Sliding fast-slow oscillations are interesting oscillation patterns discovered recently in the Duffing system with frequency switching.Such oscillations have been obtained with a fixed 1:2 low frequency ratio in the p...Sliding fast-slow oscillations are interesting oscillation patterns discovered recently in the Duffing system with frequency switching.Such oscillations have been obtained with a fixed 1:2 low frequency ratio in the previous work.The present paper aims to explore composite fast-slow dynamics when the frequency ratio is variable.As a result,a novel route to composite fast-slow dynamics is obtained.We find that,when presented with variable frequency ratios in a 1:n fashion,the sliding fast-slow oscillations may turn into the ones characterized by the fact that the clusters of large-amplitude oscillations of relaxational type are exhibited in each period of the oscillations,and hence the mixedmode fast-slow oscillations.Depending on whether the transition of the trajectory is from the upper subsystem via the fold bifurcation or not,these interesting oscillations are divided into two classes,both of which are investigated numerically.Our study shows that,when the frequency ratio n is increased from n=3,newly created boundary equilibrium bifurcation points may appear on the original sliding boundary line,which is divided into smaller parts,showing sliding and downward crossing dynamical characteristics.This is the root cause of the clusters,showing large-amplitude oscillations of relaxational type,resulting in the formation of mixed-mode fast-slow oscillations.Thus,a novel route to composite fast-slow dynamics by frequency switching is explained.Besides,the effects of the forcing on the mixed-mode fast-slow oscillations are explored.The magnitude of the forcing frequency may have some effects on the number of large-amplitude oscillations in the clusters.The magnitude of the forcing amplitude determines whether the fast-slow characteristics can be produced.展开更多
We establish a slow manifold for a fast-slow dynamical system with anomalous diffusion,where both fast and slow components are influenced by white noise.Furthermore,we verify the exponential tracking property for the ...We establish a slow manifold for a fast-slow dynamical system with anomalous diffusion,where both fast and slow components are influenced by white noise.Furthermore,we verify the exponential tracking property for the established random slow manifold,which leads to a lower dimensional reduced system.Alongside this we consider a parameter estimation method for a nonlocal fast-slow stochastic dynamical system,where only the slow component is observable.In terms of quantifying parameters in stochastic evolutionary systems,the provided method offers the advantage of dimension reduction.展开更多
The Morris-Lecar model is a neuronal model designed to replicate the oscillatory activity of barnacle giant muscle fibers.This work presents a three-dimensional Morris-Lecar model with a novel fast-slow structure.The ...The Morris-Lecar model is a neuronal model designed to replicate the oscillatory activity of barnacle giant muscle fibers.This work presents a three-dimensional Morris-Lecar model with a novel fast-slow structure.The model introduces a current containing slow variables,thereby forming a new fast-slow structure with the membrane potential.Numerical results reveal the existence of two independent unstable foci and complex dynamical behaviors that include period-doubling bifurcations and spiking/bursting activities.Two types of bifurcation mechanisms for bursting activities are elucidated through theoretical analysis based on four typical bursting activities.Finally,a digital neuronal circuit was developed based on FPGA,and experimental results show good consistency with numerical results.展开更多
We study the generation of quadruple-transparency windows and the implementation of a conversion between slow and fast light in a hybrid optomechanical system. By demonstrating the generation of these transparency win...We study the generation of quadruple-transparency windows and the implementation of a conversion between slow and fast light in a hybrid optomechanical system. By demonstrating the generation of these transparency windows one by one, we analyze the physical mechanism through which each transparency window forms in detail. Additionally, we discuss how the system parameters affect the formation of transparency windows and conclude that the location, width, and absorption of each transparency window can be arbitrarily manipulated by varying the appropriate parameters. Moreover, when the pump field is changed from red to blue detuning, conversions between slow and fast light occur in the output field. These interesting properties of the output field can be applied to achieve the coherent control and manipulation of light pulses using cavity optomechanical system.展开更多
We demonstrate multiple transparency windows in a cavity opto-magnomechanical system containing a ferromagnetic material yttrium iron garnet(YIG)crystal.The probe output spectrum reveals the simultaneous emergence of ...We demonstrate multiple transparency windows in a cavity opto-magnomechanical system containing a ferromagnetic material yttrium iron garnet(YIG)crystal.The probe output spectrum reveals the simultaneous emergence of three distinct phenomena:magnon-induced transparency(MIT)arising from microwave–magnon coupling;magnomechanically induced transparency(MMIT)through phonon–magnon interaction,and optomechanically induced transparency(OMIT)mediated by optical cavity–photon coupling.Crucially,these transparency features demonstrate dynamic tunability through precise manipulation of the number of interacting modes and coupling strengths.Our study reveals the effects of magnon–microwave and optomechanical coupling on probe results and the role of quantum interference mechanisms in a resonant system.Moreover,the fast-slow light effect can be enhanced and switched by choosing appropriate coupling parameters.Our work has potential applications in multi-band quantum storage and multi-channel photonic information processing devices.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.12272150,12072132,12372093)。
文摘Sliding fast-slow oscillations are interesting oscillation patterns discovered recently in the Duffing system with frequency switching.Such oscillations have been obtained with a fixed 1:2 low frequency ratio in the previous work.The present paper aims to explore composite fast-slow dynamics when the frequency ratio is variable.As a result,a novel route to composite fast-slow dynamics is obtained.We find that,when presented with variable frequency ratios in a 1:n fashion,the sliding fast-slow oscillations may turn into the ones characterized by the fact that the clusters of large-amplitude oscillations of relaxational type are exhibited in each period of the oscillations,and hence the mixedmode fast-slow oscillations.Depending on whether the transition of the trajectory is from the upper subsystem via the fold bifurcation or not,these interesting oscillations are divided into two classes,both of which are investigated numerically.Our study shows that,when the frequency ratio n is increased from n=3,newly created boundary equilibrium bifurcation points may appear on the original sliding boundary line,which is divided into smaller parts,showing sliding and downward crossing dynamical characteristics.This is the root cause of the clusters,showing large-amplitude oscillations of relaxational type,resulting in the formation of mixed-mode fast-slow oscillations.Thus,a novel route to composite fast-slow dynamics by frequency switching is explained.Besides,the effects of the forcing on the mixed-mode fast-slow oscillations are explored.The magnitude of the forcing frequency may have some effects on the number of large-amplitude oscillations in the clusters.The magnitude of the forcing amplitude determines whether the fast-slow characteristics can be produced.
基金supported by NSF (1620449)NSFC (11531006 and 11771449)
文摘We establish a slow manifold for a fast-slow dynamical system with anomalous diffusion,where both fast and slow components are influenced by white noise.Furthermore,we verify the exponential tracking property for the established random slow manifold,which leads to a lower dimensional reduced system.Alongside this we consider a parameter estimation method for a nonlocal fast-slow stochastic dynamical system,where only the slow component is observable.In terms of quantifying parameters in stochastic evolutionary systems,the provided method offers the advantage of dimension reduction.
基金supported by the National Natural Science Foundation of China(Grant Nos.62271088,62201094)the Joint Guidance Project of the Natural Science Foundation of Heilongjiang Province(Grant No.LH2020F022)the Scientific Research Foundation of Jiangsu Provincial Education Department of China(Grant No.22KJB510001).
文摘The Morris-Lecar model is a neuronal model designed to replicate the oscillatory activity of barnacle giant muscle fibers.This work presents a three-dimensional Morris-Lecar model with a novel fast-slow structure.The model introduces a current containing slow variables,thereby forming a new fast-slow structure with the membrane potential.Numerical results reveal the existence of two independent unstable foci and complex dynamical behaviors that include period-doubling bifurcations and spiking/bursting activities.Two types of bifurcation mechanisms for bursting activities are elucidated through theoretical analysis based on four typical bursting activities.Finally,a digital neuronal circuit was developed based on FPGA,and experimental results show good consistency with numerical results.
基金supported by the National Natural Science Foundation of China(Grant Nos.61822114,11465020,61465013,and 11264042)the Project of Jilin Science and Technology Development for Leading Talent of Science and Technology Innovation in Middle and Young and Team Project(Grant No.20160519022JH)
文摘We study the generation of quadruple-transparency windows and the implementation of a conversion between slow and fast light in a hybrid optomechanical system. By demonstrating the generation of these transparency windows one by one, we analyze the physical mechanism through which each transparency window forms in detail. Additionally, we discuss how the system parameters affect the formation of transparency windows and conclude that the location, width, and absorption of each transparency window can be arbitrarily manipulated by varying the appropriate parameters. Moreover, when the pump field is changed from red to blue detuning, conversions between slow and fast light occur in the output field. These interesting properties of the output field can be applied to achieve the coherent control and manipulation of light pulses using cavity optomechanical system.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.62071376,62405041,52175531,and 62005211)the National Key Laboratory of Science and Technology on Space Microwave(Grant No.HTKJ2024KL504002)+1 种基金the Program of State Key Laboratory of Quantum Optics and Quantum Optics Devices(Grant No.KF202408)the Natural Science Foundation of Chongqing(Grant No.CSTB2024NSCQ-MSX0746)。
文摘We demonstrate multiple transparency windows in a cavity opto-magnomechanical system containing a ferromagnetic material yttrium iron garnet(YIG)crystal.The probe output spectrum reveals the simultaneous emergence of three distinct phenomena:magnon-induced transparency(MIT)arising from microwave–magnon coupling;magnomechanically induced transparency(MMIT)through phonon–magnon interaction,and optomechanically induced transparency(OMIT)mediated by optical cavity–photon coupling.Crucially,these transparency features demonstrate dynamic tunability through precise manipulation of the number of interacting modes and coupling strengths.Our study reveals the effects of magnon–microwave and optomechanical coupling on probe results and the role of quantum interference mechanisms in a resonant system.Moreover,the fast-slow light effect can be enhanced and switched by choosing appropriate coupling parameters.Our work has potential applications in multi-band quantum storage and multi-channel photonic information processing devices.
