Sheng-Jun Wang

Hierarchical modular structure enhances the robustness of self-organized criticality in neural networks

One of the most prominent architecture properties of neural networks in the brain is the hierarchical modular structure. How does the structure property constrain or improve brain function? It is thought that operating near criticality can be beneficial for brain function. Here, we find that networks with modular structure can extend the parameter region of coupling strength over which critical states are reached compared to non-modular networks. Moreover, we find that one aspect of network function—dynamical range—is highest for the same parameter region. Thus, hierarchical modularity enhances robustness of criticality as well as function. However, too much modularity constrains function by preventing the neural networks from reaching critical states, because the modular structure limits the spreading of avalanches. Our results suggest that the brain may take advantage of the hierarchical modular structure to attain criticality and enhanced function.

Projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random networks

We study projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random networks. We relax some limitations of previous work, where projective-anticipating and projective-lag synchronization can be achieved only on two coupled chaotic systems. In this paper, we realize projective-anticipating and projective-lag synchronization on complex dynamical networks composed of a large number of interconnected components. At the same time, although previous work studied projective synchronization on complex dynamical networks, the dynamics of the nodes are coupled partially linear chaotic systems. In this paper, the dynamics of the nodes of the complex networks are time-delayed chaotic systems without the limitation of the partial linearity. Based on the Lyapunov stability theory, we suggest a generic method to achieve the projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random dynamical networks, and we find both its existence and sufficient stability conditions. The validity of the proposed method is demonstrated and verified by examining specific examples using Ikeda and Mackey-Glass systems on Erdos-Renyi networks.

Response of degree-correlated scale-free networks to stimuli.

The response of degree-correlated scale-free attractor networks to stimuli is studied. We show that degree-correlated scale-free networks are robust to random stimuli as well as the uncorrelated scale-free networks, while assortative (disassortative) scale-free networks are more (less) sensitive to directed stimuli than uncorrelated networks. We find that the degree correlation of scale-free networks makes the dynamics of attractor systems different from uncorrelated ones. The dynamics of correlated scale-free attractor networks results in the effects of degree correlation on the response to stimuli.

Effects of degree distribution in mutual synchronization of neural networks

We study the effects of the degree distribution in mutual synchronization of two-layer neural networks. We carry out three coupling strategies: large-large coupling, random coupling, and small-small coupling. By computer simulations and analytical methods, we find that couplings between nodes with large degree play an important role in the synchronization. For large-large coupling, less couplings are needed for inducing synchronization for both random and scale-free networks. For random coupling, cutting couplings between nodes with large degree is very efficient for preventing neural systems from synchronization, especially when subnetworks are scale free.

Effect of information transmission on cooperative behavior

Considering the fact, in the real world, that information is transmitted with a time delay, we study an evolutionary spatial prisoners dilemma game where agents update strategies according to certain information that they have learned. In our study, the game dynamics are classified by the modes of information learning as well as game interaction, and four different combinations, i.e. the mean-field case, case I, case II and local case, are studied comparatively. It is found that the time delay in case II smoothes the phase transition from the absorbing states of C (or D) to their mixing state, and promotes cooperation for most parameter values. Our work provides insights into the temporal behavior of information and the memory of the system, and may be helpful in understanding the cooperative behavior induced by the time delay in social and biological systems.

Influence of synaptic interaction on firing synchronization and spike death in excitatory neuronal networks.

We investigate the influence of efficacy of synaptic interaction on firing synchronization in excitatory neuronal networks. We find spike death phenomena: namely, the state of neurons transits from the limit cycle to a fixed point or transient state. The phenomena occur under the perturbation of an excitatory synaptic interaction, which has a high efficacy. We show that the decrease of synaptic current results in spike death through depressing the feedback of the sodium ionic current. In the networks with the spike death property the degree of synchronization is lower and insensitive to the heterogeneity of neurons. The mechanism of the influence is that the transition of the neuron state disrupts the adjustment of the rhythm of the neurons oscillation and prevents a further increase of the firing synchronization.

Coupling Parameter In Synchronization Of Small-World Neural Networks

We investigate the critical features of coupling parameters in the synchronization of the ensemble of identical neural networks with small-world connectivity. An exponential decay form is observed in the extreme case of global coupling among subsystems and full connection in each networks: there exists a maximum and a minimum of the critical coupling intensity for synchronization in this spatially extended system. For partial coupling, we present the primary result about the critical coupling fraction for various linked degree of subnetworks.