Generalized and partial synchronization of coupled neural networks

Pasemann, Frank; Wennekers, Thomas

doi:10.1088/0954-898x_11_1_303

Cited by 6 publications

(2 citation statements)

References 49 publications

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“…Using nonlinear synchronization as a formalization of complex interactions is intriguing with respect to information processing in the brain where oscillatory and synchronization phenomena are frequently reported [21]. Theoretical studies [12] also show the existence of generalized partial synchronization in a variety of artificial neural networks. In this context, Volterra series could be a natural model of neural transient interactions [6].…”

Section: Discussionmentioning

confidence: 99%

Statistical modeling approach for detecting generalized synchronization

2012

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Detecting nonlinear correlations between time series presents a hard problem for data analysis. We present a generative statistical modeling method for detecting nonlinear generalized synchronization. Truncated Volterra series are used to approximate functional interactions. The Volterra kernels are modeled as linear combinations of basis splines, whose coefficients are estimated via l1 and l2 regularized maximum likelihood regression. The regularization manages the high number of kernel coefficients and allows feature selection strategies yielding sparse models. The method's performance is evaluated on different coupled chaotic systems in various synchronization regimes and analytical results for detecting m:n phase synchrony are presented. Experimental applicability is demonstrated by detecting nonlinear interactions between neuronal local field potentials recorded in different parts of macaque visual cortex.

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Section: Discussionmentioning

confidence: 99%

Statistical modeling approach for detecting generalized synchronization

2012

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“…Then the bias terms can be arranged in such a way, so that this condition holds. This is the case, because neurons 2 and 3 are synchronized in the general sense [41]; i.e. This can be satisfied only if w 12 w 21 < 0 and/or w 13 w 23 < 0, and for respecting Dale's rule we choose w 21 , w 31 < 0.…”

Section: A 3-chain With Self-inhibiting Centre Neuronmentioning

confidence: 99%

Complex dynamics and the structure of small neural networks

Pasemann¹

2002

Network: Computation in Neural Systems

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The discrete-time dynamics of small neural networks is studied empirically, with emphasis laid on non-trivial bifurcation scenarios. For particular two- and three-neuron networks interesting dynamical properties like periodic, quasi-periodic and chaotic attractors are observed, many of them co-existing for one and the same set of parameters. An appropriate equivalence class of networks is defined, describing them as parametrized dynamical systems with identical dynamical capacities. Combined symmetries in phase space and parameter space are shown to generate different representatives of such a class. Moreover, conditions on the connectivity structure are suggested, which guarantee the existence of complex dynamics for a considered equivalence class of network configurations.

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Neurosemantics, neurons and system theory

Breidbach

2007

Theory Biosci.

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Following the concept of internal representations, signal processing in a neuronal system has to be evaluated exclusively based on internal system characteristics. Thus, this approach omits the external observer as a control function for sensory integration. Instead, the configuration of the system and its computational performance are the effects of endogenous factors. Such self-referential operation is due to a strictly local computation in a network and, thereby, computations follow a set of rules that constitute the emergent behaviour of the system. These rules can be shown to correspond to a "logic" that is intrinsic to the system, an idea which provides the basis for neurosemantics.

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Generalized and partial synchronization of coupled neural networks

Cited by 6 publications

References 49 publications

Statistical modeling approach for detecting generalized synchronization

Statistical modeling approach for detecting generalized synchronization

Complex dynamics and the structure of small neural networks

Neurosemantics, neurons and system theory

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