We consider a classical space-clamped Hodgkin–Huxley (HH) model neuron stimulated by a current which has a mean μ together with additive Gaussian white noise of amplitude σ. A system of 14 deterministic first-order nonlinear differential equations is derived for the first- and second-order...

We consider a general nonlinear diffusion, typified by those deriving from Fitzhugh–Nagumo or Hindmarsh–Rose models of nerve-cell dynamics, perturbed also by 2-parameter white noise. In order to investigate the effects of the nonlinearity, we find for general boundary conditions the mean to...

The time to first spike is an experimentally observed quantity in laboratory experiments. In the auditory, somatic and visual sensory modalities, the times of first spikes in the corresponding cortical neurons have been implicated as coding much of the information about stimulus properties. We...

We consider a new and extended spatial neuron model in which the neuronal electrical depolarization from resting level satisfies a cable partial differential equation. The synaptic input current is also a function of space and time and satisfies a first order linear partial differential equation...

Purpose: This research explores how investment and central bankers cope with strategic uncertainty when they anticipate prices. The uncertainty originates from others' decisions and their consequences, and cannot be meaningfully reduced to risk. The authors postulate that, in order to cope with...

Levels of a complex system are characterized by the fact that they admit a closed functional description in terms of concepts and quantities intrinsic to that level. Several ideas have come up so far in order to make the notion of a closed description precise. In this paper, we present four of...

We introduce and study an evolutionary complementarity game where in each round a player of population 1 is paired with a member of population 2. The game is symmetric, and each player tries to obtain an advantageous deal, but when one of them pushes too hard, no deal at all can be concluded,...

We study the effect of learning dynamics on network topology. A network of discrete dynamical systems is considered for this purpose and the coupling strengths are made to evolve according to a temporal learning rule that is based on the paradigm of spike-time-dependent plasticity. This...

We develop an analysis of complex systems in terms of statistical correlations between the dynamics of its subsystems as a formal framework within which to understand processes of system differentiation.

We study the dynamics of the structure of a formal neural network wherein the strengths of the synapses are governed by spike-timing-dependent plasticity (STDP). For properly chosen input signals, there exists a steady state with a residual network. We compare the motif profile of such a network...