Complex dynamics in one‐dimensional CNNs

SUMMARYA couple of iterative models for the theoretical study of fractal networks whose topologies are generated via iterated function systems is presented: a lumped-parameter impedor-oriented one and a two-portnetwork-oriented one. With the former, the voltage and current patterns give a detailed understanding of the electromagnetic fields' self-similar distribution throughout the network; on the other hand, model complexity exponentially increases with the prefractal iteration order. The latter 'black-box' model only controls port-oriented global parameters that are the ones commonly used in the integration of different electronic systems, and its complexity is independent of prefractal order. Sierpinski gasket and carpet topologies are reported as examples.

Section: From Incidence To Admittancesmentioning

confidence: 99%

On models of fractal networks

Arrighetti

Cupis

Gerosa

2008

“…Different CNN models showing this type of complexity are known and various techniques for their analysis have been derived, see e.g. [18][19][20][21][22]. As an example of spiral wave generation, let us check the system composed by oscillatory cells with the following parameters: Note that condition in Equation (10) .…”

Section: Reaction-diffusion Oscillatory Cnnmentioning

confidence: 99%

Awakening dynamics via passive coupling and synchronization mechanism in oscillatory cellular neural/nonlinear networks

Szatmári

Chua

2008

SUMMARYWe have studied synchronization mechanism in locally coupled nonlinear oscillators. Here, synchronization takes place by passive coupling based on a reaction-diffusion process. We will compare this mechanism with basic synchronization techniques, showing their similarities and specific properties. In addition to synchronization, passive and local coupling can also 'awaken' non-oscillating cell circuits and trigger oscillation, provided that cells are locally active. This result resembles Turing's and Smale's works showing that locally communicating simple elements can produce very different patterns even if separate elements do not show any activity. This property will be demonstrated for two second-order cells and also for a large ensemble of oscillatory cells. In latter case, the network of oscillatory cells exhibits very sophisticated spatio-temporal waves, e.g. spiral waves.

“…Therefore, an initial state and boundary conditions have to be specified. It has been shown in several publications that even comparatively simple CNNs exhibit various complex phenomena such as pattern formation and chaos [11,33,34].…”

Section: Cellular Nonlinear Networkmentioning

confidence: 99%

Toward an autonomous platform for spatio‐temporal EEG‐signal analysis based on cellular nonlinear networks

Gollas

Niederhofer

Tetzlaff

2008

SUMMARYAlthough in the field of epileptic seizure prediction many spatio-temporal approaches have been carried out, the precursor detection problem remains unsolved up to now. It can be observed that an increasing number of algorithms are developed based on cellular nonlinear networks (CNNs). They are dealing with the extraction of signal features using intracranial EEG recordings in order to detect possible preseizure states. In general, reliable precursor detections cannot be obtained for all treated cases. The performance of these algorithms can be enhanced by adapting them to specific patients. Combining different features in a feature vector in a future seizure anticipation platform may lead to a reliably working seizure prediction system.In this contribution we focus on two different CNN-based algorithms-a nonlinear identification approach and a prediction algorithm. They will be discussed in detail and recently obtained results will be given.