Optimal size of a complex network

Two system-size-resonance behaviors for calcium signaling: for optimal cell size and for optimal network size

We have studied the collective calcium signaling behavior of an array of coupled N cells, taking into account the internal noises resulting from the small cell size V. The system's performance was characterized by the reciprocal coefficient of variance (RCV) of the calcium spike train. Two system-size resonances were observed, namely, the RCV value shows a clear peak when both N and V are optimal. Therefore, an optimal number of cells of optimal size work the best as a whole.

Internal signal transmission in one-way coupled excitable system: noise and coupling effects

We study the spatiotemporal dynamics of a one-way coupled FitzHugh-Nagumo system of twenty neurons, which is subject to external noise at the first neuron. It is shown that noise-induced oscillation (NIO) triggered at the first neuron is propagated along the chain with noise suppression, such that a rather "regular" signal is obtained at the last neuron, which can provide a mechanism for the creation of the informative signal in a neural network. Coherence resonance or coherence biresonance behavior appears in the transmission of NIO at appropriate coupling and the information flow in each neuron can be simultaneously optimized at the optimal value of noise.

Entropically enhanced excitability in small systems

We consider the dynamics of small excitable systems, ubiquitous in physics, chemistry, and biology. Spontaneous excitation rates induced by system-size fluctuations exhibit sharp maxima at multiple, small system sizes at which also the system's response to external perturbations is strongly enhanced. This novel effect is traced back to algebraic features of small integers and thus generic.

System-size resonance in a binary attractor neural network

System size resonance (SSR) is a phenomenon in which the response of a system is optimal for a certain finite size, but poorer as the size goes to zero or infinity. In order to show SSR effects in binary attractor neural networks, we study the response of a network, in the ferromagnetic phase, to an external, time-dependent stimulus. Under the presence of such a stimulus, the network shows SSR, as is demonstrated by the measure of the signal amplification both analytically and by simulation.