Control of low-dimensional spatiotemporal chaos in Fourier space

Lourenço, Carlos; Hougardy, Marc; Babloyantz, Agnessa

doi:10.1103/physreve.52.1528

Cited by 15 publications

(10 citation statements)

References 13 publications

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“…Yet, that was already the case with the Kuramoto-Sivashinsky partial differential equation investigated in [18]. In the present paper, the high dimensionality comes also from a spatial distribution, but especially from the presence of delay terms in the evolution equations.…”

Section: Let Us Consider a Poincaré Section Atmentioning

confidence: 50%

“…In view of the spatially correlated activity of the neurons, we adopt a spatial mode analysis that had already been useful with other extended systems such as physical systems described by partial differential equations [18]. However, here we are dealing with a spatially discrete system and hence we replace the integrals of [18] with finite sums.…”

Section: Looking At Spatial Modesmentioning

confidence: 99%

“…However, here we are dealing with a spatially discrete system and hence we replace the integrals of [18] with finite sums. As in [18], Fourier spatial modes are chosen for their convenience. The modes are monitored by computing their respective coefficients:…”

Section: Looking At Spatial Modesmentioning

confidence: 99%

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Dynamical computation reservoir emerging within a biological model network

Lourenço

2007

Neurocomputing

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Chaos in dynamical systems potentially provides many different dynamical states arising from a single attractor. We call this the reservoir property and give here a precise meaning to two aspects of such property. In both cases, the high flexibility of chaos comes into play, as compared to more regular regimes. In this article, we especially focus on the fact that chaotic attractors are known to possess an infinite number of embedded Unstable Periodic Orbits. In brain modeling, or for the purpose of suggesting computational devices that could take advantage of chaos, the different embedded dynamical states can be interpreted as different behaviors or computational modes suitable for particular tasks. Previously we proposed a rather abstract neural network model that mimicked cortex to some extent but where biological realism was not the major concern. In the present paper we show that the same potential for computation can be displayed by a more realistic neural model. The latter features spatiotemporal chaos of a type thus far only found in more "artificial" models. We also note that certain network-related properties, previously overlooked, turn out to be essential for the generation of complex behavior.

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Section: Let Us Consider a Poincaré Section Atmentioning

confidence: 50%

Section: Looking At Spatial Modesmentioning

confidence: 99%

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Dynamical computation reservoir emerging within a biological model network

Lourenço

2007

Neurocomputing

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“…Our approach does not require the existence of such a global parameter; rather it is based on applying OGY-like feedback perturbations to a single degree of freedom of the system [11], at a single point in space. The spatiotemporal system successfully controlled here seems to be significantly more complicated than the previously controlled discrete systems of coupled chaotic elements [4,6], or relatively simple or isotropic 1D or 2D systems of PDE's [3,5,7,8].…”

Section: (Received 28 March 1997)mentioning

confidence: 99%

“…There has been significant interest in recent years in the control of low-order chaotic dynamical systems using small systematic perturbations that lead to the stabilization of unstable periodic orbits (UPO) [1,2]. Controlling large-or infinite-dimensional systems, however, such as spatiotemporal systems that are governed by partial differential equations, is still in its infancy [3][4][5][6][7][8][9][10]. We present here a new approach to the control of spatiotemporal systems that are continuous in both space and time.…”

Section: (Received 28 March 1997)mentioning

confidence: 99%