Oscillation propagation in neural networks with different topologies

Winfree loop sustained oscillation in two-dimensional excitable lattices: Prediction and realization

The problem of self-sustained oscillations in excitable complex networks is the central issue under investigation, among which the prediction and the realization of self-sustained oscillations in different kinds of excitable networks are the challenging tasks. In this paper, we extensively investigate the prediction and the realization of a Winfree loop sustained oscillation (WLSO) in two-dimensional (2D) excitable lattices. By analyzing the network structure, the fundamental oscillation source structure (FOSS) of WLSO in a 2D excitable lattice is exposed explicitly. For the suitable combinations of system parameters, the Winfree loop can self-organize on the FOSS to form an oscillation source sustaining the oscillation, and these suitable parameter combinations are predicted by calculating the minimum Winfree loop length and have been further confirmed in numerical simulations. However, the FOSS cannot spontaneously offer the WLSO in 2D excitable lattices in usual cases due to the coupling bidirectionality and the symmetry properties of the lattice. A targeted protection scheme of the oscillation source is proposed by overcoming these two drawbacks. Finally, the WLSO is realized in the 2D excitable lattice successfully.

Emergence of self-sustained oscillations in excitable Erdös-Rényi random networks

We investigate the emergence of self-sustained oscillations in excitable Erdös-Rényi random networks (EERRNs). Interestingly, periodical self-sustained oscillations have been found at a moderate connection probability P. For smaller or larger P, the system evolves into a homogeneous rest state with distinct mechanisms. One-dimensional Winfree loops are discovered as the sources to maintain the oscillations. Moreover, by analyzing these oscillation sources, we propose two criteria to explain the spatiotemporal dynamics obtained in EERRNs. Finally, the two critical connection probabilities for which self-sustained oscillations can emerge are approximately predicted based on these two criteria.

Simulating dynamic plastic continuous neural networks by finite elements

We introduce dynamic plastic continuous neural network (DPCNN), which is comprised of neurons distributed in a nonlinear plastic medium where wire-like connections of neural networks are replaced with the continuous medium. We use finite element method to model the dynamic phenomenon of information processing within the DPCNNs. During the training, instead of weights, the properties of the continuous material at its different locations and some properties of neurons are modified. Input and output can be vectors and/or continuous functions over lines and/or areas. Delay and feedback from neurons to themselves and from outputs occur in the DPCNNs. We model a simple form of the DPCNN where the medium is a rectangular plate of bilinear material, and the neurons continuously fire a signal, which is a function of the horizontal displacement.

Synchronization and stochastic resonance of the small-world neural network based on the CPG

According to biological knowledge, the central nervous system controls the central pattern generator (CPG) to drive the locomotion. The brain is a complex system consisting of different functions and different interconnections. The topological properties of the brain display features of small-world network. The synchronization and stochastic resonance have important roles in neural information transmission and processing. In order to study the synchronization and stochastic resonance of the brain based on the CPG, we establish the model which shows the relationship between the small-world neural network (SWNN) and the CPG. We analyze the synchronization of the SWNN when the amplitude and frequency of the CPG are changed and the effects on the CPG when the SWNN's parameters are changed. And we also study the stochastic resonance on the SWNN. The main findings include: (1) When the CPG is added into the SWNN, there exists parameters space of the CPG and the SWNN, which can make the synchronization of the SWNN optimum. (2) There exists an optimal noise level at which the resonance factor Q gets its peak value. And the correlation between the pacemaker frequency and the dynamical response of the network is resonantly dependent on the noise intensity. The results could have important implications for biological processes which are about interaction between the neural network and the CPG.

Effects of time delay and random rewiring on the stochastic resonance in excitable small-world neuronal networks

The effects of time delay and rewiring probability on stochastic resonance and spatiotemporal order in small-world neuronal networks are studied in this paper. Numerical results show that, irrespective of the pacemaker introduced to one single neuron or all neurons of the network, the phenomenon of stochastic resonance occurs. The time delay in the coupling process can either enhance or destroy stochastic resonance on small-world neuronal networks. In particular, appropriately tuned delays can induce multiple stochastic resonances, which appear intermittently at integer multiples of the oscillation period of the pacemaker. More importantly, it is found that the small-world topology can significantly affect the stochastic resonance on excitable neuronal networks. For small time delays, increasing the rewiring probability can largely enhance the efficiency of pacemaker-driven stochastic resonance. We argue that the time delay and the rewiring probability both play a key role in determining the ability of the small-world neuronal network to improve the noise-induced outreach of the localized subthreshold pacemaker.

Cluster synchronization of spiking induced by noise and interaction delays in homogenous neuronal ensembles

Properties of spontaneously formed clusters of synchronous dynamics in a structureless network of noisy excitable neurons connected via delayed diffusive couplings are studied in detail. Several tools have been applied to characterize the synchronization clusters and to study their dependence on the neuronal and the synaptic parameters. Qualitative explanation of the cluster formation is discussed. The interplay between the noise, the interaction time-delay and the excitable character of the neuronal dynamics is shown to be necessary and sufficient for the occurrence of the synchronization clusters. We have found the two-cluster partitions where neurons are firmly bound to their subsets, as well as the three-cluster ones, which are dynamical by nature. The former turn out to be stable under small disparity of the intrinsic neuronal parameters and the heterogeneity in the synaptic connectivity patterns.

Constraints on the synchronization of entorhinal cortex stellate cells

Synchronized oscillations of large numbers of central neurons are believed to be important for a wide variety of cognitive functions, including long-term memory recall and spatial navigation. It is therefore plausible that evolution has optimized the biophysical properties of central neurons in some way for synchronized oscillations to occur. Here, we use computational models to investigate the relationships between the presumably genetically determined parameters of stellate cells in layer II of the entorhinal cortex and the ability of coupled populations of these cells to synchronize their intrinsic oscillations: in particular, we calculate the time it takes circuits of two or three cells with initially randomly distributed phases to synchronize their oscillations to within one action potential width, and the metabolic energy they consume in doing so. For recurrent circuit topologies, we find that parameters giving low intrinsic firing frequencies close to those actually observed are strongly advantageous for both synchronization time and metabolic energy consumption.

Spontaneous formation of synchronization clusters in homogenous neuronal ensembles induced by noise and interaction delays

The spontaneous formation of clusters of synchronized spiking in a structureless ensemble of equal stochastically perturbed excitable neurons with delayed coupling is demonstrated for the first time. The effect is a consequence of a subtle interplay between interaction delays, noise, and the excitable character of a single neuron. The dependence of the cluster properties on the time lag, noise intensity, and the synaptic strength is investigated.

Stochastic resonance on a modular neuronal network of small-world subnetworks with a subthreshold pacemaker

We study the phenomenon of stochastic resonance on a modular neuronal network consisting of several small-world subnetworks with a subthreshold periodic pacemaker. Numerical results show that the correlation between the pacemaker frequency and the dynamical response of the network is resonantly dependent on the intensity of additive spatiotemporal noise. This effect of pacemaker-driven stochastic resonance of the system depends extensively on the local and the global network structure, such as the intra- and inter-coupling strengths, rewiring probability of individual small-world subnetwork, the number of links between different subnetworks, and the number of subnetworks. All these parameters play a key role in determining the ability of the network to enhance the noise-induced outreach of the localized subthreshold pacemaker, and only they bounded to a rather sharp interval of values warrant the emergence of the pronounced stochastic resonance phenomenon. Considering the rather important role of pacemakers in real-life, the presented results could have important implications for many biological processes that rely on an effective pacemaker for their proper functioning.