Evolution of avalanche conducting states in electrorheological liquids

Charge transport in electrorheological fluids is studied experimentally under strongly nonequlibrium conditions. By injecting an electrical current into a suspension of conducting nanoparticles we are able to initiate a process of self-organization which leads, in certain cases, to formation of a stable pattern which consists of continuous conducting chains of particles. The evolution of the dissipative state in such system is a complex process. It starts as an avalanche process characterized by nucleation, growth, and thermal destruction of such dissipative elements as continuous conducting chains of particles as well as electroconvective vortices. A power-law distribution of avalanche sizes and durations, observed at this stage of the evolution, indicates that the system is in a self-organized critical state. A sharp transition into an avalanche-free state with a stable pattern of conducting chains is observed when the power dissipated in the fluid reaches its maximum. We propose a simple evolution model which obeys the maximum power condition and also shows a power-law distribution of the avalanche sizes.Comment: 15 pages, 6 figure

On Synchronization in a Lattice Model of Pulse-Coupled Oscillators

We analyze the collective behavior of a lattice model of pulse-coupled oscillators. By means of computer simulations we find the relation between the intrinsic dynamics of each member of the population and their mutual interaction that ensures, in a general context, the existence of a fully synchronized regime. This condition turns out to be the same than the obtained for the globally coupled population. When the condition is not completely satisfied we find different spatial structures. This also gives some hints about self-organized criticality.Comment: 4 pages, RevTex, 1 PostScript available upon request, To appear in Phys. Rev. Let

Dynamic instabilities induced by asymmetric influence: Prisoners' dilemma game on small-world networks

A two-dimensional small-world type network, subject to spatial prisoners' dilemma dynamics and containing an influential node defined as a special node with a finite density of directed random links to the other nodes in the network, is numerically investigated. It is shown that the degree of cooperation does not remain at a steady state level but displays a punctuated equilibrium type behavior manifested by the existence of sudden breakdowns of cooperation. The breakdown of cooperation is linked to an imitation of a successful selfish strategy of the influential node. It is also found that while the breakdown of cooperation occurs suddenly, the recovery of it requires longer time. This recovery time may, depending on the degree of steady state cooperation, either increase or decrease with an increasing number of long range connections.Comment: 5 pages, 6 figure

How spiking neurons give rise to a temporal-feature map

A temporal-feature map is a topographic neuronal representation of temporal attributes of phenomena or objects that occur in the outside world. We explain the evolution of such maps by means of a spike-based Hebbian learning rule in conjunction with a presynaptically unspecific contribution in that, if a synapse changes, then all other synapses connected to the same axon change by a small fraction as well. The learning equation is solved for the case of an array of Poisson neurons. We discuss the evolution of a temporal-feature map and the synchronization of the single cells’ synaptic structures, in dependence upon the strength of presynaptic unspecific learning. We also give an upper bound for the magnitude of the presynaptic interaction by estimating its impact on the noise level of synaptic growth. Finally, we compare the results with those obtained from a learning equation for nonlinear neurons and show that synaptic structure formation may profit from the nonlinearity

Subthreshold Membrane-Potential Resonances Shape Spike-Train Patterns in the Entorhinal Cortex

Many neurons exhibit subthreshold membrane-potential resonances, such that the largest voltage responses occur at preferred stimulation frequencies. Because subthreshold resonances are known to influence the rhythmic activity at the network level, it is vital to understand how they affect spike generation on the single-cell level. We therefore investigated both resonant and nonresonant neurons of rat entorhinal cortex. A minimal resonate-and-fire type model based on measured physiological parameters captures fundamental properties of neuronal firing statistics surprisingly well and helps to shed light on the mechanisms that shape spike patterns: 1) subthreshold resonance together with a spike-induced reset of subthreshold oscillations leads to spike clustering and 2) spike-induced dynamics influence the fine structure of interspike interval (ISI) distributions and are responsible for ISI correlations appearing at higher firing rates (≥3 Hz). Both mechanisms are likely to account for the specific discharge characteristics of various cell types