In this paper we suggest that this circumstance occurs only when we deal with such ANN as isolated systems. If we introduce a suitable control, coming from the interaction with a reactive external environment, then the disordered nature of ANN dynamics can be reduced, or even disappear. To support this claim we resort to a simple example based on a version of Hopfield autoassociative memory model interacting with an external environment which modifies the network weights as a function of the equilibrium state coming from retrieval dynamics.