The Lorenz attractor was introduced in 1963 by E. N. Lorenz as one of the first examples of strange attractors. However Lorenz’ research was mainly based on (non-rigourous) numerical simulations and, until recently, the proof of the existence of the Lorenz attractor remained elusive. To address that problem some authors introduced geometric Lorenz models and proved that geometric Lorenz models ...

We investigate a population dynamics model that exhibits a Neimark-Sacker bifurcation with a period that is naturally close to 4. Beyond the bifurcation, the period soon becomes locked at 4 due to a strong resonance, and a second attractor of period 2 emerges, which coexists with the first attractor over a considerable parameter range. A linear stability analysis and a numerical investigation o...

The autoassociative memory model of hippocampal field CA3 postulates that Hebbian associations among external input features produce attractor states embedded in a recurrent synaptic matrix. In contrast, the attractor-map model postulates that a two-dimensional continuum of attractor states is preconfigured in the network during development and that transitions among these states are governed p...

Attractor networks are a popular computational construct used to model different brain systems. These networks allow elegant computations that are thought to represent a number of aspects of brain function. Although there is good reason to believe that the brain displays attractor dynamics, it has proven difficult to test experimentally whether any particular attractor architecture resides in a...

Line attractor networks have long served as the standard model of short-term memory systems for analogue variables. In this study, we investigate the stability of attractor states for a line attractor with monotonic tuning curves. We furthermore quantify the stability of network states against noise and show how the lifetime of short-term memory states depends on the level of neural noise.

Representation error arises from the inability of the forecast model to accurately simulate the climatology of the truth. We present a rigorous framework for understanding this kind of error of representation. This framework shows that the lack of an inverse in the relationship between the true climatology (true attractor) and the forecast climatology (forecast attractor) leads to the error of ...

Attractor networks, which map an input space to a discrete output space, are useful for pattern completion—cleaning up noisy or missing input features. However, designing a net to have a given set of attractors is notoriously tricky; training procedures are CPU intensive and often produce spurious attractors and ill-conditioned attractor basins. These difficulties occur because each connection ...