Excitation of coherent oscillations in a noisy medium.

We numerically study the influence of neuronal threshold modulation on the properties of cortical traveling waves. For that reason we simplify a Wilson-Cowan-type integrodifferential equation model of propagating neocortical activity to a spatially discrete version. Further we introduce a noisy threshold. Depending on the noise level we find different states of the network activity, ranging from asynchronous oscillations, traveling waves, to synchronous oscillations. Finally, we induce the transition between these different states by an external modulation.

Stochastic gain in finite populations.

Flexible learning rates can lead to increased payoffs under the influence of noise. In a previous paper [Traulsen, Phys. Rev. Lett. 93, 028701 (2004)], we have demonstrated this effect based on a replicator dynamics model which is subject to external noise. Here, we utilize recent advances on finite population dynamics and their connection to the replicator equation to extend our findings and demonstrate the stochastic gain effect in finite population systems. Finite population dynamics is inherently stochastic, depending on the population size and the intensity of selection, which measures the balance between the deterministic and the stochastic parts of the dynamics. This internal noise can be exploited by a population using an appropriate microscopic update process, even if learning rates are constant.

Impact of fraud on the mean-field dynamics of cooperative social systems.

The evolution of costly cooperation between selfish individuals seems to contradict Darwinian selection, as it reduces the fitness of a cooperating individual. However, several mechanisms such as repeated interactions or spatial structure can lead to the evolution of cooperation. One such mechanism for the evolution of cooperation, in particular among humans, is indirect reciprocity, in which individuals base their decision to cooperate on the reputation of the potential receiver, which has been established in previous interactions. Cooperation can evolve in these systems if individuals preferably cooperate with those that have shown to be cooperative in the past. We analyze the impact of fake reputations or fraud on the dynamics of reputation and on the success of the reputation system itself, using a mean-field description for evolutionary games given by the replicator equation. This allows us to classify the qualitative dynamics of our model analytically. Our results show that cooperation based on indirect reciprocity is robust with respect to fake reputations and can even be enhanced by them. We conclude that fraud per se does not necessarily have a detrimental effect on social systems.

Role of inhibitory feedback for information processing in thalamocortical circuits.

The information transfer in the thalamus is blocked dynamically during sleep, in conjunction with the occurrence of spindle waves. In order to describe the dynamic mechanisms which control the sensory transfer of information, it is necessary to have a qualitative model for the response properties of thalamic neurons. As the theoretical understanding of the mechanism remains incomplete, we analyze two modeling approaches for a recent experiment by Le Masson et al. [Nature (London) 417, 854 (2002)] on the thalamocortical loop. We use a conductance based model in order to motivate an extension of the Hindmarsh-Rose model, which mimics experimental observations of Le Masson et al. Typically, thalamic neurons possess two different firing modes, depending on their membrane potential. At depolarized potentials, the cells fire in a single spike mode and relay synaptic inputs in a one-to-one manner to the cortex. If the cell gets hyperpolarized, T-type calcium currents generate burst-mode firing which leads to a decrease in the spike transfer. In thalamocortical circuits, the cell membrane gets hyperpolarized by recurrent inhibitory feedback loops. In the case of reciprocally coupled excitatory and inhibitory neurons, inhibitory feedback leads to metastable self-sustained oscillations, which mask the incoming input, and thereby reduce the information transfer significantly.

Improved control of delayed measured systems.

In this paper, we address the question of how the control of delayed measured chaotic systems can be improved. Both unmodified Ott-Grebogi-Yorke control and difference control can be successfully applied only for a certain range of Lyapunov numbers depending on the delay time. We show that this limitation can be overcome by at least two classes of methods, namely, by rhythmic control and by the memory methods of linear predictive logging control and memory difference control.

Minimal model for tag-based cooperation.

Recently, Riolo et al. [Nature (London) 414, 441 (2001)] showed by computer simulations that cooperation can arise without reciprocity when agents donate only to partners who are sufficiently similar to themselves. One striking outcome of their simulations was the observation that the number of tolerant agents that support a wide range of players was not constant in time, but showed characteristic fluctuations. The cause and robustness of these tides of tolerance remained to be explored. Here we clarify the situation by solving a minimal version of the model of Riolo et al. It allows us to identify a net surplus of random changes from intolerant to tolerant agents as a necessary mechanism that produces these oscillations of tolerance, which segregate different agents in time. This provides a new mechanism for maintaining different agents, i.e., for creating biodiversity. In our model the transition to the oscillating state is caused by a saddle node bifurcation. The frequency of the oscillations increases linearly with the transition rate from tolerant to intolerant agents.

Simple model for 1/f(alpha) noise.

We present a simple stochastic mechanism which generates pulse trains exhibiting a power-law distribution of the pulse intervals and a 1/f(alpha) power spectrum over several decades at low frequencies with alpha close to 1. The essential ingredient of our model is a fluctuating threshold which performs a Brownian motion. Whenever an increasing potential V(t) hits the threshold, V(t) is reset to the origin and a pulse is emitted. We show that if V(t) increases linearly in time, the pulse intervals can be approximated by a random walk with multiplicative noise. Our model agrees with recent experiments in neurobiology and explains the high interpulse interval variability and the occurrence of 1/f(alpha) noise observed in cortical neurons and earthquake data.

Sierpinski signal generates 1/f alpha spectra.

We investigate the row sum of the binary pattern generated by the Sierpinski automaton: Interpreted as a time series we calculate the power spectrum of this Sierpinski signal analytically and obtain a unique rugged fine structure with underlying power law decay with an exponent of approximately 1.15. Despite the simplicity of the model, it can serve as a model for 1/f(alpha) spectra in a certain class of experimental and natural systems such as catalytic reactions and mollusc patterns.

Corticothalamic projections control synchronization in locally coupled bistable thalamic oscillators.

Thalamic circuits are able to generate state-dependent oscillations of different frequencies and degrees of synchronization. However, little is known about how synchronous oscillations, such as spindle oscillations in the thalamus, are organized in the intact brain. Experimental findings suggest that the simultaneous occurrence of spindle oscillations over widespread territories of the thalamus is due to the corticothalamic projections, as the synchrony is lost in the decorticated thalamus. In this Letter we study the influence of corticothalamic projections on the synchrony in a thalamic network, and uncover the underlying control mechanism, leading to a control method which is applicable for several types of oscillations in the central nervous system.

Stochastic gain in population dynamics.

We introduce an extension of the usual replicator dynamics to adaptive learning rates. We show that a population with a dynamic learning rate can gain an increased average payoff in transient phases and can also exploit external noise, leading the system away from the Nash equilibrium, in a resonancelike fashion. The payoff versus noise curve resembles the signal to noise ratio curve in stochastic resonance. Seen in this broad context, we introduce another mechanism that exploits fluctuations in order to improve properties of the system. Such a mechanism could be of particular interest in economic systems.