## Synchronous Chaos in Highdimensional Modular Neural Networks (1996)

Venue: | Int. J. Bifurcat. Chaos |

Citations: | 5 - 5 self |

### BibTeX

@ARTICLE{Wennekers96synchronouschaos,

author = {Thomas Wennekers and Abteilung Neuroinformatik and D- Ulm and Frank Pasemann},

title = {Synchronous Chaos in Highdimensional Modular Neural Networks},

journal = {Int. J. Bifurcat. Chaos},

year = {1996},

volume = {6},

pages = {2055--2067}

}

### OpenURL

### Abstract

The relationship between certain types of highdimensional neural networks and low-dimensional prototypical equations (neuromodules) is investigated. The high-dimensional systems consist of nitely many pools containing identical, dissipative and nonlinear single-units operating in discrete time. Under the assumption of random connections inside and between pools, the system can be reduced to a set of only a few equations, which - asymptotically in time and system size - describe the behavior of every single unit arbitrarily well. This result can be viewed as synchronization of the single units in each pool. It is stated as a theorem on systems of nonlinear coupled maps, which gives explicit conditions on the single unit dynamics and the nature of the random connections. As an application we compare a 2-pool network with the corresponding 2-dimensional dynamics. The bifurcation diagrams of both systems become very similar even for moderate system size (N=50) and large disor...