A recent study has found an explosive synchronization in a Kurammoto model on scale-free networks when the natural frequencies of oscillators are equal to their degrees. In this work, we introduce a quantity to charac...A recent study has found an explosive synchronization in a Kurammoto model on scale-free networks when the natural frequencies of oscillators are equal to their degrees. In this work, we introduce a quantity to characterize the correlation between the structural and the dynamical properties and investigate the impacts of the correlation on the synchronization transition in the Kuramoto model on scale-free networks. We find that the synchronization transition may be either a continuous one or a discontinuous one depending on the correlation and that strong correlation always postpones both the transitions from the incoherent state to a synchronous one and the transition from a synchronous state to the incoherent one. We find that the dependence of the synchronization transition on the correlation is also valid for other types of distributions of natural frequency.展开更多
This paper presents an alternative representation of a system of differential equations qualitatively showing the behavior of the biological rhythm of a crayfish during their transition from juvenile to adult stages. ...This paper presents an alternative representation of a system of differential equations qualitatively showing the behavior of the biological rhythm of a crayfish during their transition from juvenile to adult stages. The model focuses on the interaction of four cellular oscillators coupled by diffusion of a hormone, a parameter μ is used to simu- late the quality of communication among the oscillators, in biological terms, it mea- sures developmental maturity of the crayfish. Since some quorum-sensing mechanism is assumed to be responsible for the synchronization of the biological oscillators, it is nat- ural to investigate the possibility that the underlying diffusion process is not standard, i.e. it may be a so-called anomalous diffusion. In this case, it is well understood that diffusion equations with fractional derivatives describe these processes in a more realis- tic way. The alternative formulation of these equations contains fractional operators of Liouville-Caputo and Caputo-Fabrizio type. The numerical simulations of the equations reflect synchronization of ultradian rhythms leading to a circadian rhythm. The classical behavior is recovered when the order of the fractional derivative is V = 1. We discuss possible biological implications.展开更多
Astrocytes have potential to break synchrony between neurons. Authors＇ recent researches reveal that astrocytes vary the synchronization threshold and provide an appropriate feedback control in stabilizing neural act...Astrocytes have potential to break synchrony between neurons. Authors＇ recent researches reveal that astrocytes vary the synchronization threshold and provide an appropriate feedback control in stabilizing neural activities. In this study, we propose an astrocyte-inspired controller for desynchronization of two coupled limit-cycle oscillators as a minimal network model. The design procedure consists of two parts. First, based on the astrocyte model, the structure of the dynamic controller is suggested. Then, to have an emcient controller, parameters of controller are tuned through an optimization algo- rithm. The proposed bio-inspired controller takes advantages of three important proper- ties： （1） the controller desynchronizes the oscillators without any undesirable effects （e.g. stopping, annihilating or starting divergent oscillations）; （2） it consumes little effort to preserve the desirable desynchronized state; and （3） the controller is robust with respect to parameters＇ variations. Simulation results reveal the ability of the proposed controller.展开更多
基金Supported by National Natural Science Foundation of China under Grant No.71301012
文摘A recent study has found an explosive synchronization in a Kurammoto model on scale-free networks when the natural frequencies of oscillators are equal to their degrees. In this work, we introduce a quantity to characterize the correlation between the structural and the dynamical properties and investigate the impacts of the correlation on the synchronization transition in the Kuramoto model on scale-free networks. We find that the synchronization transition may be either a continuous one or a discontinuous one depending on the correlation and that strong correlation always postpones both the transitions from the incoherent state to a synchronous one and the transition from a synchronous state to the incoherent one. We find that the dependence of the synchronization transition on the correlation is also valid for other types of distributions of natural frequency.
文摘This paper presents an alternative representation of a system of differential equations qualitatively showing the behavior of the biological rhythm of a crayfish during their transition from juvenile to adult stages. The model focuses on the interaction of four cellular oscillators coupled by diffusion of a hormone, a parameter μ is used to simu- late the quality of communication among the oscillators, in biological terms, it mea- sures developmental maturity of the crayfish. Since some quorum-sensing mechanism is assumed to be responsible for the synchronization of the biological oscillators, it is nat- ural to investigate the possibility that the underlying diffusion process is not standard, i.e. it may be a so-called anomalous diffusion. In this case, it is well understood that diffusion equations with fractional derivatives describe these processes in a more realis- tic way. The alternative formulation of these equations contains fractional operators of Liouville-Caputo and Caputo-Fabrizio type. The numerical simulations of the equations reflect synchronization of ultradian rhythms leading to a circadian rhythm. The classical behavior is recovered when the order of the fractional derivative is V = 1. We discuss possible biological implications.
文摘Astrocytes have potential to break synchrony between neurons. Authors＇ recent researches reveal that astrocytes vary the synchronization threshold and provide an appropriate feedback control in stabilizing neural activities. In this study, we propose an astrocyte-inspired controller for desynchronization of two coupled limit-cycle oscillators as a minimal network model. The design procedure consists of two parts. First, based on the astrocyte model, the structure of the dynamic controller is suggested. Then, to have an emcient controller, parameters of controller are tuned through an optimization algo- rithm. The proposed bio-inspired controller takes advantages of three important proper- ties： （1） the controller desynchronizes the oscillators without any undesirable effects （e.g. stopping, annihilating or starting divergent oscillations）; （2） it consumes little effort to preserve the desirable desynchronized state; and （3） the controller is robust with respect to parameters＇ variations. Simulation results reveal the ability of the proposed controller.
