Neural Information Processing: between synchrony and chaos

The brain is characterized by performing many different processing tasks ranging from elaborate processes such as pattern recognition, memory or decision-making to more simple functionalities such as linear filtering in image processing. Understanding the mechanisms by which the brain is able to produce such a different range of cortical operations remains a fundamental problem in neuroscience. Some recent empirical and theoretical results support the notion that the brain is naturally poised between ordered and chaotic states. As the largest number of metastable states exists at a point near the transition, the brain therefore has access to a larger repertoire of behaviours. Consequently, it is of high interest to know which type of processing can be associated with both ordered and disordered states. Here we show an explanation of which processes are related to chaotic and synchronized states based on the study of in-silico implementation of biologically plausible neural systems. The measurements obtained reveal that synchronized cells (that can be understood as ordered states of the brain) are related to non-linear computations, while uncorrelated neural ensembles are excellent information transmission systems that are able to implement linear transformations (as the realization of convolution products) and to parallelize neural processes. From these results we propose a plausible meaning for Hebbian and non-Hebbian learning rules as those biophysical mechanisms by which the brain creates ordered or chaotic ensembles depending on the desired functionality. The measurements that we obtain from the hardware implementation of different neural systems endorse the fact that the brain is working with two different states, ordered and chaotic, with complementary functionalities that imply non-linear processing (synchronized states) and information transmission and convolution (chaotic states)

A pseudo-matched filter for chaos

A matched filter maximizes the signal-to-noise ratio of a signal. In the recent work of Corron et al. [Chaos 20, 023123 (2010)], a matched filter is derived for the chaotic waveforms produced by a piecewise-linear system. Motivated by these results, we describe a pseudo-matched filter, which removes noise from the same chaotic signal. It consists of a notch filter followed by a first-order, low-pass filter. We compare quantitatively the matched filter's performance to that of our pseudo-matched filter using correlation functions in a simulated radar application. On average, the pseudo-matched filter performs with a correlation signal-to-noise ratio that is 2.0 dB below that of the matched filter. Our pseudo-matched filter, though somewhat inferior in comparison to the matched filter, is easily realizable at high speed (> 1 GHz) for potential radar applications

Lag synchronization and scaling of chaotic attractor in coupled system

We report a design of delay coupling for lag synchronization in two unidirectionally coupled chaotic oscillators. A delay term is introduced in the definition of the coupling to target any desired lag between the driver and the response. The stability of the lag synchronization is ensured by using the Hurwitz matrix stability. We are able to scale up or down the size of a driver attractor at a response system in presence of a lag. This allows compensating the attenuation of the amplitude of a signal during transmission through a delay line. The delay coupling is illustrated with numerical examples of 3D systems, the Hindmarsh-Rose neuron model, the R\"ossler system and a Sprott system and, a 4D system. We implemented the coupling in electronic circuit to realize any desired lag synchronization in chaotic oscillators and scaling of attractors.Comment: 10 pages, 7 figure

Chaotic imaging in frequency downconversion

We analyze and realize the recovery, by means of spatial intensity correlations, of the image obtained by a seeded frequency downconversion process in which the seed field is chaotic and an intensity modulation is encoded on the pump field. Although the generated field is as chaotic as the seed field and does not carry any information about the modulation of the pump, an image of the pump can be extracted by measuring the spatial intensity correlations between the generated field and one Fourier component of the seed

Langevin approach to synchronization of hyperchaotic time-delay dynamics

In this paper, we characterize the synchronization phenomenon of hyperchaotic scalar non-linear delay dynamics in a fully-developed chaos regime. Our results rely on the observation that, in that regime, the stationary statistical properties of a class of hyperchaotic attractors can be reproduced with a linear Langevin equation, defined by replacing the non-linear delay force by a delta-correlated noise. Therefore, the synchronization phenomenon can be analytically characterized by a set of coupled Langevin equations. We apply this formalism to study anticipated synchronization dynamics subject to external noise fluctuations as well as for characterizing the effects of parameter mismatch in a hyperchaotic communication scheme. The same procedure is applied to second order differential delay equations associated to synchronization in electro-optical devices. In all cases, the departure with respect to perfect synchronization is measured through a similarity function. Numerical simulations in discrete maps associated to the hyperchaotic dynamics support the formalism.Comment: 12 pages, 6 figure

Periodic orbit quantization of chaotic systems with strong pruning

The three-disk system, which for many years has served as a paradigm for the usefulness of cycle expansion methods, represents an extremely hard problem to semiclassical quantization when the disks are moved closer and closer together, since (1) pruning of orbits sets in, rendering the symbolic code incomplete, and (2) the number of orbits necessary to obtain accurate semiclassical eigenvalues proliferates exponentially. In this note we show that an alternative method, viz. harmonic inversion, which does not rely on the existence of complete symbolic dynamics or other specific properties of systems, provides a key to solving the problem of semiclassical quantization of systems with strong pruning. For the closed three-disk system we demonstrate how harmonic inversion, augmented by a signal cross-correlation technique, allows one to semiclassically calculate the energies up to the 28th excited state with high accuracy.Comment: 9 pages, 3 figures, submitted to Phys. Lett.