Storing cycles in Hopfield-type networks with pseudoinverse learning rule: admissibility and network topology.

Cyclic patterns of neuronal activity are ubiquitous in animal nervous systems, and partially responsible for generating and controlling rhythmic movements such as locomotion, respiration, swallowing and so on. Clarifying the role of the network connectivities for generating cyclic patterns is fundamental for understanding the generation of rhythmic movements. In this paper, the storage of binary cycles in Hopfield-type and other neural networks is investigated.

Steady state-Hopf mode interactions at the onset of electroconvection in the nematic liquid crystal Phase V.

We report on a new mode interaction found in electroconvection experiments on the nematic liquid crystal mixture Phase V in planar geometry. The mode interaction (codimension two) point occurs at a critical value of the frequency of the driving AC voltage. For frequencies below this value the primary pattern-forming instability at the onset voltage is an oblique stationary instability involving oblique rolls, and above this value it is an oscillatory instability giving rise to normal traveling rolls (oriented perpendicular to and traveling in the director direction).

Quantitative and qualitative characterization of zigzag spatiotemporal chaos in a system of amplitude equations for nematic electroconvection.

It has been suggested by experimentalists that a weakly nonlinear analysis of the recently introduced equations of motion for the nematic electroconvection by M. Treiber and L. Kramer [Phys.

Parametrically forced pattern formation.

Pattern formation in a nonlinear damped Mathieu-type partial differential equation defined on one space variable is analyzed. A bifurcation analysis of an averaged equation is performed and compared to full numerical simulations. Parametric resonance leads to periodically varying patterns whose spatial structure is determined by amplitude and detuning of the periodic forcing.