Coherence resonance induced by rewiring in complex networks

Network rewiring and plasticity promotes synchronization of suprachiasmatic nucleus neurons

In mammals, circadian rhythms throughout the body are orchestrated by the master clock in the hypothalamic suprachiasmatic nucleus (SCN), where SCN neurons are coupled with neurotransmitters to generate a uniform circadian rhythm. How the SCN circadian rhythm is so robust and flexible is, however, unclear. In this paper, we propose a temporal SCN network model and investigate the effects of dynamical rewiring and flexible coupling due to synaptic plasticity on the synchronization of the neural network in SCN. In networks consisting of simple Poincaré oscillators and complex circadian clocks, we found that dynamical rewiring and coupling plasticity enhance the synchronization in inhomogeneous networks. We verified the effect of enhanced synchronization in different architectures of random, scale-free, and small-world networks. A simple mean-field analysis for synchronization in plastic networks is proposed. Intuitively, the synchronization is greatly enhanced because both the random rewiring and coupling plasticity in the heterogeneous network have effectively increased the coupling strength in the whole network. Our results suggest that a proper network model for the master SCN circadian rhythm needs to take into account the effects of dynamical changes in topology and plasticity in neuron interactions that could help the brain to generate a robust circadian rhythm for the whole body.

Enhanced corticomuscular coherence by external stochastic noise

Noise can have beneficial effects as shown by the stochastic resonance (SR) phenomenon which is characterized by performance improvement when an optimal noise is added. Modern attempts to improve human performance utilize this phenomenon. The purpose of the present study was to investigate whether performance improvement by addition of optimum noise (ON) is related to increased cortical motor spectral power (SP) and increased corticomuscular coherence. Eight subjects performed a visuomotor task requiring to compensate with the right index finger a static force (SF) generated by a manipulandum on which Gaussian noise was applied. The finger position was displayed on-line on a monitor as a small white dot which the subjects had to maintain in the center of a green bigger circle. Electroencephalogram from the contralateral motor area, electromyogram from active muscles and finger position were recorded. The performance was measured by the mean absolute deviation (MAD) of the white dot from the zero position. ON compared to the zero noise condition induced an improvement in motor accuracy together with an enhancement of cortical motor SP and corticomuscular coherence in beta-range. These data suggest that the improved sensorimotor performance via SR is consistent with an increase in the cortical motor SP and in the corticomuscular coherence.

Quantifying the dynamics of coupled networks of switches and oscillators

Complex network dynamics have been analyzed with models of systems of coupled switches or systems of coupled oscillators. However, many complex systems are composed of components with diverse dynamics whose interactions drive the system's evolution. We, therefore, introduce a new modeling framework that describes the dynamics of networks composed of both oscillators and switches. Both oscillator synchronization and switch stability are preserved in these heterogeneous, coupled networks. Furthermore, this model recapitulates the qualitative dynamics for the yeast cell cycle consistent with the hypothesized dynamics resulting from decomposition of the regulatory network into dynamic motifs. Introducing feedback into the cell-cycle network induces qualitative dynamics analogous to limitless replicative potential that is a hallmark of cancer. As a result, the proposed model of switch and oscillator coupling provides the ability to incorporate mechanisms that underlie the synchronized stimulus response ubiquitous in biochemical systems.

Self-organized network of phase oscillators coupled by activity-dependent interactions

We investigate a network of coupled phase oscillators whose interactions evolve dynamically depending on the relative phases between the oscillators. We found that this coevolving dynamical system robustly yields three basic states of collective behavior with their self-organized interactions. The first is the two-cluster state, in which the oscillators are organized into two synchronized groups. The second is the coherent state, in which the oscillators are arranged sequentially in time. The third is the chaotic state, in which the relative phases between oscillators and their coupling weights are chaotically shuffled. Furthermore, we demonstrate that self-assembled multiclusters can be designed by controlling the weight dynamics. Note that the phase patterns of the oscillators and the weighted network of interactions between them are simultaneously organized through this coevolving dynamics. We expect that these results will provide new insight into self-assembly mechanisms by which the collective behavior of a rhythmic system emerges as a result of the dynamics of adaptive interactions.

Harmonics and intermodulation in subthreshold FitzHugh-Nagumo neuron

Intermodulation and harmonics are important in frequency analysis of nonlinear systems. In neuron research, most investigations are taken in studying synchronization between the external stimuli and the output of neuron, but harmonics and intermodulation are often ignored. In this paper, harmonics and intermodulation of the subthreshold FitzHugh-Nagumo neuron are investigated and their magnitudes are used to predict frequency response of the neuron. Furthermore, through analyzing the magnitudes of harmonics, the intrinsic frequencies of the neuron could be identified.