We study evolutionary games in two-layer networks by introducing the correlation between two layers through the C-dominance or the D-dominance. We assume that individuals play prisoner＇s dilemma game （PDG） in one l...We study evolutionary games in two-layer networks by introducing the correlation between two layers through the C-dominance or the D-dominance. We assume that individuals play prisoner＇s dilemma game （PDG） in one layer and snowdrift game （SDG） in the other. We explore the dependences of the fraction of the strategy cooperation in different layers on the game parameter and initial conditions. The results on two-layer square lattices show that, when cooperation is the dominant strategy, initial conditions strongly influence cooperation in the PDG layer while have no impact in the SDG layer. Moreover, in contrast to the result for PDG in single-layer square lattices, the parameter regime where cooperation could be maintained expands significantly in the PDG layer. We also investigate the effects of mutation and network topology. We find that different mutation rates do not change the cooperation behaviors. Moreover, similar behaviors on cooperation could be found in two-layer random networks.展开更多
Chimera states consisting of spatially coherent and incoherent domains have been observed in differ- ent topologies such as rings, spheres, and complex networks. In this paper, we investigate bipartite networks of non...Chimera states consisting of spatially coherent and incoherent domains have been observed in differ- ent topologies such as rings, spheres, and complex networks. In this paper, we investigate bipartite networks of nonlocally coupled FitzHugh-Nagumo （FHN） oscillators in which the units are allocated evenly to two layers, and FHN units interact with each other only when they are in different lay- ers. We report the existence of chimera states in bipartite networks. Owing to the interplay between chimera states in the two layers, many types of chimera states such as in-phase chimera states, an- tiphase chimera states, and out-of-phase chimera states are classified. Stability diagrams of several typical chimera states in the coupling strength-coupling radius plane, which show strong multistability of chimera states, are explored.展开更多
Chimera states,a symmetry-breaking spatiotemporal pattern in nonlocally coupled dynamical units,prevail in a variety of systems.However,the interaction structures among oscillators are static in most of studies on chi...Chimera states,a symmetry-breaking spatiotemporal pattern in nonlocally coupled dynamical units,prevail in a variety of systems.However,the interaction structures among oscillators are static in most of studies on chimera state.In this work,we consider a population of agents.Each agent carries a phase oscillator.We assume that agents perform Brownian motions on a ring and interact with each other with a kernel function dependent on the distance between them.When agents are motionless,the model allows for several dynamical states including two different chimera states (the type-Ⅰ and the type-Ⅱ chimeras).The movement of agents changes the relative positions among them and produces perpetual noise to impact on the model dynamics.We find that the response of the coupled phase oscillators to the movement of agents depends on both the phase lag α,determining the stabilities of chimera states,and the agent mobility D.For low mobility,the synchronous state transits to the type-Ⅰ chimera state for α close to π/2 and attracts other initial states otherwise.For intermediate mobility,the coupled oscillators randomly jump among different dynamical states and the jump dynamics depends on α.We investigate the statistical properties in these different dynamical regimes and present the scaling laws between the transient time and the mobility for low mobility and relations between the mean lifetimes of different dynamical states and the mobility for intermediate mobility.展开更多
Chimera states,a symmetry-breaking spatiotemporal pattern in nonlocally coupled identical dynamical units,have been identified in various systems and generalized to coupled nonidentical oscillators.It has been shown t...Chimera states,a symmetry-breaking spatiotemporal pattern in nonlocally coupled identical dynamical units,have been identified in various systems and generalized to coupled nonidentical oscillators.It has been shown that strong heterogeneity in the frequencies of nonidentical oscillators might be harmful to chimera states.In this work,we consider a ring of nonlocally coupled bicomponent phase oscillators in which two types of oscillators are randomly distributed along the ring:some oscillators with natural.frequency w1 and others with w2.In this model,the heterogeneity in frequency is measured by frequency mismatch|w1-w2|between the oscillators in these two subpopulations.We report that the nonlocally coupled bicomponent phase oscillators allow for chimera states no matter how large the frequency mismatch is.The bicomponent oscillators are composed of two chimera states,one supported by oscillators with natural frequency wI and the other by oscillators with natural frequency w2.The two chimera states in two subpopulations are synchronized at weak frequency mismatch,in which the coberent oscillators in thern share similar mean phase velocity,and are desynchronized at large frequency mismatch,in which the coherent oscillators in different subpopulations have distinct mean phase velocities.The synchronization-desynchronization transition between chimera states in these two subpopulations is observed with the increase in the frequency mismatch.The observed phenomena are theoretically analyzed by passing to the continuum limit and using the Ott-Antonsen approach.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos 11575036,71301012,and 11505016
文摘We study evolutionary games in two-layer networks by introducing the correlation between two layers through the C-dominance or the D-dominance. We assume that individuals play prisoner＇s dilemma game （PDG） in one layer and snowdrift game （SDG） in the other. We explore the dependences of the fraction of the strategy cooperation in different layers on the game parameter and initial conditions. The results on two-layer square lattices show that, when cooperation is the dominant strategy, initial conditions strongly influence cooperation in the PDG layer while have no impact in the SDG layer. Moreover, in contrast to the result for PDG in single-layer square lattices, the parameter regime where cooperation could be maintained expands significantly in the PDG layer. We also investigate the effects of mutation and network topology. We find that different mutation rates do not change the cooperation behaviors. Moreover, similar behaviors on cooperation could be found in two-layer random networks.
基金This work was supported by the National Natural Science Foundation of China under Grant Nos. 11575036 and 11505016.
文摘Chimera states consisting of spatially coherent and incoherent domains have been observed in differ- ent topologies such as rings, spheres, and complex networks. In this paper, we investigate bipartite networks of nonlocally coupled FitzHugh-Nagumo （FHN） oscillators in which the units are allocated evenly to two layers, and FHN units interact with each other only when they are in different lay- ers. We report the existence of chimera states in bipartite networks. Owing to the interplay between chimera states in the two layers, many types of chimera states such as in-phase chimera states, an- tiphase chimera states, and out-of-phase chimera states are classified. Stability diagrams of several typical chimera states in the coupling strength-coupling radius plane, which show strong multistability of chimera states, are explored.
基金supported by the National Natural Science Foundation of China (Grant Nos.11575036,11805021, and 11505016).Compliance with ethical standards. The authors declare that they have no conflict of interest concerning the publication of this manuscript.
文摘Chimera states,a symmetry-breaking spatiotemporal pattern in nonlocally coupled dynamical units,prevail in a variety of systems.However,the interaction structures among oscillators are static in most of studies on chimera state.In this work,we consider a population of agents.Each agent carries a phase oscillator.We assume that agents perform Brownian motions on a ring and interact with each other with a kernel function dependent on the distance between them.When agents are motionless,the model allows for several dynamical states including two different chimera states (the type-Ⅰ and the type-Ⅱ chimeras).The movement of agents changes the relative positions among them and produces perpetual noise to impact on the model dynamics.We find that the response of the coupled phase oscillators to the movement of agents depends on both the phase lag α,determining the stabilities of chimera states,and the agent mobility D.For low mobility,the synchronous state transits to the type-Ⅰ chimera state for α close to π/2 and attracts other initial states otherwise.For intermediate mobility,the coupled oscillators randomly jump among different dynamical states and the jump dynamics depends on α.We investigate the statistical properties in these different dynamical regimes and present the scaling laws between the transient time and the mobility for low mobility and relations between the mean lifetimes of different dynamical states and the mobility for intermediate mobility.
基金This work was supported by the National Natural Science Foundation of China(Grants Nos.11575036 and 11805021).
文摘Chimera states,a symmetry-breaking spatiotemporal pattern in nonlocally coupled identical dynamical units,have been identified in various systems and generalized to coupled nonidentical oscillators.It has been shown that strong heterogeneity in the frequencies of nonidentical oscillators might be harmful to chimera states.In this work,we consider a ring of nonlocally coupled bicomponent phase oscillators in which two types of oscillators are randomly distributed along the ring:some oscillators with natural.frequency w1 and others with w2.In this model,the heterogeneity in frequency is measured by frequency mismatch|w1-w2|between the oscillators in these two subpopulations.We report that the nonlocally coupled bicomponent phase oscillators allow for chimera states no matter how large the frequency mismatch is.The bicomponent oscillators are composed of two chimera states,one supported by oscillators with natural frequency wI and the other by oscillators with natural frequency w2.The two chimera states in two subpopulations are synchronized at weak frequency mismatch,in which the coberent oscillators in thern share similar mean phase velocity,and are desynchronized at large frequency mismatch,in which the coherent oscillators in different subpopulations have distinct mean phase velocities.The synchronization-desynchronization transition between chimera states in these two subpopulations is observed with the increase in the frequency mismatch.The observed phenomena are theoretically analyzed by passing to the continuum limit and using the Ott-Antonsen approach.
