Newman-Watts Small-world Networks Research Articles

Modeling and adaptive pinning synchronization control for a chaotic-motion motor in complex network

We introduce a chaos model for a permanent-magnet synchronous motor and construct a coupled chaotic motor in a complex dynamic network using the Newman–Watts small-world network algorithm. We apply adaptive pinning control theory for complex networks to obtain suitable adaptive feedback gain and the number of nodes to be pinned. Nodes of low degree are pinned to realize global asymptotic synchronization in the complex network. The proposed adaptive pinning controller is added to the complex motor network for simulation and verification. • The chaotic motor complex dynamic networks are constructed. • The sufficient conditions for the adaptive pinning synchronization are derived. • The suitable adaptive feedback controllers are designed. • Nodes selective algorithm is discussed.

Learning Algorithm and the Cooperation Behavior of Continuous Prisoner's Dilemma Game on Complex Networks

The standard evolutionary Prisoner’s Dilemma Game (PDG), which is the most widely used model for investigating the evolution of cooperation, does not allow for changeable degrees of cooperation and the players can either cooperate or defect in each time. In this paper, we study Continuous Prisoner’s Dilemma Games (CPDG) on complex networks (or Spatial Continuous Prisoner’s Dilemma Games (SCPDG)); in which each agent locates on a vertex of the network and interacts with all his neighboring agents by making an investment. Each agent’s investment will benefit all its neighbors and incur a cost to the focus agent. The investment which can be varied continuously exhibits variable degrees of cooperation. The cooperative level of the group is characterized by the average investment of the population. Unlike the imitation of the best neighbors learning rule, the probability based imitation learning rule and the Moran process based learning rule that usually used in the standard evolutionary SPDG, we propose a new learning algorithm in the continuous condition. Three parameters to describe the imitation ability of the best neighbors, the memory length of the individual and uncertainty effect of the environment are introduced. We investigate the co-effect of these parameters on the cooperation level of the population on the Barabasi-Albert (BA) scale-free networks, the nearest-neighbor coupled networks and the Newman-Watts (NW) small-world networks. Our results may provide some new conclusion on the study of evolutionary games on networks.

The Wireless Sensor Network Routing Algorithm Based on the Small World Model

Small-world networks have the higher clustering coefficient and shorter average path length. According to the design requirements of topology and routing algorithm of the WSN, we apply small world theory into the WSN, and propose the routing algorithm based on Newman Watts small-world network model. This algorithm judge the cluster number whether same to decide the communication type. Data is transmitted to super node firstly, and then the packets are sent by the shortest transmission paths which get from the super node ring. Experiments show that the routing algorithm improves the network throughput and network transmission efficiency, the common node energy consumption become small, so the service life of wireless sensor network is prolonged.

Effects of target routing model on the occurrence of extreme events in complex networks

This paper investigates the effect of routing protocol on the occurrence of extreme events (EE) in complex networks, as an extension of [V. Kishore, M.S. Santhanam, R.E. Amritkar, Phys. Rev. Lett. 106, 188701 (2011)]. The target routing model [W.X. Wang, B.H. Wang, C.Y. Yin, Y.B. Xie, T. Zhou, Phys. Rev. E 73, 026111 (2006)] is considered. In the model, a tunable power parameter α controls the packets’ preference of forwarding direction. We derive exact expressions for the stationary distribution probability of packets and estimate the occurrence probability of EE on the nodes. The occurrence of EE strongly depends on the routing parameter. For Barabasi-Albert scale-free network, Erdos-Renyi random network and Newman-Watts small-world network, it is shown that the minimal occurrence of EE is achieved at α = −1.

Quantum strategies win in a defector-dominated population

Quantum strategies are introduced into evolutionary games. The agents using quantum strategies are regarded as invaders, whose fraction generally is 1% of a population, in contrast to the 50% of the population that are defectors. In this paper, the evolution of strategies on networks is investigated in a defector-dominated population, when three networks (square lattice, Newman–Watts small-world network, and scale-free network) are constructed and three games (Prisoners’ Dilemma, Snowdrift, and Stag-Hunt) are employed. As far as these three games are concerned, the results show that quantum strategies can always invade the population successfully. Comparing the three networks, we find that the square lattice is most easily invaded by agents that adopt quantum strategies. However, a scale-free network can be invaded by agents adopting quantum strategies only if a hub is occupied by an agent with a quantum strategy or if the fraction of agents with quantum strategies in the population is significant.

Multiple coherence resonance induced by time-periodic coupling in stochastic Hodgkin–Huxley neuronal networks

In this paper, we study the effect of time-periodic coupling strength (TPCS) on the spiking coherence of Newman-Watts small-world networks of stochastic Hodgkin-Huxley (HH) neurons and investigate the relations between the coupling strength and channel noise when coherence resonance (CR) occurs. It is found that, when the amplitude of TPCS is varied, the spiking induced by channel noise can exhibit CR and coherence bi-resonance (CBR), and the CR moves to a smaller patch area (bigger channel noise) when the amplitude increases; when the frequency of TPCS is varied, the intrinsic spiking can exhibit CBR and multiple CR, and the CR always occurs when the frequency is equal to or multiple of the spiking period, manifesting as the locking between the frequencies of the intrinsic spiking and the coupling strength. These results show that TPCS can greatly enhance and optimize the intrinsic spiking coherence, and favors the spiking with bigger channel noise to exhibit CR. This implies that, compared to constant coupling strength, TPCS may play a more efficient role for improving the time precision of the information processing in stochastic neuronal networks.

EXCITEMENT AND SYNCHRONIZATION OF SMALL-WORLD NEURONAL NETWORKS WITH SHORT-TERM SYNAPTIC PLASTICITY

Excitement and synchronization of electrically and chemically coupled Newman-Watts (NW) small-world neuronal networks with a short-term synaptic plasticity described by a modified Oja learning rule are investigated. For each type of neuronal network, the variation properties of synaptic weights are examined first. Then the effects of the learning rate, the coupling strength and the shortcut-adding probability on excitement and synchronization of the neuronal network are studied. It is shown that the synaptic learning suppresses the over-excitement, helps synchronization for the electrically coupled network but impairs synchronization for the chemically coupled one. Both the introduction of shortcuts and the increase of the coupling strength improve synchronization and they are helpful in increasing the excitement for the chemically coupled network, but have little effect on the excitement of the electrically coupled one.

Insensitive dependence of delay-induced oscillation death on complex networks

Oscillation death (also called amplitude death), a phenomenon of coupling induced stabilization of an unstable equilibrium, is studied for an arbitrary symmetric complex network with delay-coupled oscillators, and the critical conditions for its linear stability are explicitly obtained. All cases including one oscillator, a pair of oscillators, regular oscillator networks, and complex oscillator networks with delay feedback coupling, can be treated in a unified form. For an arbitrary symmetric network, we find that the corresponding smallest eigenvalue of the Laplacian λ(N) (0 >λ(N) ≥ -1) completely determines the death island, and as λ(N) is located within the insensitive parameter region for nearly all complex networks, the death island keeps nearly the largest and does not sensitively depend on the complex network structures. This insensitivity effect has been tested for many typical complex networks including Watts-Strogatz (WS) and Newman-Watts (NW) small world networks, general scale-free (SF) networks, Erdos-Renyi (ER) random networks, geographical networks, and networks with community structures and is expected to be helpful for our understanding of dynamics on complex networks.

Multiple resonances with time delays and enhancement by non-Gaussian noise in Newman–Watts networks of Hodgkin–Huxley neurons

In this paper, we study the effect of time delay on the spiking activity in Newman–Watts small-world networks of Hodgkin–Huxley neurons with non-Gaussian noise, and investigate how the non-Gaussian noise affects the delay-induced behaviors. It was found that, as the delay increases, the neuron spiking intermittently performs the most ordered and synchronized behavior when the delay lengths are integer multiples of the spiking periods, which shows multiple temporal resonances and spatial synchronizations, and reveals that the locking between the delay lengths and the spiking periods might be the mechanism behind the behaviors. It was also found that the delay-optimized spiking behaviors could be enhanced when non-Gaussian noise's deviation from the Gaussian noise is appropriate. These results show that time delay and non-Gaussian noise would cooperate to play more constructive and efficient roles in the information processing of neural networks.

NON-GAUSSIAN NOISE- AND COUPLING-INDUCED FIRING TRANSITIONS OF NEWMAN-WATTS NEURONAL NETWORKS

In this Letter, we study firing transitions induced by a particular kind of non-Gaussian noise (NGN) and coupling in Newman-Watts small-world neuronal networks. It is found that chaotic bursting can be tamed by the coupling and evolves to regular spiking or bursting behavior as the coupling increases. As the NGN's deviation from Gaussian noise changes, the neurons exhibit firing transitions from irregular spiking to regular bursting, and the number of spikes inside per burst varies with the change of the deviation. These results show that the NGN and the coupling play crucial roles in the firing activity of the neurons, and hence are of great importance to the information processing and transmission in the neuronal networks.

Harmonic stochastic resonance-enhanced signal detecting in NW small-world neural network

The harmonic stochastic resonance-enhanced signal detecting in Newman-Watts small-world neural network is studied using the Hodgkin-Huxley dynamical equation with noise. If the connection probability p, coupling strength gsyn and noise intensity D matches well, higher order resonance will be found and an optimal signal-to-noise ratio will be obtained. Then, the reasons are given to explain the mechanism of this appearance.

Memory-based evolutionary game on small-world network with tunable heterogeneity

Most papers about evolutionary games on graph assume agents have no memory. Yet, in the real world, interaction history can also affect an agent’s decision. So we introduce a memory-based agent model and investigate the Prisoner’s Dilemma game on a Heterogeneous Newman–Watts small-world network based on a Genetic Algorithm, focusing on heterogeneity’s role in the emergence of cooperative behaviors. In contrast with previous results, we find that a different heterogeneity parameter domain range imposes an entirely different impact on the cooperation fraction. In the parameter range corresponding to networks with extremely high heterogeneity, the decrease in heterogeneity greatly promotes the proportion of cooperation strategy, while in the remaining parameter range, which relates to relatively homogeneous networks, the variation of heterogeneity barely affects the cooperation fraction. Also our study provides a detailed insight into the microscopic factors that contribute to the performance of cooperation frequency.

Generalized synchronization of complex dynamical networks via impulsive control

This paper investigates the generalized synchronization (GS) of two typical complex dynamical networks, small-world networks and scale-free networks, in terms of impulsive control strategy. By applying the auxiliary-system approach to networks, we demonstrate theoretically that for any given coupling strength, GS can take place in complex dynamical networks consisting of nonidentical systems. Particularly, for Barabasi-Albert scale-free networks, we look into the relations between GS error and topological parameter m, which denotes the number of edges linking to a new node at each time step, and find out that GS speeds up with increasing m. And for Newman-Watts small-world networks, the time needed to achieve GS decreases as the probability of adding random edges increases. We further reveal how node dynamics affects GS speed on both small-world and scale-free networks. Finally, we analyze how the development of GS depends on impulsive control gains. Some abnormal but interesting phenomena regarding the GS process are also found in simulations.

Evolutionary Games on Weighted Newman–Watts Small-World Networks

We investigate the evolutionary prisoner's dilemma game (PDG) on weighted Newman–Watts (NW) networks. In weighted NW networks, the link weight wij is assigned to the link between the nodes i and j as: wij = (κi · κj)β, where κi(κj) is the degree of node i(j) and β represents the strength of the correlations. Obviously, the link weight can be tuned by only one parameter β. We focus on the cooperative behavior and wealth distribution in the system. Simulation results show that the cooperator frequency is promoted by a large range of β and there is a minimal cooperation frequency around β = – 1. Moreover, we also employ the Gini coefficient to study the wealth distribution in the population. Numerical results show that the Gini coefficient reaches its minimum when β ≈ – 1. Our work may be helpful in understanding the emergence of cooperation and unequal wealth distribution in society.

Stochastic resonance on Newman–Watts networks of Hodgkin–Huxley neurons with local periodic driving

We study the phenomenon of stochastic resonance on Newman–Watts small-world networks consisting of biophysically realistic Hodgkin–Huxley neurons with a tunable intensity of intrinsic noise via voltage-gated ion channels embedded in neuronal membranes. Importantly thereby, the subthreshold periodic driving is introduced to a single neuron of the network, thus acting as a pacemaker trying to impose its rhythm on the whole ensemble. We show that there exists an optimal intensity of intrinsic ion channel noise by which the outreach of the pacemaker extends optimally across the whole network. This stochastic resonance phenomenon can be further amplified via fine-tuning of the small-world network structure, and depends significantly also on the coupling strength among neurons and the driving frequency of the pacemaker. In particular, we demonstrate that the noise-induced transmission of weak localized rhythmic activity peaks when the pacemaker frequency matches the intrinsic frequency of subthreshold oscillations. The implications of our findings for weak signal detection and information propagation across neural networks are discussed.

Evolutionary Prisoner's Dilemma Game Based on Pursuing Higher Average Payoff

We investigate the prisoner's dilemma game based on a new rule: players will change their current strategies to opposite strategies with some probability if their neighbours' average payoffs are higher than theirs. Compared with the cases on regular lattices (RL) and Newman–Watts small world network (NW), cooperation can be best enhanced on the scale-free Barabási–Albert network (BA). It is found that cooperators are dispersive on RL network, which is different from previously reported results that cooperators will form large clusters to resist the invasion of defectors. Cooperative behaviours on the BA network are discussed in detail. It is found that large-degree individuals have lower cooperation level and gain higher average payoffs than that of small-degree individuals. In addition, we find that small-degree individuals more frequently change strategies than do large-degree individuals.

Evolutionary snowdrift game on heterogeneous Newman–Watts small-world network

We study the evolutionary snowdrift game in a heterogeneous Newman–Watts small-world network. The heterogeneity of the network is controlled by the number of hubs. It is found that the moderate heterogeneity of the network can promote the cooperation best. Besides, we study how the hubs affect the evolution of cooperative behaviours of the heterogeneous Newman–Watts small-world network. Simulation results show that both the initial states of hubs and the connections between hubs can play an important role. Our work gives a further insight into the effect of hubs on the heterogeneous networks.

Emergence of synchronization induced by the interplay between two prisoner’s dilemma games with volunteering in small-world networks

We studied synchronization between prisoner's dilemma games with voluntary participation in two Newman-Watts small-world networks. It was found that there are three kinds of synchronization: partial phase synchronization, total phase synchronization, and complete synchronization, for varied coupling factors. Besides, two games can reach complete synchronization for the large enough coupling factor. We also discussed the effect of the coupling factor on the amplitude of oscillation of cooperator density.

Promotion of cooperation induced by appropriate payoff aspirations in a small-world networked game

Based on learning theory, we adopt a stochastic learning updating rule to investigate the evolution of cooperation in the Prisoner's Dilemma game on Newman-Watts small-world networks with different payoff aspiration levels. Interestingly, simulation results show that the mechanism of intermediate aspiration promoting cooperation resembles a resonancelike behavior, and there exists a ping-pong vibration of cooperation for large payoff aspiration. To explain the nontrivial dependence of the cooperation level on the aspiration level, we investigate the fractions of links, provide analytical results of the cooperation level, and find that the simulation results are in close agreement with analytical ones. Our work may be helpful in understanding the cooperative behavior induced by the aspiration level in society.

Transport Properties of Random Walks on Scale-Free/Regular-Lattice Hybrid Networks

We study numerically the mean access times for random walks on hybrid disordered structures formed by embedding scale-free networks into regular lattices, considering different transition rates for steps across lattice bonds ($F$) and across network shortcuts ($f$). For fast shortcuts ($f/F\gg 1 $) and low shortcut densities, traversal time data collapse onto an universal curve, while a crossover behavior that can be related to the percolation threshold of the scale-free network component is identified at higher shortcut densities, in analogy to similar observations reported recently in Newman-Watts small-world networks. Furthermore, we observe that random walk traversal times are larger for networks with a higher degree of inhomogeneity in their shortcut distribution, and we discuss access time distributions as functions of the initial and final node degrees. These findings are relevant, in particular, when considering the optimization of existing information networks by the addition of a small number of fast shortcut connections.