No abstract

We investigate the dynamical states of a two-dimensional network of Hindmarsh-Rose spiking neurons, in the vicinity of the current threshold where the single neuron becomes active. Each neuron is electrically coupled with neurons in its close neighborhood. The existence of multistable synchronization states is established and discussed. We also show that, provided adequate initial conditions, the collective behavior is able to keep the network in activity, even for current values far below the activity threshold of the single neuron. A phase diagram of the different network states is presented for a large interval of the coupling-current parameter space.

The retrieval behavior and thermodynamic properties of symmetrically diluted Q-Ising neural networks are derived and studied in replica-symmetric mean-field theory generalizing earlier works on either the fully connected or the symmetrical extremely diluted network. Capacity-gain parameter phase diagrams are obtained for the Q = 3, Q = 4 and Q = ∞ state networks with uniformly distributed patterns of low activity in order to search for the effects of a gradual dilution of the synapses. It is shown that enlarged regions of continuous changeover into a region of optimal performance are obtained for finite stochastic noise and small but finite connectivity. The de Almeida-Thouless lines of stability are obtained for arbitrary connectivity, and the resulting phase diagrams are used to draw conclusions on the behavior of symmetrically diluted networks with other pattern distributions of either high or low activity.

We show that the breaking of the rotation symmetry of spiral waves in two-dimensional complex (period-doubled or chaotic) oscillatory media by synchronization defect lines (SDLs) is accompanied by an intrinsic drift of the pattern. Single vortex motion changes from ballistic flights at a well-defined angle from the SDLs to Brownian-like diffusion when the turbulent character of the medium increases. It gives rise, in nonturbulent multispiral regimes, to a novel "vortex liquid."

In the present paper we investigate the process of energy transfer in the Zakharov equations. Energy is initially injected into modes with small wave vectors. When the modulational instability threshold is exceeded, some additional modes with small wave vectors are excited and solitons are formed if one lies in a quasiintegrable regime and if the number of excited modes is large enough. These solitons are formed as a direct result of the modulational instability and in fact saturate the instability. However, use of a low-dimensional formalism based on collective variables shows that if the largest length scale of the linearly excited modes is much longer than the most unstable, these solitons may be greatly influenced as they interact with ion-acoustic waves. In those cases, full simulation of the space-time problem indicates that energy is progressively transferred to modes with very small length scales. Since we work with one spatial dimension, collapse is absent and energy transfer is due to the stochastic dynamics. ͓S1063-651X͑98͒02303-4͔ PACS number͑s͒: 05.45.ϩb, 52.35.Ra