We report on synchronization between two identical time delay chaotic systems under parameter mismatch. It overcomes some limitations of the previous work where synchronization and antisynchronization has been investi...We report on synchronization between two identical time delay chaotic systems under parameter mismatch. It overcomes some limitations of the previous work where synchronization and antisynchronization has been investigated only in finite-dimensional chaotic systems under parameter mismatch, so we can achieve synchronization and antisynchronization in infinite- dimensional chaotic systems under parameter mismatch, For infinite-dimensional systems modelled by delay differential equations, we find stable synchronization and antisynehronization in long-, moderate- and short-time delay regions, in particular for the hyperchaotic ease.展开更多
The effect of heterogeneous influence of different individuals on the maintenance of co-operative behaviour is studied in an evolutionary Prisoner＇s Dilemma game with players located on the sites of regular small-wor...The effect of heterogeneous influence of different individuals on the maintenance of co-operative behaviour is studied in an evolutionary Prisoner＇s Dilemma game with players located on the sites of regular small-world networks. The players interacting with their neighbours can either co-operate or defect and update their states by choosing one of the neighbours and adopting its strategy with a probability depending on the pay off difference. The selection of the neighbour obeys a preferential rule： the more influential a neighbour, the larger the probability it is picked. It is found that this simple preferential selection rule can promote continuously the co-operation of the whole population with the strengthening of the disorder of the underlying network.展开更多
For the first time, we report on projective synchronization between two time delay chaotic systems with single time delays. It overcomes some limitations of the previous work, where projective synchronization has been...For the first time, we report on projective synchronization between two time delay chaotic systems with single time delays. It overcomes some limitations of the previous work, where projective synchronization has been investigated only in finite-dimensional chaotic systems, so we can achieve projective synchronization in infinitedimensional chaotic systems. We give a general method with which we can achieve projective synchronization in time-delayed chaotic systems. The method is illustrated using the famous delay-differential equations related to optical bistability. Numerical simulations fully support the analytical approach.展开更多
We investigate a spatial Prisoner＇s Dilemma game with nonlinear attractive effect on regular small-world networks. The players located on the sites of networks can either cooperate with their neighbours or defect. In...We investigate a spatial Prisoner＇s Dilemma game with nonlinear attractive effect on regular small-world networks. The players located on the sites of networks can either cooperate with their neighbours or defect. In every generation, each player updates its strategy by firstly choosing one of the neighbours with a probability proportional to .A^α denoting the attractiveness of the neighbour, where .4 is the collected payoff and ^α （-〉0） is a free parameter characterizing the extent of nonlinear effect. Then each player adopts its strategy with a probability dependent on their payoff difference. Using Monte Carlo simulations, we investigate the density pc of cooperators in the stationary state for various values of α and the rewiring probability q of the network. It is shown that the introduction of such attractive effect remarkably promotes the emergence and persistence of cooperation over a wide range of the temptation to defect for the same network structures. We also point out that long-range connections either enhance or inhibit the cooperation, which depends on the value of α and the payoff parameter b.展开更多
We have studied the Langevin description of stochastic dynamics of financial time series. A sliding-window algorithm is used for our analysis. We find that the fluctuation of stock prices can be understood from the vi...We have studied the Langevin description of stochastic dynamics of financial time series. A sliding-window algorithm is used for our analysis. We find that the fluctuation of stock prices can be understood from the view of a time-dependent drift force corresponding to the drift parameter in Langevin equation. It is revealed that the statistical results of the drift force estimated from financial time series can be approximately considered as a linear restoring force. We investigate the significance of this linear restoring force to the prices evolution from its two coefficients, the equilibrium position and the slope coefficient. The daily log-returns of S＆P 500 index from 1950 to 1999 are especially analysed. The new simple form of the restoring force obtained both from mathematical and numerical analyses suggests that the Langevin approach can effectively present not only the macroscopical but also the detailed properties of the price evolution.展开更多
We investigate the dynamics of random walks on weighted networks. Assuming that the edge weight and the node strength are used as local information by a random walker. Two kinds of walks, weight-dependent walk and str...We investigate the dynamics of random walks on weighted networks. Assuming that the edge weight and the node strength are used as local information by a random walker. Two kinds of walks, weight-dependent walk and strength-dependent walk, are studied. Exact expressions for stationary distribution and average return time are derived and confirmed by computer simulations. The distribution of average return time and the mean-square displacement are calculated for two walks on the Barrat-Barthelemy-Vespignani （BBV） networks. It is found that a weight-dependent walker can arrive at a new territory more easily than a strength-dependent one.展开更多
We study a memory-based Boolean game （MBBG） taking place on a regular ring, wherein each agent acts according to its local optimal states of the last M time steps recorded in memory, and the agents in the minority a...We study a memory-based Boolean game （MBBG） taking place on a regular ring, wherein each agent acts according to its local optimal states of the last M time steps recorded in memory, and the agents in the minority are rewarded. One free parameter p between 0 and 1 is introduced to denote the strength of the agent willing to make a decision according to its memory. It is found that giving proper willing strength p, the MBBG system can spontaneously evolve to a state of performance better than the random game; while for larger p, the herd behaviour emerges to reduce the system profit. By analysing the dependence of dynamics of the system on the memory capacity M, we find that a higher memory capacity favours the emergence of the better performance state, and effectively restrains the herd behaviour, thus increases the system profit. Considering the high cost of long-time memory, the enhancement of memory capacity for restraining the herd behaviour is also discussed, and M =5 is suggested to be a good choice.展开更多
We investigate responses of the Hodgkin-Huxley globally neuronal systems to periodic spike-train inputs. The firing activities of the neuronal networks show different rhythmic patterns for different parameters. These ...We investigate responses of the Hodgkin-Huxley globally neuronal systems to periodic spike-train inputs. The firing activities of the neuronal networks show different rhythmic patterns for different parameters. These rhyth- mic patterns can be used to explain cycles of firing in real brain. These activity patterns, average activity and coherence measure are affected by two quantities such as the percentage of excitatory couplings and stimulus intensity, in which the percentage of excitatory couplings is more important than stimulus intensity since the transition phenomenon of average activity comes about.展开更多
A nonchaotic attractor is observed in an infinite-dimensional system which is related to optical bistability and described by a nonlinear time-delay differential equation. The observed nonchaotic attractor is characte...A nonchaotic attractor is observed in an infinite-dimensional system which is related to optical bistability and described by a nonlinear time-delay differential equation. The observed nonchaotic attractor is characterized by the strange trajectory of attractor but with negative value for the largest Lyapunov exponent, as well as the Fourier power spectra.展开更多
We investigate an evolutionary snowdrift game on a square N ： L × L lattice with periodic boundary conditions, where a population of no （no ≤ N） players located on the sites of this lattice can either coopera...We investigate an evolutionary snowdrift game on a square N ： L × L lattice with periodic boundary conditions, where a population of no （no ≤ N） players located on the sites of this lattice can either cooperate with or defect from their nearest neighbours. After each generation, every player moves with a certain probability p to one of the player＇s nearest empty sites. It is shown that, when p = 0, the cooperative behaviour can be enhanced in disordered structures. When p 〉 0, the effect of mobility on cooperation remarkably depends on the payoff parameter r and the density of individuals ρ （ρ = no/N）. Compared with the results of p = 0, for small r, the persistence of cooperation is enhanced at not too small values of p; whereas for large r, the introduction of mobility inhibits the emergence of cooperation at any p 〈 1; for the intermediate value of r, the cooperative behaviour is sometimes enhanced and sometimes inhibited, depending on the values of p and p. In particular, the cooperator density can reach its maximum when the values of p and p reach their respective optimal values. In addition, two absorbing states of all cooperators and all defectors can emerge respectively for small and large r in the case of p 〉 0.展开更多
In this paper multiple delay feedback control （MDFC） with different and independent delay times is shown to be an efficient method for stabilizing fixed points in finite-dimensional dynamical systems. Whether MDFC c...In this paper multiple delay feedback control （MDFC） with different and independent delay times is shown to be an efficient method for stabilizing fixed points in finite-dimensional dynamical systems. Whether MDFC can be applied to infinite-dimensional systems has been an open question. In this paper we find that for infinite-dimensional systems modelled by delay differential equations, MDFC works well for stabilizing （unstable） steady states in long, moderate- and short-time delay regions, in particular for the hyperchaotic case.展开更多
An evolutionary prisoner＇s dilemma game is investigated on two-layered complex networks respectively representing interaction and learning networks in one and two dimensions. A parameter q is introduced to denote the...An evolutionary prisoner＇s dilemma game is investigated on two-layered complex networks respectively representing interaction and learning networks in one and two dimensions. A parameter q is introduced to denote the correlation degree between the two-layered networks. Using Monte Carlo simulations we studied the effects of the correlation degree on cooperative behaviour and found that the cooperator density nontrivially changes with q for different payoff parameter values depending on the detailed strategy updating and network dimension. An explanation for the obtained results is provided.展开更多
This paper studies consensus problems in weighted scale-free networks of asymmetrically coupled dynamical units, where the asymmetry in a given link is deter：mined by the relative degree of the involved nodes. It sho...This paper studies consensus problems in weighted scale-free networks of asymmetrically coupled dynamical units, where the asymmetry in a given link is deter：mined by the relative degree of the involved nodes. It shows that the asymmetry of interactions has a great effect on the consensus. Especially, when the interactions are dominant from higher- to lower-degree nodes, both the convergence speed and the robustness to communication delay are enhanced.展开更多
By using the well-known Ikeda model as the node dynamics, this paper studies synchronization of time-delay systems on small-world networks where the connections between units involve time delays. It shows that, in con...By using the well-known Ikeda model as the node dynamics, this paper studies synchronization of time-delay systems on small-world networks where the connections between units involve time delays. It shows that, in contrast with the undelayed case, networks with delays can actually synchronize more easily. Specifically, for randomly distributed delays, time-delayed mutual coupling suppresses the chaotic behaviour by stabilizing a fixed point that is unstable for the uncoupled dynamical system.展开更多
The collective synchronization of a system of coupled logistic maps on random community networks is investigated. It is found that the synchronizability of the community network is affected by two factors when the siz...The collective synchronization of a system of coupled logistic maps on random community networks is investigated. It is found that the synchronizability of the community network is affected by two factors when the size of the network and the number of connections are fixed. One is the number of communities denoted by the parameter rn, and the other is the ratio σ of the connection probability p of each pair of nodes within each community to the connection probability q of each pair of nodes among different communities. Theoretical analysis and numerical results indicate that larger rn and smaller σ are the key to the enhancement of network synchronizability. We also testify synchronous properties of the system by analysing the largest Lyapunov exponents of the system.展开更多
We investigate the collection behaviour of coupled phase oscillators on Newman-Watts small-world networks in one and two dimensions. Each component of the network is assumed as an oscillator and each interacts with th...We investigate the collection behaviour of coupled phase oscillators on Newman-Watts small-world networks in one and two dimensions. Each component of the network is assumed as an oscillator and each interacts with the others following the Kuramoto model We then study the onset of global synchronization of phases and frequencies based on dynamic simulations and finite-size scaling. Both the phase and frequency synchronization are observed to emerge in the presence of a tiny fraction of shortcuts and enhanced with the increases of nearest neighbours and lattice dimensions.展开更多
We have investigated the influence of the average degree （k） of network on the location of an order-disorder transition in opinion dynamics. For this purpose, a variant of majority rule （VMR） model is applied to W...We have investigated the influence of the average degree （k） of network on the location of an order-disorder transition in opinion dynamics. For this purpose, a variant of majority rule （VMR） model is applied to Watts-Strogatz （WS） small-world networks and Barabasi-Albert （BA） scale-free networks which may describe some non-trivial properties of social systems. Using Monte Carlo simulations, we find that the order-disorder transition point of the VMR model is greatly affected by the average degree （k） of the networks; a larger value of （k） results in a more ordered state of the system. Comparing WS networks with BA networks, we find WS networks have better orderliness than BA networks when the average degree （k） is small. With the increase of （k）, BA networks have a more ordered state. By implementing finite-size scaling analysis, we also obtain critical exponents β/v, γ/u and 1/v for several values of average degree （k）. Our results may be helpful to understand structural effects on order-disorder phase transition in the context of the majority rule model.展开更多
We investigate different types of synchronization between two unidirectionally nonlinearly coupled identical delay- differential systems related to optical bistable or hybrid optical bistable devices. This system can ...We investigate different types of synchronization between two unidirectionally nonlinearly coupled identical delay- differential systems related to optical bistable or hybrid optical bistable devices. This system can represent some kinds of delay-differential models, i.e. Ikeda model, Vall^e model, sine-square model, Mackey Glass model, and so on. We find existence and sufficient stability conditions by theoretical analysis and test the correctness by＂ numerical simulations. Lag, complete and anticipating synchronization are observed, respectively. It is found that the time-delay system can be divided into two parts~ one is the instant term and the other is the delay term. Synchronization between two identical chaotic systems can be derived by adding a coupled term to the delay term in the driven system.展开更多
文摘We report on synchronization between two identical time delay chaotic systems under parameter mismatch. It overcomes some limitations of the previous work where synchronization and antisynchronization has been investigated only in finite-dimensional chaotic systems under parameter mismatch, so we can achieve synchronization and antisynchronization in infinite- dimensional chaotic systems under parameter mismatch, For infinite-dimensional systems modelled by delay differential equations, we find stable synchronization and antisynehronization in long-, moderate- and short-time delay regions, in particular for the hyperchaotic ease.
文摘The effect of heterogeneous influence of different individuals on the maintenance of co-operative behaviour is studied in an evolutionary Prisoner＇s Dilemma game with players located on the sites of regular small-world networks. The players interacting with their neighbours can either co-operate or defect and update their states by choosing one of the neighbours and adopting its strategy with a probability depending on the pay off difference. The selection of the neighbour obeys a preferential rule： the more influential a neighbour, the larger the probability it is picked. It is found that this simple preferential selection rule can promote continuously the co-operation of the whole population with the strengthening of the disorder of the underlying network.
文摘For the first time, we report on projective synchronization between two time delay chaotic systems with single time delays. It overcomes some limitations of the previous work, where projective synchronization has been investigated only in finite-dimensional chaotic systems, so we can achieve projective synchronization in infinitedimensional chaotic systems. We give a general method with which we can achieve projective synchronization in time-delayed chaotic systems. The method is illustrated using the famous delay-differential equations related to optical bistability. Numerical simulations fully support the analytical approach.
文摘We investigate a spatial Prisoner＇s Dilemma game with nonlinear attractive effect on regular small-world networks. The players located on the sites of networks can either cooperate with their neighbours or defect. In every generation, each player updates its strategy by firstly choosing one of the neighbours with a probability proportional to .A^α denoting the attractiveness of the neighbour, where .4 is the collected payoff and ^α （-〉0） is a free parameter characterizing the extent of nonlinear effect. Then each player adopts its strategy with a probability dependent on their payoff difference. Using Monte Carlo simulations, we investigate the density pc of cooperators in the stationary state for various values of α and the rewiring probability q of the network. It is shown that the introduction of such attractive effect remarkably promotes the emergence and persistence of cooperation over a wide range of the temptation to defect for the same network structures. We also point out that long-range connections either enhance or inhibit the cooperation, which depends on the value of α and the payoff parameter b.
基金Project supported by the National Natural Science Foundation of China （Grant No 10305005）, the Fundamental Research Fund for Physics and Mathematics of Lanzhou University （Grant No Lzu05008）. We would like to thank Professor Zhao Hong and Dr Xu Xin-Jian for helpful discussions.
文摘We have studied the Langevin description of stochastic dynamics of financial time series. A sliding-window algorithm is used for our analysis. We find that the fluctuation of stock prices can be understood from the view of a time-dependent drift force corresponding to the drift parameter in Langevin equation. It is revealed that the statistical results of the drift force estimated from financial time series can be approximately considered as a linear restoring force. We investigate the significance of this linear restoring force to the prices evolution from its two coefficients, the equilibrium position and the slope coefficient. The daily log-returns of S＆P 500 index from 1950 to 1999 are especially analysed. The new simple form of the restoring force obtained both from mathematical and numerical analyses suggests that the Langevin approach can effectively present not only the macroscopical but also the detailed properties of the price evolution.
文摘We investigate the dynamics of random walks on weighted networks. Assuming that the edge weight and the node strength are used as local information by a random walker. Two kinds of walks, weight-dependent walk and strength-dependent walk, are studied. Exact expressions for stationary distribution and average return time are derived and confirmed by computer simulations. The distribution of average return time and the mean-square displacement are calculated for two walks on the Barrat-Barthelemy-Vespignani （BBV） networks. It is found that a weight-dependent walker can arrive at a new territory more easily than a strength-dependent one.
文摘We study a memory-based Boolean game （MBBG） taking place on a regular ring, wherein each agent acts according to its local optimal states of the last M time steps recorded in memory, and the agents in the minority are rewarded. One free parameter p between 0 and 1 is introduced to denote the strength of the agent willing to make a decision according to its memory. It is found that giving proper willing strength p, the MBBG system can spontaneously evolve to a state of performance better than the random game; while for larger p, the herd behaviour emerges to reduce the system profit. By analysing the dependence of dynamics of the system on the memory capacity M, we find that a higher memory capacity favours the emergence of the better performance state, and effectively restrains the herd behaviour, thus increases the system profit. Considering the high cost of long-time memory, the enhancement of memory capacity for restraining the herd behaviour is also discussed, and M =5 is suggested to be a good choice.
文摘We investigate responses of the Hodgkin-Huxley globally neuronal systems to periodic spike-train inputs. The firing activities of the neuronal networks show different rhythmic patterns for different parameters. These rhyth- mic patterns can be used to explain cycles of firing in real brain. These activity patterns, average activity and coherence measure are affected by two quantities such as the percentage of excitatory couplings and stimulus intensity, in which the percentage of excitatory couplings is more important than stimulus intensity since the transition phenomenon of average activity comes about.
文摘A nonchaotic attractor is observed in an infinite-dimensional system which is related to optical bistability and described by a nonlinear time-delay differential equation. The observed nonchaotic attractor is characterized by the strange trajectory of attractor but with negative value for the largest Lyapunov exponent, as well as the Fourier power spectra.
基金Project supported by the National Natural Science Foundation of China （Grant No 10775060）.
文摘We investigate an evolutionary snowdrift game on a square N ： L × L lattice with periodic boundary conditions, where a population of no （no ≤ N） players located on the sites of this lattice can either cooperate with or defect from their nearest neighbours. After each generation, every player moves with a certain probability p to one of the player＇s nearest empty sites. It is shown that, when p = 0, the cooperative behaviour can be enhanced in disordered structures. When p 〉 0, the effect of mobility on cooperation remarkably depends on the payoff parameter r and the density of individuals ρ （ρ = no/N）. Compared with the results of p = 0, for small r, the persistence of cooperation is enhanced at not too small values of p; whereas for large r, the introduction of mobility inhibits the emergence of cooperation at any p 〈 1; for the intermediate value of r, the cooperative behaviour is sometimes enhanced and sometimes inhibited, depending on the values of p and p. In particular, the cooperator density can reach its maximum when the values of p and p reach their respective optimal values. In addition, two absorbing states of all cooperators and all defectors can emerge respectively for small and large r in the case of p 〉 0.
文摘In this paper multiple delay feedback control （MDFC） with different and independent delay times is shown to be an efficient method for stabilizing fixed points in finite-dimensional dynamical systems. Whether MDFC can be applied to infinite-dimensional systems has been an open question. In this paper we find that for infinite-dimensional systems modelled by delay differential equations, MDFC works well for stabilizing （unstable） steady states in long, moderate- and short-time delay regions, in particular for the hyperchaotic case.
基金supported by the National Natural Science Foundation of China (Grant No. 10775060)
文摘An evolutionary prisoner＇s dilemma game is investigated on two-layered complex networks respectively representing interaction and learning networks in one and two dimensions. A parameter q is introduced to denote the correlation degree between the two-layered networks. Using Monte Carlo simulations we studied the effects of the correlation degree on cooperative behaviour and found that the cooperator density nontrivially changes with q for different payoff parameter values depending on the detailed strategy updating and network dimension. An explanation for the obtained results is provided.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10775060 and 10805033)the Doctoral Education Foundation of National Education Committeethe Natural Science Foundation of Gansu Province
文摘This paper studies consensus problems in weighted scale-free networks of asymmetrically coupled dynamical units, where the asymmetry in a given link is deter：mined by the relative degree of the involved nodes. It shows that the asymmetry of interactions has a great effect on the consensus. Especially, when the interactions are dominant from higher- to lower-degree nodes, both the convergence speed and the robustness to communication delay are enhanced.
基金Project supported by the National Natural Science Foundation of China (Grant No 10775060)in part by Doctoral Education Foundation of the Education Department of China and the Natural Science Foundation of Gansu Province
文摘By using the well-known Ikeda model as the node dynamics, this paper studies synchronization of time-delay systems on small-world networks where the connections between units involve time delays. It shows that, in contrast with the undelayed case, networks with delays can actually synchronize more easily. Specifically, for randomly distributed delays, time-delayed mutual coupling suppresses the chaotic behaviour by stabilizing a fixed point that is unstable for the uncoupled dynamical system.
基金Project supported by the National Natural Science Foundation of China (Grant No 10775060)
文摘The collective synchronization of a system of coupled logistic maps on random community networks is investigated. It is found that the synchronizability of the community network is affected by two factors when the size of the network and the number of connections are fixed. One is the number of communities denoted by the parameter rn, and the other is the ratio σ of the connection probability p of each pair of nodes within each community to the connection probability q of each pair of nodes among different communities. Theoretical analysis and numerical results indicate that larger rn and smaller σ are the key to the enhancement of network synchronizability. We also testify synchronous properties of the system by analysing the largest Lyapunov exponents of the system.
文摘We investigate the collection behaviour of coupled phase oscillators on Newman-Watts small-world networks in one and two dimensions. Each component of the network is assumed as an oscillator and each interacts with the others following the Kuramoto model We then study the onset of global synchronization of phases and frequencies based on dynamic simulations and finite-size scaling. Both the phase and frequency synchronization are observed to emerge in the presence of a tiny fraction of shortcuts and enhanced with the increases of nearest neighbours and lattice dimensions.
基金Project supported by the National Natural Science Foundation of China (Grant No.10775060)
文摘We have investigated the influence of the average degree （k） of network on the location of an order-disorder transition in opinion dynamics. For this purpose, a variant of majority rule （VMR） model is applied to Watts-Strogatz （WS） small-world networks and Barabasi-Albert （BA） scale-free networks which may describe some non-trivial properties of social systems. Using Monte Carlo simulations, we find that the order-disorder transition point of the VMR model is greatly affected by the average degree （k） of the networks; a larger value of （k） results in a more ordered state of the system. Comparing WS networks with BA networks, we find WS networks have better orderliness than BA networks when the average degree （k） is small. With the increase of （k）, BA networks have a more ordered state. By implementing finite-size scaling analysis, we also obtain critical exponents β/v, γ/u and 1/v for several values of average degree （k）. Our results may be helpful to understand structural effects on order-disorder phase transition in the context of the majority rule model.
文摘We investigate different types of synchronization between two unidirectionally nonlinearly coupled identical delay- differential systems related to optical bistable or hybrid optical bistable devices. This system can represent some kinds of delay-differential models, i.e. Ikeda model, Vall^e model, sine-square model, Mackey Glass model, and so on. We find existence and sufficient stability conditions by theoretical analysis and test the correctness by＂ numerical simulations. Lag, complete and anticipating synchronization are observed, respectively. It is found that the time-delay system can be divided into two parts~ one is the instant term and the other is the delay term. Synchronization between two identical chaotic systems can be derived by adding a coupled term to the delay term in the driven system.
