Zhigang Zheng | Huaqiao University (original) (raw)
Papers by Zhigang Zheng
Communications in Theoretical Physics, 2002
ABSTRACT
Communications in Theoretical Physics, 2005
ABSTRACT Recent developments in studies of directed transport processes in interacting particle s... more ABSTRACT Recent developments in studies of directed transport processes in interacting particle systems are retrospected. Due to the interactions among elements, the directed transport process exhibits complicated and novel cooperative dynamics. We considered various possibilities in achieving ratchet motion by breaking different symmetries of many-body systems. It is shown that the directional transport can even be induced by breaking the coupling symmetry and the spatiotemporal symmetries.
Chinese Physics B, 2008
ABSTRACT Nonlinear dynamics of the time-delayed Mackey–Glass systems is explored. Coexistent mult... more ABSTRACT Nonlinear dynamics of the time-delayed Mackey–Glass systems is explored. Coexistent multiple chaotic attractors are found. Attractors with double-scroll structures can be well classified in terms of different return times within one period of the delay time by constructing the Poincaré section. Synchronizations of the drive–response Mackey–Glass oscillators are investigated. The critical coupling strength for the emergence of generalized synchronization against the delay time exhibits the interesting resonant behaviour. We reveal that stronger resonance effect may be observed when different attractors are applied to the drivers, i.e., more resonance peaks can be found.
Chinese Physics, 2006
ABSTRACT Dynamical behaviours of the motion of particles in a periodic potential under a constant... more ABSTRACT Dynamical behaviours of the motion of particles in a periodic potential under a constant driving velocity by a spring at one end are explored. In the stationary case, the stable equilibrium position of the particle experiences an elasticity instability transition. When the driving velocity is nonzero, depending on the elasticity coefficient and the pulling velocity, the system exhibits complicated and interesting dynamics, such as periodic and chaotic motions. The results obtained here may shed light on studies of dynamical processes in sliding friction.
Physical Review Research
A topological mechanism of the emergence of chimeralike oscillation modes (CLOMs) consisting of c... more A topological mechanism of the emergence of chimeralike oscillation modes (CLOMs) consisting of coherent synchronous firings and incoherent nonsynchronous oscillations is proposed in excitable scale-free networks (ESFNs). It is revealed that the topology heterogeneity of the network is responsible for forming and maintaining the CLOM in the ESFN, which is definitely different from the mechanism of the normal oscillation mode (NOM) possessing only a single dynamical mode in homogeneous excitable systems. An effective-driving approach is proposed, which provides a criterion for the formation of the CLOM in excitable complex networks. Our contributions may shed light on a perspective of CLOMs in complex systems, and can help us understand competitions and self-organizations of NOM and CLOM in excitable systems with topological homogeneity and heterogeneity.
Nonlinear Dynamics, 2021
The classical Kuramoto model serves as a useful tool for studying synchronization transitions in ... more The classical Kuramoto model serves as a useful tool for studying synchronization transitions in coupled oscillators that is limited to the sinusoidal and pairwise interactions. In this paper, we extend the classical Kuramoto model to incorporate the high-order structures and non-pairwise interactions into the coupling function. Using a self-consistent approach and constructing parametric functions, we describe the extensive multi-cluster states induced by high-order structures and identify various types of phase transitions toward synchrony. In particular, we establish the universal scaling relation for each branch of multiclusters, which describes the asymptotic dependence of the order parameters (Kuramoto and Daido) on the coupling strength near the critical points.
The transport of a walker in rocking feedback-controlled ratchets are investigated. The walker co... more The transport of a walker in rocking feedback-controlled ratchets are investigated. The walker consists of two coupled "feet" that allow the interchange of the order of the particles while the walker moves. In the underdamped case, the deterministic dynamics of the walker in a tilted asymmetric ratchet with an external periodic force is considered. It is found that the delayed feedback ratchets with a switching-on-and-off dependence of the states of the system can lead to the absolute negative mobility (ANM). In such a novel phenomenon the particles move against the bias. Moreover, the walker can acquire a series of resonant steps for different values of the current. Remarkably, it is interesting to find that the resonant current of the walker are induced by the phase locked motion that corresponds to the synchronization of the motion with the change in the frequency of the external driving. These resonant steps can be well predicted in terms of time-space symmetry analysi...
Kink dynamics of the damped Frenkel-Kontorova (discrete sine-Gordon) chain driven by a constant e... more Kink dynamics of the damped Frenkel-Kontorova (discrete sine-Gordon) chain driven by a constant external force are investigated. Resonant steplike transitions of the average velocity occur due to the competitions between the moving kinks and their radiated phasonlike modes. A mean-field consideration is introduced to give a precise prediction of the resonant steps. Slip-stick motion and spatiotemporal dynamics on those resonant steps are discussed. Our results can be applied to studies of the fluxon dynamics of 1D Josephson-junction arrays and ladders, dislocations, tribology and other fields.
In this paper, we propose a framework to investigate the collective dynamics in ensembles of glob... more In this paper, we propose a framework to investigate the collective dynamics in ensembles of globally coupled phase oscillators when higher-order modes dominate the coupling. The spatiotemporal properties of the attractors in various regions of parameter space are analyzed. Furthermore, a detailed linear stability analysis proves that the stationary symmetric distribution is only neutrally stable in the marginal regime which stems from the generalized time-reversal symmetry. Moreover, the critical parameters of the transition among various regimes are determined analytically by both the Ott-Antonsen method and linear stability analysis, the transient dynamics are further revealed in terms of the characteristic curves method. Finally, for the more general initial condition the symmetric dynamics could be reduced to a rigorous three-dimensional manifold which shows that the neutrally stable chaos could also occur in this model for particular parameter. Our theoretical analysis and num...
The spatiotemporal propagation behavior of a solitary wave is investigated on a Fermi-Pasta-Ulam ... more The spatiotemporal propagation behavior of a solitary wave is investigated on a Fermi-Pasta-Ulam ring. We observe the emergence of a cnoidal wave excited by the solitary wave. The cnoidal wave may coexist with the solitary wave for a long time associated with the periodic exchange of energy between these two nonlinear waves. The module of the cnoidal wave, which is considered as an indicator of the nonlinearity, is found to oscillate with the same period of the energy exchange. After the stage of coexistence, the interaction between these two nonlinear waves leads to the destruction of the cnoidal wave by the radiation of phonons. Finally, the interaction of the solitary wave with phonons leads to the loss of stability of the solitary wave.
The behaviors of coupled chaotic oscillators before complete synchronization were investigated. W... more The behaviors of coupled chaotic oscillators before complete synchronization were investigated. We report three phenomena: (1) The emergence of long-time residence of trajectories besides one of the saddle foci; (2) The tendency that orbits of the two oscillators get close becomes faster with increasing the coupling strength; (3) The diffusion of two oscillator's phase difference is first enhanced and then suppressed. There are exact correspondences among these phenomena. The mechanism of these correspondences is explored. These phenomena uncover the route to synchronization of coupled chaotic oscillators.
Collective behaviors of coupled oscillators have attracted much attention. In this Letter, we pro... more Collective behaviors of coupled oscillators have attracted much attention. In this Letter, we propose an ensemble order parameter(EOP) equation that enables us to grasp the essential low-dimensional dynamical mechanism of the explosive synchronization in heterogeneous networks. Dif- ferent solutions of the EOP equation build correspondences with diverse collective states, and different bifurcations reveal various transitions among these collective states. The structural relationship between the incoherent state and synchronous state leads to different routes of transitions to synchronization, either continuous or discontinuous. The explosive synchronization is determined by the bistable state where the measure of each state and the critical points are obtained analytically by using the EOP equation. Our method and results hold for heterogeneous networks with star graph motifs such as scale-free networks, and hence, provide an effective approach in understanding the routes to synchro...
We generalize the Kuramoto model for the synchronization transition of globally coupled phase osc... more We generalize the Kuramoto model for the synchronization transition of globally coupled phase oscillators to populations by incorporating an additional heterogeneity with the coupling strength, where each oscillator pair interacts with different coupling strength weighted by a genera; function of their natural frequency. The expression for the critical coupling can be straightforwardly extended to a generalized explicit formula analytically, and s self-consistency approach is developed to predict the stationary states in the thermodynamic limit. The landau damping effect is further revealed by means of the linear stability analysis and resonance poles theory above the critical threshold which turns to be far more generic. Furthermore, the dimensionality reduction technique of the Ott-Antonsen is implemented to capture the analytical description of relaxation dynamics of the steady states valid on a globally attracting manifold. Our theoretical analysis and numerical results are cons...
2008 IEEE Conference on Computer Vision and Pattern Recognition, 2008
This paper presents a new stereo matching algorithm based on interregional cooperative optimizati... more This paper presents a new stereo matching algorithm based on interregional cooperative optimization. The proposed algorithm uses regions as matching primitives and defines the corresponding region energy functional for matching by utilizing the color Statistics of regions and the constraints on smoothness and occlusion between adjacent regions. In order to obtain a more reasonable disparity map, a cooperative optimization procedure has been employed to minimize the matching costs of all regions by introducing the cooperative and competitive mechanism between regions. Firstly, a color based segmentation method is used to segment the reference image into regions with homogeneous color. Secondly, a local window-based matching method is used to determine the initial disparity estimate of each image pixel. And then, a voting based plane fitting technique is applied to obtain the parameters of disparity plane corresponding to each image region. Finally, the disparity plane parameters of all regions are iteratively optimized by an interregional cooperative optimization procedure until a reasonable disparity map is obtained. The experimental Results on Middlebury test set and real stereo images indicate that the performance of our method is competitive with the best stereo matching algorithms and the disparity maps recovered are close to the ground truth data.
1 Science Education Department, Beijing Institute of Graphic Communication, Beijing 102600, China... more 1 Science Education Department, Beijing Institute of Graphic Communication, Beijing 102600, China College of Science, Hebei University of Architecture, Zhangjiakou 075000, China School of science, Tianjin University, Tianjin 300072, China 4 School of science, Hebei University of Technology, Tianjin 300401, China Institute of Systems Science and College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China Corresponding author. E-mail: † zgzheng@hqu.edu.cn
arXiv: Adaptation and Self-Organizing Systems, 2015
The OA ansatz has attracted much attention recently, infinite-dimensional Kuramoto model could co... more The OA ansatz has attracted much attention recently, infinite-dimensional Kuramoto model could collapses to a two-dimensional system of order differential equations with it. In this paper, we propose the ensemble order parameter (EOP) equations to describe the dynamics for networks with a finite size. To verify the effectiveness of this method, we apply it into the star network and star-connected network. In the star network, numerous phase transitions among different synchronous states are observed, three processes of synchronization, one process of de-synchronization and a group of hybrid phase transitions, the processes of those transitions are revealed by the EOP dynamics and other nolinear tools such as time reversibility analysis and linear stability analysis. Also in the star-connected network, the two-step synchronization transition is observed. The process of it is still be revealed by the similar methods in the single star network.
Frontiers and Progress of Current Soft Matter Research, 2020
Journal of Statistical Mechanics: Theory and Experiment, 2016
Traditionally, time delay in overdamped Brownian ratchet systems reduces the rectified transport.... more Traditionally, time delay in overdamped Brownian ratchet systems reduces the rectified transport. Strikingly, in our delayed feedback ratchets, which are alternatively switched on and o in dependence of the state of the system, time delay can have significant positive-eects that the average velocity of the coupled ratchets are improved with the presence of the delayed time. Moreover, the anomalous transport can arise and then the negative mobility phenomenon appears by changing the bias force. Meanwhile, the bias force F can facilitate Stokes eciency of delayed feedback ratchets in the anomalous transport region. Remarkably, it is interesting to find that the coupled ratchets can acquire a series of resonant steps that are induced by frequency locking. More importantly, the optimal delay time can also facilitate Stokes eciency. The theoretical results may provide a new operating technique in which micro-and nano-motor performance could be improved by the state or information of the delayed feedback coupled ratchets.
Frontiers of Physics, 2017
Collective behaviors of populations of coupled oscillators have attracted much attention in recen... more Collective behaviors of populations of coupled oscillators have attracted much attention in recent years. In this paper, an order parameter approach is proposed to study the low-dimensional dynamical mechanism of collective synchronizations by adopting the star-topology of coupled oscillators as a prototype system. The order parameter equation of star-linked phase oscillators can be obtained in terms of the Watanabe-Strogatz transformation, Ott-Antonsen ansatz, and the ensemble order parameter approach. Different solutions of the order parameter equation correspond to diverse collective states, and different bifurcations reveal various transitions among these collective states. The properties of various transitions are revealed in the star-network model by using tools of nonlinear dynamics such as time reversibility analysis and linear stability analysis.
Communications in Theoretical Physics, 2001
ABSTRACT
Communications in Theoretical Physics, 2002
ABSTRACT
Communications in Theoretical Physics, 2005
ABSTRACT Recent developments in studies of directed transport processes in interacting particle s... more ABSTRACT Recent developments in studies of directed transport processes in interacting particle systems are retrospected. Due to the interactions among elements, the directed transport process exhibits complicated and novel cooperative dynamics. We considered various possibilities in achieving ratchet motion by breaking different symmetries of many-body systems. It is shown that the directional transport can even be induced by breaking the coupling symmetry and the spatiotemporal symmetries.
Chinese Physics B, 2008
ABSTRACT Nonlinear dynamics of the time-delayed Mackey–Glass systems is explored. Coexistent mult... more ABSTRACT Nonlinear dynamics of the time-delayed Mackey–Glass systems is explored. Coexistent multiple chaotic attractors are found. Attractors with double-scroll structures can be well classified in terms of different return times within one period of the delay time by constructing the Poincaré section. Synchronizations of the drive–response Mackey–Glass oscillators are investigated. The critical coupling strength for the emergence of generalized synchronization against the delay time exhibits the interesting resonant behaviour. We reveal that stronger resonance effect may be observed when different attractors are applied to the drivers, i.e., more resonance peaks can be found.
Chinese Physics, 2006
ABSTRACT Dynamical behaviours of the motion of particles in a periodic potential under a constant... more ABSTRACT Dynamical behaviours of the motion of particles in a periodic potential under a constant driving velocity by a spring at one end are explored. In the stationary case, the stable equilibrium position of the particle experiences an elasticity instability transition. When the driving velocity is nonzero, depending on the elasticity coefficient and the pulling velocity, the system exhibits complicated and interesting dynamics, such as periodic and chaotic motions. The results obtained here may shed light on studies of dynamical processes in sliding friction.
Physical Review Research
A topological mechanism of the emergence of chimeralike oscillation modes (CLOMs) consisting of c... more A topological mechanism of the emergence of chimeralike oscillation modes (CLOMs) consisting of coherent synchronous firings and incoherent nonsynchronous oscillations is proposed in excitable scale-free networks (ESFNs). It is revealed that the topology heterogeneity of the network is responsible for forming and maintaining the CLOM in the ESFN, which is definitely different from the mechanism of the normal oscillation mode (NOM) possessing only a single dynamical mode in homogeneous excitable systems. An effective-driving approach is proposed, which provides a criterion for the formation of the CLOM in excitable complex networks. Our contributions may shed light on a perspective of CLOMs in complex systems, and can help us understand competitions and self-organizations of NOM and CLOM in excitable systems with topological homogeneity and heterogeneity.
Nonlinear Dynamics, 2021
The classical Kuramoto model serves as a useful tool for studying synchronization transitions in ... more The classical Kuramoto model serves as a useful tool for studying synchronization transitions in coupled oscillators that is limited to the sinusoidal and pairwise interactions. In this paper, we extend the classical Kuramoto model to incorporate the high-order structures and non-pairwise interactions into the coupling function. Using a self-consistent approach and constructing parametric functions, we describe the extensive multi-cluster states induced by high-order structures and identify various types of phase transitions toward synchrony. In particular, we establish the universal scaling relation for each branch of multiclusters, which describes the asymptotic dependence of the order parameters (Kuramoto and Daido) on the coupling strength near the critical points.
The transport of a walker in rocking feedback-controlled ratchets are investigated. The walker co... more The transport of a walker in rocking feedback-controlled ratchets are investigated. The walker consists of two coupled "feet" that allow the interchange of the order of the particles while the walker moves. In the underdamped case, the deterministic dynamics of the walker in a tilted asymmetric ratchet with an external periodic force is considered. It is found that the delayed feedback ratchets with a switching-on-and-off dependence of the states of the system can lead to the absolute negative mobility (ANM). In such a novel phenomenon the particles move against the bias. Moreover, the walker can acquire a series of resonant steps for different values of the current. Remarkably, it is interesting to find that the resonant current of the walker are induced by the phase locked motion that corresponds to the synchronization of the motion with the change in the frequency of the external driving. These resonant steps can be well predicted in terms of time-space symmetry analysi...
Kink dynamics of the damped Frenkel-Kontorova (discrete sine-Gordon) chain driven by a constant e... more Kink dynamics of the damped Frenkel-Kontorova (discrete sine-Gordon) chain driven by a constant external force are investigated. Resonant steplike transitions of the average velocity occur due to the competitions between the moving kinks and their radiated phasonlike modes. A mean-field consideration is introduced to give a precise prediction of the resonant steps. Slip-stick motion and spatiotemporal dynamics on those resonant steps are discussed. Our results can be applied to studies of the fluxon dynamics of 1D Josephson-junction arrays and ladders, dislocations, tribology and other fields.
In this paper, we propose a framework to investigate the collective dynamics in ensembles of glob... more In this paper, we propose a framework to investigate the collective dynamics in ensembles of globally coupled phase oscillators when higher-order modes dominate the coupling. The spatiotemporal properties of the attractors in various regions of parameter space are analyzed. Furthermore, a detailed linear stability analysis proves that the stationary symmetric distribution is only neutrally stable in the marginal regime which stems from the generalized time-reversal symmetry. Moreover, the critical parameters of the transition among various regimes are determined analytically by both the Ott-Antonsen method and linear stability analysis, the transient dynamics are further revealed in terms of the characteristic curves method. Finally, for the more general initial condition the symmetric dynamics could be reduced to a rigorous three-dimensional manifold which shows that the neutrally stable chaos could also occur in this model for particular parameter. Our theoretical analysis and num...
The spatiotemporal propagation behavior of a solitary wave is investigated on a Fermi-Pasta-Ulam ... more The spatiotemporal propagation behavior of a solitary wave is investigated on a Fermi-Pasta-Ulam ring. We observe the emergence of a cnoidal wave excited by the solitary wave. The cnoidal wave may coexist with the solitary wave for a long time associated with the periodic exchange of energy between these two nonlinear waves. The module of the cnoidal wave, which is considered as an indicator of the nonlinearity, is found to oscillate with the same period of the energy exchange. After the stage of coexistence, the interaction between these two nonlinear waves leads to the destruction of the cnoidal wave by the radiation of phonons. Finally, the interaction of the solitary wave with phonons leads to the loss of stability of the solitary wave.
The behaviors of coupled chaotic oscillators before complete synchronization were investigated. W... more The behaviors of coupled chaotic oscillators before complete synchronization were investigated. We report three phenomena: (1) The emergence of long-time residence of trajectories besides one of the saddle foci; (2) The tendency that orbits of the two oscillators get close becomes faster with increasing the coupling strength; (3) The diffusion of two oscillator's phase difference is first enhanced and then suppressed. There are exact correspondences among these phenomena. The mechanism of these correspondences is explored. These phenomena uncover the route to synchronization of coupled chaotic oscillators.
Collective behaviors of coupled oscillators have attracted much attention. In this Letter, we pro... more Collective behaviors of coupled oscillators have attracted much attention. In this Letter, we propose an ensemble order parameter(EOP) equation that enables us to grasp the essential low-dimensional dynamical mechanism of the explosive synchronization in heterogeneous networks. Dif- ferent solutions of the EOP equation build correspondences with diverse collective states, and different bifurcations reveal various transitions among these collective states. The structural relationship between the incoherent state and synchronous state leads to different routes of transitions to synchronization, either continuous or discontinuous. The explosive synchronization is determined by the bistable state where the measure of each state and the critical points are obtained analytically by using the EOP equation. Our method and results hold for heterogeneous networks with star graph motifs such as scale-free networks, and hence, provide an effective approach in understanding the routes to synchro...
We generalize the Kuramoto model for the synchronization transition of globally coupled phase osc... more We generalize the Kuramoto model for the synchronization transition of globally coupled phase oscillators to populations by incorporating an additional heterogeneity with the coupling strength, where each oscillator pair interacts with different coupling strength weighted by a genera; function of their natural frequency. The expression for the critical coupling can be straightforwardly extended to a generalized explicit formula analytically, and s self-consistency approach is developed to predict the stationary states in the thermodynamic limit. The landau damping effect is further revealed by means of the linear stability analysis and resonance poles theory above the critical threshold which turns to be far more generic. Furthermore, the dimensionality reduction technique of the Ott-Antonsen is implemented to capture the analytical description of relaxation dynamics of the steady states valid on a globally attracting manifold. Our theoretical analysis and numerical results are cons...
2008 IEEE Conference on Computer Vision and Pattern Recognition, 2008
This paper presents a new stereo matching algorithm based on interregional cooperative optimizati... more This paper presents a new stereo matching algorithm based on interregional cooperative optimization. The proposed algorithm uses regions as matching primitives and defines the corresponding region energy functional for matching by utilizing the color Statistics of regions and the constraints on smoothness and occlusion between adjacent regions. In order to obtain a more reasonable disparity map, a cooperative optimization procedure has been employed to minimize the matching costs of all regions by introducing the cooperative and competitive mechanism between regions. Firstly, a color based segmentation method is used to segment the reference image into regions with homogeneous color. Secondly, a local window-based matching method is used to determine the initial disparity estimate of each image pixel. And then, a voting based plane fitting technique is applied to obtain the parameters of disparity plane corresponding to each image region. Finally, the disparity plane parameters of all regions are iteratively optimized by an interregional cooperative optimization procedure until a reasonable disparity map is obtained. The experimental Results on Middlebury test set and real stereo images indicate that the performance of our method is competitive with the best stereo matching algorithms and the disparity maps recovered are close to the ground truth data.
1 Science Education Department, Beijing Institute of Graphic Communication, Beijing 102600, China... more 1 Science Education Department, Beijing Institute of Graphic Communication, Beijing 102600, China College of Science, Hebei University of Architecture, Zhangjiakou 075000, China School of science, Tianjin University, Tianjin 300072, China 4 School of science, Hebei University of Technology, Tianjin 300401, China Institute of Systems Science and College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China Corresponding author. E-mail: † zgzheng@hqu.edu.cn
arXiv: Adaptation and Self-Organizing Systems, 2015
The OA ansatz has attracted much attention recently, infinite-dimensional Kuramoto model could co... more The OA ansatz has attracted much attention recently, infinite-dimensional Kuramoto model could collapses to a two-dimensional system of order differential equations with it. In this paper, we propose the ensemble order parameter (EOP) equations to describe the dynamics for networks with a finite size. To verify the effectiveness of this method, we apply it into the star network and star-connected network. In the star network, numerous phase transitions among different synchronous states are observed, three processes of synchronization, one process of de-synchronization and a group of hybrid phase transitions, the processes of those transitions are revealed by the EOP dynamics and other nolinear tools such as time reversibility analysis and linear stability analysis. Also in the star-connected network, the two-step synchronization transition is observed. The process of it is still be revealed by the similar methods in the single star network.
Frontiers and Progress of Current Soft Matter Research, 2020
Journal of Statistical Mechanics: Theory and Experiment, 2016
Traditionally, time delay in overdamped Brownian ratchet systems reduces the rectified transport.... more Traditionally, time delay in overdamped Brownian ratchet systems reduces the rectified transport. Strikingly, in our delayed feedback ratchets, which are alternatively switched on and o in dependence of the state of the system, time delay can have significant positive-eects that the average velocity of the coupled ratchets are improved with the presence of the delayed time. Moreover, the anomalous transport can arise and then the negative mobility phenomenon appears by changing the bias force. Meanwhile, the bias force F can facilitate Stokes eciency of delayed feedback ratchets in the anomalous transport region. Remarkably, it is interesting to find that the coupled ratchets can acquire a series of resonant steps that are induced by frequency locking. More importantly, the optimal delay time can also facilitate Stokes eciency. The theoretical results may provide a new operating technique in which micro-and nano-motor performance could be improved by the state or information of the delayed feedback coupled ratchets.
Frontiers of Physics, 2017
Collective behaviors of populations of coupled oscillators have attracted much attention in recen... more Collective behaviors of populations of coupled oscillators have attracted much attention in recent years. In this paper, an order parameter approach is proposed to study the low-dimensional dynamical mechanism of collective synchronizations by adopting the star-topology of coupled oscillators as a prototype system. The order parameter equation of star-linked phase oscillators can be obtained in terms of the Watanabe-Strogatz transformation, Ott-Antonsen ansatz, and the ensemble order parameter approach. Different solutions of the order parameter equation correspond to diverse collective states, and different bifurcations reveal various transitions among these collective states. The properties of various transitions are revealed in the star-network model by using tools of nonlinear dynamics such as time reversibility analysis and linear stability analysis.
Communications in Theoretical Physics, 2001
ABSTRACT