Zhihai Rong

Decentralized Adaptive Pinning Control for Cluster Synchronization of Complex Dynamical Networks

In this brief, we investigate pinning control for cluster synchronization of undirected complex dynamical networks using a decentralized adaptive strategy. Unlike most existing pinning-control algorithms with or without an adaptive strategy, which require global information of the underlying network such as the eigenvalues of the coupling matrix of the whole network or a centralized adaptive control scheme, we propose a novel decentralized adaptive pinning-control scheme for cluster synchronization of undirected networks using a local adaptive strategy on both coupling strengths and feedback gains. By introducing this local adaptive strategy on each node, we show that the network can synchronize using weak coupling strengths and small feedback gains. Finally, we present some simulations to verify and illustrate the theoretical results.

Cooperation percolation in spatial prisoner's dilemma game

The paradox of cooperation among selfish individuals still puzzles scientific communities. Although a large amount of evidence has demonstrated that cooperator clusters in spatial games are effective to protect cooperators against the invasion of defectors, we continue to lack the condition for the formation of a giant cooperator cluster that assures the prevalence of cooperation in a system. Here, we study the dynamical organization of cooperator clusters in spatial prisoners dilemma game to offer the condition for the dominance of cooperation, finding that a phase transition characterized by the emergence of a large spanning cooperator cluster occurs when the initial fraction of cooperators exceeds a certain threshold. Interestingly, the phase transition belongs to different universality classes of percolation determined by the temptation to defect

Impact of heterogeneous activity and community structure on the evolutionary success of cooperators in social networks.

b

Effects of diverse inertia on scale-free–networked prisoner's dilemma games

. Specifically, on square lattices,

Extortion provides alternative routes to the evolution of cooperation in structured populations

1<b<4/3

On decentralized adaptive pinning synchronization of complex dynamical networks

leads to a phase transition pertaining to the class of regular site percolation, whereas

Effect of clustering coefficient on cooperation in scale-free public goods game

3/2<b<2

EFFECTS OF HETEROGENEOUS INFLUENCE OF INDIVIDUALS ON THE GLOBAL CONSENSUS

gives rise to a phase transition subject to invasion percolation with trapping. Our findings offer deeper understanding of the cooperative behaviors in nature and society.

The emergence of cooperation-extortion alliance on scale-free networks with normalized payoff

Zhi-Xi Wu, ∗ Zhihai Rong, 3, † and Han-Xin Yang ‡ Institute of Computational Physics and Complex Systems, Lanzhou University, Lanzhou, Gansu 730000, China Web Sciences Center, University of Electronic Science and Technology of China, Chengdu Sichuan 611731, China Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong Department of Physics, Fuzhou University, Fuzhou 350108, China (Dated: Received: date / Revised version: date)

Assortative degree-mixing patterns inhibit behavioral diversity of a scale-free structured population in high-mutation situations

We study an evolutionary prisoners dilemma game on a scale-free network by a modified Fermi updating rule, where each player is assigned an inertia index that controls its learning activity. An interesting finding is that the cooperation level can be significantly improved when the individual inertia is introduced. More importantly, a parameter β is also introduced to control the diversity level of inertia among the individuals. It is found that there exists an optimal value of β leading to the highest cooperation level. The observed results are explained by the feedback mechanism and the characteristic of the Fermi function. Our analysis also reveals that the players with moderate degrees play a critical role in the evolution of the whole system.