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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... 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.
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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... 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.
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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... 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.
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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... 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.
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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... 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...
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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... 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.
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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... 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...
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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... 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.
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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... 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.
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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... 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 oscillators to populations by incorporating an additional heterogeneity with the coupling strength, where each oscillator pair interacts with... 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...
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Research Interests: Mathematics, Computer Science, Statistics, Iterative Methods, Statistical Analysis, and 14 moreClustering Algorithms, Image segmentation, Estimation Theory, Labeling, Computer Vision and Pattern Recognition, Stereo Vision, Layout, Regional Cooperation, Waste minimisation, Stereo Matching, Ground Truth, Cost Function, Pixel, and Energy function
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... 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
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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)... 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.
Research Interests: Mathematics and Physics
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ABSTRACT Multiple-clustering synchronization is a common scenario of global phase synchronization. However, a novel single-clustering type of phase synchronization in a ring of Kuramoto oscillators has been recently reported in studying... more
ABSTRACT Multiple-clustering synchronization is a common scenario of global phase synchronization. However, a novel single-clustering type of phase synchronization in a ring of Kuramoto oscillators has been recently reported in studying the influence of the permutation of the natural frequencies of oscillators on the synchronization efficiency (Wu et al 2012 Europhys. Lett. 97 40005). It was found that it occurs for a particular spatial frequency distribution and gives rise to a very small critical coupling strength Kc even if the oscillator number is large. Here we focus on this particular type of synchronization and study its generality. We provide some solid evidence for the convergence of Kc to a small constant in the thermodynamic limit, based on the finite size analysis. Further we demonstrate that it is robust in the sense of either switching the natural frequencies of any two oscillators or randomly perturbing the frequencies of all coupled oscillators. All these findings prove that the single-clustering synchronization is indeed generically observable, with merit for potential engineering applications.
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ABSTRACT Nonlinear dynamics of the sliding process of a chain driven with a constant velocity at one end in a periodic substrate potential is investigated. The driven chain exhibits distinctly different dynamical characteristics at... more
ABSTRACT Nonlinear dynamics of the sliding process of a chain driven with a constant velocity at one end in a periodic substrate potential is investigated. The driven chain exhibits distinctly different dynamical characteristics at different velocities. In the low velocity region, the chain moves in a stick–slip manner. When the driving velocity is increased, the stick–slip behaviour is replaced by complicated and regular oscillatory motions. The dependence of the dynamics on the coupling strength is studied and the step-like behaviour is found, where different steps correspond to different dynamical phases.
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The usual linear variable feedback control method is extended to a generalized function feedback scheme. The scheme is applied to high-dimensional spatiotemporal systems. By a combination of local generalized feedback control and the... more
The usual linear variable feedback control method is extended to a generalized function feedback scheme. The scheme is applied to high-dimensional spatiotemporal systems. By a combination of local generalized feedback control and the spatial coupling effect among elements, turbulent motion can be successfully eliminated.
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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 dynam- ical mechanism of collective... 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 dynam- ical 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 col- lective 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.
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The dynamical responses of an excitable FitzHugh–Nagumo (FHN) system under the drive of an external noise are studied. Noise can induce a sequence of firings. The n:m coherent resonance of the FHN oscillator with an intrinsic natural... more
The dynamical responses of an excitable FitzHugh–Nagumo (FHN) system under the drive of an external noise are studied. Noise can induce a sequence of firings. The n:m coherent resonance of the FHN oscillator with an intrinsic natural frequency is shown. This effect is discussed by resorting to the phase dynamics of a spike train and the phase synchronization index γnm.
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Heterogeneous coupling patterns among interacting elements are ubiquitous in real systems ranging from physics, chemistry to biology communities, which have attracted much attention during recent years. In this paper, we extend the... more
Heterogeneous coupling patterns among interacting elements are ubiquitous in real systems ranging from physics, chemistry to biology communities, which have attracted much attention during recent years. In this paper, we extend the Kuramoto model by considering a particular heterogeneous coupling scheme in an ensemble of phase oscillators, where each oscillator pair interacts with different coupling strength that is weighted by a general function of the natural frequency. The Kuramoto theory for the transition to synchronization can be explicitly generalized, such as the expression for the critical coupling strength. Also, a self-consistency approach is developed to predict the stationary states in the thermodynamic limit. Moreover, Landau damping effects are further revealed by means of linear stability analysis and resonance poles theory below the critical threshold, which turns to be far more generic. Our theoretical analysis and numerical results are consistent with each other, ...
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... 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 parameters. Our theoretical analysis and nu...
Coupled phase-oscillators are important models related to synchronization. Recently, Ott-Antonsen(OA) ansatz is developed and used to get low-dimensional collective behaviors in coupled oscillator systems. In this paper, we develop a... more
Coupled phase-oscillators are important models related to synchronization. Recently, Ott-Antonsen(OA) ansatz is developed and used to get low-dimensional collective behaviors in coupled oscillator systems. In this paper, we develop a simple and concise approach based on equations of order parameters, namely, order parameter analysis, with which we point out that OA ansatz is rooted in the dynamical symmetry of order parameters. With our approach the scope of OA ansatz is identified as two conditions, i.e., the limit of infinitely many oscillators and only three nonzero Fourier coefficients of the coupling function. Coinciding with each of the conditions, a distinctive system out of the scope is taken into account and discussed with the order parameter analysis. Two approximation methods are introduced respectively, namely the expectation assumption and the dominating-term assumption.
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Phase synchronized entrainment of coupled oscillators with distributed natural frequencies is studied by exploring the dynamical manifestation. The route from partial to complete phase synchronization is identified as a cascade of... more
Phase synchronized entrainment of coupled oscillators with distributed natural frequencies is studied by exploring the dynamical manifestation. The route from partial to complete phase synchronization is identified as a cascade of transitions from high-to low-...
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It is generally expected that the interface coupling leads to the suppression of thermal transport through coupled nanostructures due to the additional interface phonon-phonon scattering. However, recent experiments demonstrated that the... more
It is generally expected that the interface coupling leads to the suppression of thermal transport through coupled nanostructures due to the additional interface phonon-phonon scattering. However, recent experiments demonstrated that the interface van der Waals interactions can significantly enhance the thermal transfer of bonding boron nanoribbons compared to a single freestanding nanoribbon. To obtain a more in-depth understanding on the important role of the nonlinear interface coupling in the heat transports, in the present paper, we explore the effect of nonlinearity in the interface interaction on the phonon transport by studying the coupled one-dimensional (1D) Frenkel-Kontorova lattices. It is found that the thermal conductivity increases with increasing interface nonlinear intensity for weak inter-chain nonlinearity. By developing the effective phonon theory of coupled systems, we calculate the dependence of heat conductivity on interfacial nonlinearity in weak inter-chain ...