We investigated the influence of efficacy of synaptic interaction on firing synchronization in excitatory neuronal networks. We found spike death phenomena, namely, the state of neurons transits from limit cycle to fixed point or transient state. The phenomena occur under the perturbation of excitatory synaptic interaction that has a high efficacy. We showed that the decrease of synaptic current results in spike death through depressing the feedback of sodium ionic current. In the networks with spike death property the degree of synchronization is lower and unsensitive to the heterogeneity of neurons. The mechanism of the influence is that the transition of neuron state disrupts the adjustment of the rhythm of neuron oscillation and prevents further increase of firing synchronization.
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 can realize projective-anticipating and projective-lag synchronization on complex dynamical networks composed by 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 find both the 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.
The emergence and maintenance of cooperation within sizable groups of unrelated humans offer many challenges for our understanding. We propose that the humans capacity of communication, such as how many and how far away the fellows can build up mutual communications, may affect the evolution of cooperation. We study this issue by means of the public goods game (PGG) with a two-layered network of contacts. Players obtain payoffs from five-person public goods interactions on a square lattice (the interaction layer). Also, they update strategies after communicating with neighbours in learning layer, where two players build up mutual communication with a power law probability depending on their spatial distance. Our simulation results indicate that the evolution of cooperation is indeed sensitive to how players choose others to communicate with, including the amount as well as the locations. The tendency of localised communication is proved to be a new mechanism to promote cooperation.
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 result in the effects of degree correlation on the response to stimuli.
