In this work, we investigate the amplitude death in coupled system with small number of nonlinear oscillators. We show how the transitions to the partial and the complete amplitude deathes happen. We also show that th...In this work, we investigate the amplitude death in coupled system with small number of nonlinear oscillators. We show how the transitions to the partial and the complete amplitude deathes happen. We also show that the partial amplitude death can be found in globally coupled oscillators either.展开更多
Synchronization of neurons plays an important role in vision, movement and memory. However, many neurological disorders such as epilepsies, Parkinson disease and essen- tial tremor are related to excessive synchroniza...Synchronization of neurons plays an important role in vision, movement and memory. However, many neurological disorders such as epilepsies, Parkinson disease and essen- tial tremor are related to excessive synchronization of neurons. In the line of therapy, stimulations to these pathologically synchronized neurons should be capable of breaking synchrony. As the first step of designing an effective stimulation, we consider desynchro- nization problem of coupled limit-cycle oscillators ensemble. First, the desynchronization problem is redefined in a nonlinear output regulation framework. Then, we design an output regulator （stimulation） which forces limit-cycle oscillators to track exogenous sinusoidal references with different phases. The proposed stimulation is robust against variations of oscillators＇ frequencies. Mathematical analysis and simulation results reveal the efficiency of the proposed technique.展开更多
Models of circadian genetic oscillators involving interlinked feedback processes in molecular level genetic networks in Drosophila melanogaster and Neurospora crassa are studied, and mechanisms whereby synchronization...Models of circadian genetic oscillators involving interlinked feedback processes in molecular level genetic networks in Drosophila melanogaster and Neurospora crassa are studied, and mechanisms whereby synchronization can arise in an assembly of cells are examined. The individual subcellular circadian oscillatory processes are stochastic in nature due to the small numbers of molecules that are involved, and are subject to large fluctuations. The authors investigate and present the simulations of the stochastic dynamics of ensembles of clock-regulating proteins in different nuclei that communicate via ancillary small molecules, environmental parameters, additive cellular noise, or through diffusive processes. The results show that the emergence of collective oscillations is a macroscopic observable which has its origins in the microscopic coupling between distinct cellular oscillators.展开更多
We have studied why PA （post-annealing） takes a long time to restore damaged crystallinity, which corresponds to repeat 10 10 times of lattice vibrations. Using a MD （molecular dynamics） simulation, we monitored t...We have studied why PA （post-annealing） takes a long time to restore damaged crystallinity, which corresponds to repeat 10 10 times of lattice vibrations. Using a MD （molecular dynamics） simulation, we monitored the time-series of the LRO （long-range order） parameter as LRO pattern, in the case of a type IIa diamond, from the beginning of ion impact by a sub-keV N2 beam implantation to a few nanoseconds, i.e., close to the feasible time limit for MD simulations. Due to the ion impact, the LRO parameter changed gradually from ＂LRO = 1＂ （crystal） to ＂LRO = 0＂ （amorphous）, showing the so-called critical slowing-down phenomenon. However, since PA was started the LRO pattern was not unique. The LRO patterns were grouped into more than three types of phases and the transition between them was also found. From the viewpoint of statistical dynamics, such chaotic variations in the LRO pattern may present that the system is a GCM （globally coupled map） of a complex system in a closed system. A GCM composed of coupled oscillators develops slowly to exhibit several different phases or ‘chaotic itinerancy＇ over time. Therefore, the long duration required for PA may be attributable to the nature of a complex system.展开更多
El Nifio and Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific sea-air interactions. An asymptotic method of solving equations for the ENSO model is proposed. Based on a class...El Nifio and Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific sea-air interactions. An asymptotic method of solving equations for the ENSO model is proposed. Based on a class of oscillator of ENSO model and by employing a simple and valid method of the variational iteration, the coupled system for a sea-air oscillator model of interdecadal climate fluctuations is studied. Firstly, by introducing a set of functionals and computing the variationals, the Lagrange multipliers are obtained. And then, the generalized variational iteration expressions are constructed. Finally, by selecting appropriate initial iteration, and from the iterations expressions, the approximations of solution for the sea-air oscillator ENSO model are solved successively. The approximate dissipative travelling wave solution of equations for corresponding ENSO model is studied. It is proved from the results that the method of the variational iteration can be used for analyzing the sea surface temperature anomaly in the equatorial Pacific of the sea-air oscillator for ENSO model.展开更多
We report some new results associated with the synchronization behavior of two coupled double-well Duffing oscillators （DDOs）. Some sufficient algebraic criteria for global chaos synchronization of the drive and res...We report some new results associated with the synchronization behavior of two coupled double-well Duffing oscillators （DDOs）. Some sufficient algebraic criteria for global chaos synchronization of the drive and response DDOs via linear state error feedback control are obtained by means of Lyapunov stability theory. The synchronization is achieved through a bistable state in which a periodic attractor co-exists with a chaotic attractor. Using the linear perturbation analysis, the prevalence of attractors in parameter space and the associated bifurcations are examined. Subcritical and supercritical Hopf bifurcations and abundance of Arnold tongues -- a signature of mode locking phenomenon are found.展开更多
A generalization of the Kuramoto model in which oscillators are coupled to the mean field with random signs is investigated in this work. We focus on a situation in which the natural frequencies of oscillators follow ...A generalization of the Kuramoto model in which oscillators are coupled to the mean field with random signs is investigated in this work. We focus on a situation in which the natural frequencies of oscillators follow a uniform probability density. By numerically simulating the model, we find that the model supports a modulated travelling wave state except for already reported 7r state and travelling wave state in the one with natural frequencies following Lorenztian probability density or a delta function. The dependence of the observed dynamics on the parameters of the model is explored and we find that the onset of synchronization in the model displays a non-monotonic dependence on both positive and negative coupling strength.展开更多
基金supported by National Natural Science Foundation of China under Grant No.10775022the New Century Excellent Talent Project of the Ministry of Education of China under Grant No.07-0112
文摘In this work, we investigate the amplitude death in coupled system with small number of nonlinear oscillators. We show how the transitions to the partial and the complete amplitude deathes happen. We also show that the partial amplitude death can be found in globally coupled oscillators either.
文摘Synchronization of neurons plays an important role in vision, movement and memory. However, many neurological disorders such as epilepsies, Parkinson disease and essen- tial tremor are related to excessive synchronization of neurons. In the line of therapy, stimulations to these pathologically synchronized neurons should be capable of breaking synchrony. As the first step of designing an effective stimulation, we consider desynchro- nization problem of coupled limit-cycle oscillators ensemble. First, the desynchronization problem is redefined in a nonlinear output regulation framework. Then, we design an output regulator （stimulation） which forces limit-cycle oscillators to track exogenous sinusoidal references with different phases. The proposed stimulation is robust against variations of oscillators＇ frequencies. Mathematical analysis and simulation results reveal the efficiency of the proposed technique.
文摘Models of circadian genetic oscillators involving interlinked feedback processes in molecular level genetic networks in Drosophila melanogaster and Neurospora crassa are studied, and mechanisms whereby synchronization can arise in an assembly of cells are examined. The individual subcellular circadian oscillatory processes are stochastic in nature due to the small numbers of molecules that are involved, and are subject to large fluctuations. The authors investigate and present the simulations of the stochastic dynamics of ensembles of clock-regulating proteins in different nuclei that communicate via ancillary small molecules, environmental parameters, additive cellular noise, or through diffusive processes. The results show that the emergence of collective oscillations is a macroscopic observable which has its origins in the microscopic coupling between distinct cellular oscillators.
文摘We have studied why PA （post-annealing） takes a long time to restore damaged crystallinity, which corresponds to repeat 10 10 times of lattice vibrations. Using a MD （molecular dynamics） simulation, we monitored the time-series of the LRO （long-range order） parameter as LRO pattern, in the case of a type IIa diamond, from the beginning of ion impact by a sub-keV N2 beam implantation to a few nanoseconds, i.e., close to the feasible time limit for MD simulations. Due to the ion impact, the LRO parameter changed gradually from ＂LRO = 1＂ （crystal） to ＂LRO = 0＂ （amorphous）, showing the so-called critical slowing-down phenomenon. However, since PA was started the LRO pattern was not unique. The LRO patterns were grouped into more than three types of phases and the transition between them was also found. From the viewpoint of statistical dynamics, such chaotic variations in the LRO pattern may present that the system is a GCM （globally coupled map） of a complex system in a closed system. A GCM composed of coupled oscillators develops slowly to exhibit several different phases or ‘chaotic itinerancy＇ over time. Therefore, the long duration required for PA may be attributable to the nature of a complex system.
基金Under the auspices of National Natural Science Foundation of China (No. 40876010)Main Direction Program of Knowledge Innovation Programs of Chinese Academy of Sciences (No. KZCX2-YW-Q03-08)+3 种基金R & D Special Fund for Public Welfare Industry (meteorology) (No.GYHY200806010)LASG State Key Laboratory Special FundFoundation of E-Institutes of Shanghai Municipal Education Commission (No. E03004)Natural Science Foundation of Zhejiang Province (No. Y6090164)
文摘El Nifio and Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific sea-air interactions. An asymptotic method of solving equations for the ENSO model is proposed. Based on a class of oscillator of ENSO model and by employing a simple and valid method of the variational iteration, the coupled system for a sea-air oscillator model of interdecadal climate fluctuations is studied. Firstly, by introducing a set of functionals and computing the variationals, the Lagrange multipliers are obtained. And then, the generalized variational iteration expressions are constructed. Finally, by selecting appropriate initial iteration, and from the iterations expressions, the approximations of solution for the sea-air oscillator ENSO model are solved successively. The approximate dissipative travelling wave solution of equations for corresponding ENSO model is studied. It is proved from the results that the method of the variational iteration can be used for analyzing the sea surface temperature anomaly in the equatorial Pacific of the sea-air oscillator for ENSO model.
基金supported by a fellowship of the Alexander von Humboldt Foundation in Bonn, Germanythe Royal Society of London, British Academy and Physical Sciences Research Council, UK, under the Newton International Fellowship scheme.
文摘We report some new results associated with the synchronization behavior of two coupled double-well Duffing oscillators （DDOs）. Some sufficient algebraic criteria for global chaos synchronization of the drive and response DDOs via linear state error feedback control are obtained by means of Lyapunov stability theory. The synchronization is achieved through a bistable state in which a periodic attractor co-exists with a chaotic attractor. Using the linear perturbation analysis, the prevalence of attractors in parameter space and the associated bifurcations are examined. Subcritical and supercritical Hopf bifurcations and abundance of Arnold tongues -- a signature of mode locking phenomenon are found.
基金Supported by National Natural Science Foundation of China under Grant No. 11247279
文摘A generalization of the Kuramoto model in which oscillators are coupled to the mean field with random signs is investigated in this work. We focus on a situation in which the natural frequencies of oscillators follow a uniform probability density. By numerically simulating the model, we find that the model supports a modulated travelling wave state except for already reported 7r state and travelling wave state in the one with natural frequencies following Lorenztian probability density or a delta function. The dependence of the observed dynamics on the parameters of the model is explored and we find that the onset of synchronization in the model displays a non-monotonic dependence on both positive and negative coupling strength.
