Memristors are extensively used to estimate the external electromagnetic stimulation and synapses for neurons.In this paper,two distinct scenarios,i.e.,an ideal memristor serves as external electromagnetic stimulation...Memristors are extensively used to estimate the external electromagnetic stimulation and synapses for neurons.In this paper,two distinct scenarios,i.e.,an ideal memristor serves as external electromagnetic stimulation and a locally active memristor serves as a synapse,are formulated to investigate the impact of a memristor on a two-dimensional Hindmarsh-Rose neuron model.Numerical simulations show that the neuronal models in different scenarios have multiple burst firing patterns.The introduction of the memristor makes the neuronal model exhibit complex dynamical behaviors.Finally,the simulation circuit and DSP hardware implementation results validate the physical mechanism,as well as the reliability of the biological neuron model.展开更多
Memristor-based chaotic systems with infinite equilibria are interesting because they generate extreme multistability.Their initial state-dependent dynamics can be explained in a reduced-dimension model by converting ...Memristor-based chaotic systems with infinite equilibria are interesting because they generate extreme multistability.Their initial state-dependent dynamics can be explained in a reduced-dimension model by converting the incremental integration of the state variables into system parameters.However,this approach cannot solve memristive systems in the presence of nonlinear terms other than the memristor term.In addition,the converted state variables may suffer from a degree of divergence.To allow simpler mechanistic analysis and physical implementation of extreme multistability phenomena,this paper uses a multiple mixed state variable incremental integration(MMSVII)method,which successfully reconstructs a four-dimensional hyperchaotic jerk system with multiple cubic nonlinearities except for the memristor term in a three-dimensional model using a clever linear state variable mapping that eliminates the divergence of the state variables.Finally,the simulation circuit of the reduced-dimension system is constructed using Multisim simulation software and the simulation results are consistent with the MATLAB numerical simulation results.The results show that the method of MMSVII proposed in this paper is useful for analyzing extreme multistable systems with multiple higher-order nonlinear terms.展开更多
Based on the two-dimensional(2D)discrete Rulkov model that is used to describe neuron dynamics,this paper presents a continuous non-autonomous memristive Rulkov model.The effects of electromagnetic induction and exter...Based on the two-dimensional(2D)discrete Rulkov model that is used to describe neuron dynamics,this paper presents a continuous non-autonomous memristive Rulkov model.The effects of electromagnetic induction and external stimulus are simultaneously considered herein.The electromagnetic induction flow is imitated by the generated current from a flux-controlled memristor and the external stimulus is injected using a sinusoidal current.Thus,the presented model possesses a line equilibrium set evolving over the time.The equilibrium set and their stability distributions are numerically simulated and qualitatively analyzed.Afterwards,numerical simulations are executed to explore the dynamical behaviors associated to the electromagnetic induction,external stimulus,and initial conditions.Interestingly,the initial conditions dependent extreme multistability is elaborately disclosed in the continuous non-autonomous memristive Rulkov model.Furthermore,an analog circuit of the proposed model is implemented,upon which the hardware experiment is executed to verify the numerically simulated extreme multistability.The extreme multistability is numerically revealed and experimentally confirmed in this paper,which can widen the future engineering employment of the Rulkov model.展开更多
The self-excited attractors and hidden attractors in a memcapacitive system which has three elements are studied in this paper.The critical parameter of stable and unstable states is calculated by identifying the eige...The self-excited attractors and hidden attractors in a memcapacitive system which has three elements are studied in this paper.The critical parameter of stable and unstable states is calculated by identifying the eigenvalues of Jacobian matrix.Besides,complex dynamical behaviors are investigated in the system,such as coexisting attractors,hidden attractors,coexisting bifurcation modes,intermittent chaos,and multistability.From the theoretical analyses and numerical simulations,it is found that there are four different kinds of transient transition behaviors in the memcapacitive system.Finally,field programmable gate array(FPGA)is used to implement the proposed chaotic system.展开更多
Under a nonresonant condition, we theoretically investigate hybrid absorptive-dispersive optical bistability and multistability behaviours in a three-level △-type system by using a microwave field to drive a hyperfin...Under a nonresonant condition, we theoretically investigate hybrid absorptive-dispersive optical bistability and multistability behaviours in a three-level △-type system by using a microwave field to drive a hyperfine transition between two upper excited states inside a unidirectional ring cavity. We find that the optical bistability and multistability behaviours can be controlled by adjusting the intensity of the microwave field or the intensity of the coherent coupling field. Furthermore, our studies show an interesting phenomenon of the transition from the optical bistability to the optical multistability only by changing the negative detuning of the coupling field into the positive detuning of the coupling field.展开更多
An improved heterogeneous dual memristive circuit(DMC)is proposed based on Chua's circuit,which shows good symmetry and multistablility.For the difficulty in controlling the initial conditions,which restricts the ...An improved heterogeneous dual memristive circuit(DMC)is proposed based on Chua's circuit,which shows good symmetry and multistablility.For the difficulty in controlling the initial conditions,which restricts the engineering applications,the 3 rd-order model(3 OM)in flux-charge domain is derived from the 5 th-order model(5 OM)in volt-ampere domain by using the flux-charge analysis method(FCAM).The consistence of symmetry and multistability before and after dimensionality decreasing is meticulously investigated via bifurcation diagram,Lyapunov exponents,and especially attraction basins.The comparative analysis validates the effectiveness of reduction model and improves the controllability of the circuit.To avoid the noise in the analog circuit,a field-programmable gate array(FPGA)is utilized to realize the reduction model,which is rarely reported and valuable for relevant research and application.展开更多
A five-value memristor model is proposed,it is proved that the model has a typical hysteresis loop by analyzing the relationship between voltage and current.Then,based on the classical Liu-Chen system,a new memristor-...A five-value memristor model is proposed,it is proved that the model has a typical hysteresis loop by analyzing the relationship between voltage and current.Then,based on the classical Liu-Chen system,a new memristor-based fourdimensional(4D)chaotic system is designed by using the five-value memristor.The trajectory phase diagram,Poincare mapping,bifurcation diagram,and Lyapunov exponent spectrum are drawn by numerical simulation.It is found that,in addition to the general chaos characteristics,the system has some special phenomena,such as hidden homogenous multistabilities,hidden heterogeneous multistabilities,and hidden super-multistabilities.Finally,according to the dimensionless equation of the system,the circuit model of the system is built and simulated.The results are consistent with the numerical simulation results,which proves the physical realizability of the five-value memristor-based chaotic system proposed in this paper.展开更多
Memristor chaotic systems have aroused great attention in recent years with their potentials expected in engineering applications.In this paper,a five-dimension(5D)double-memristor hyperchaotic system(DMHS)is modeled ...Memristor chaotic systems have aroused great attention in recent years with their potentials expected in engineering applications.In this paper,a five-dimension(5D)double-memristor hyperchaotic system(DMHS)is modeled by introducing two active magnetron memristor models into the Kolmogorov-type formula.The boundness condition of the proposed hyperchaotic system is proved.Coexisting bifurcation diagram and numerical verification explain the bistability.The rich dynamics of the system are demonstrated by the dynamic evolution map and the basin.The simulation results reveal the existence of transient hyperchaos and hidden extreme multistability in the presented DMHS.The NIST tests show that the generated signal sequence is highly random,which is feasible for encryption purposes.Furthermore,the system is implemented based on a FPGA experimental platform,which benefits the further applications of the proposed hyperchaos.展开更多
Coupled phase oscillators usually achieve synchronization as the coupling strength among oscillators is increased beyond a critical value. The stability of synchronous state remains an open issue. In this paper, we st...Coupled phase oscillators usually achieve synchronization as the coupling strength among oscillators is increased beyond a critical value. The stability of synchronous state remains an open issue. In this paper, we study the stability of the synchronous state in coupled phase oscillators. It is found that numerical integration of differential equations of coupled phase oscillators with a finite time step may induce desynchronization at strong couplings. The mechanism behind this instability is that numerical accumulated errors in simulations may trigger the loss of stability of the synchronous state.Desynchronization critical couplings are found to increase and diverge as a power law with decreasing the integral time step. Theoretical analysis supports the local stability of the synchronized state. Globally the emergence of synchronous state depends on the initial conditions. Other metastable ordered states such as twisted states can coexist with the synchronous mode. These twisted states keep locally stable on a sparse network but lose their stability when the network becomes dense.展开更多
In this paper, the multistability issue is discussed for delayed complex-valued recurrent neural networks with discontinuous real-imaginary-type activation functions. Based on a fixed theorem and stability definition,...In this paper, the multistability issue is discussed for delayed complex-valued recurrent neural networks with discontinuous real-imaginary-type activation functions. Based on a fixed theorem and stability definition, sufficient criteria are established for the existence and stability of multiple equilibria of complex-valued recurrent neural networks. The number of stable equilibria is larger than that of real-valued recurrent neural networks, which can be used to achieve high-capacity associative memories. One numerical example is provided to show the effectiveness and superiority of the presented results.展开更多
Electrons in graphene nanoribbons can lead to exceptionally strong optical responses in the infrared and terahertz regions owing to their unusual dispersion relation.Therefore,on the basis of quantum optics and solid-...Electrons in graphene nanoribbons can lead to exceptionally strong optical responses in the infrared and terahertz regions owing to their unusual dispersion relation.Therefore,on the basis of quantum optics and solid-material scientific principles,we show that optical bistability and multistability can be generated in graphene nanostructure under strong magnetic field.We also show that by adjusting the intensity and detuning of infrared laser field,the threshold intensity and hysteresis loop can be manipulated efficiently.The effects of the electronic cooperation parameter which are directly proportional to the electronic number density and the length of the graphene sample are discussed.Our proposed model may be useful for the nextgeneration all-optical systems and information processing based on nano scale devices.展开更多
We proposed a new model for controlling the optical bistability（OB） and optical multistability（OM） in a defect slab doped with four-level GaAs/AlGaAs multiple quantum wells with 15 periods of 17.5 nm GaAs wells an...We proposed a new model for controlling the optical bistability（OB） and optical multistability（OM） in a defect slab doped with four-level GaAs/AlGaAs multiple quantum wells with 15 periods of 17.5 nm GaAs wells and 15-nm Al_（0.3）Ga_（0.7）As barriers. The effects of biexciton energy renormalization, exciton spin relaxation, and thickness of the slab on the OB and OM properties of the defect slab were theoretically investigated. We found that the transition from OB to OM or vice versa is possible by adjusting the controllable parameters in a lab. Moreover, the transmission, reflection, and absorption properties of the weak probe light through the slab were also discussed in detail.展开更多
In recent years,the phenomenon of multistability has attracted wide attention.In this paper,a memristive chaotic system with extreme multistability is constructed by using a memristor.The dynamic behavior of the syste...In recent years,the phenomenon of multistability has attracted wide attention.In this paper,a memristive chaotic system with extreme multistability is constructed by using a memristor.The dynamic behavior of the system is analyzed by Poincar´e mapping,a time series diagram,and a bifurcation diagram.The results show that the new system has several significant characteristics.First,the new system has a constant Lyapunov exponent,transient chaos and one complete Feigenbaum tree.Second,the system has the phenomenon of bifurcation map shifts that depend on the initial conditions.In addition,we find periodic bursting oscillations,chaotic bursting oscillations,and the transition of chaotic bursting oscillations to periodic bursting oscillations.In particular,when the system parameters take different discrete values,the system generates a bubble phenomenon that varies with the initial conditions,and this bubble can be shifted with the initial values,which has rarely been seen in the previous literature.The implementation by field-programmable gate array(FPGA)and analog circuit simulation show close alignment with the MATLAB numerical simulation results,validating the system’s realizability.Additionally,the image encryption algorithm integrating DNA-based encoding and chaotic systems further demonstrates its practical applicability.展开更多
The steady-state optical bistability(OB) and optical multistability(OM) behavior in the quasi——type atomic system driven by a probe field and a coherent coupling field inside a unidirectional ring cavity are shown,a...The steady-state optical bistability(OB) and optical multistability(OM) behavior in the quasi——type atomic system driven by a probe field and a coherent coupling field inside a unidirectional ring cavity are shown,and the effects of coupling-field detuning and coupling-field intensity on the OB and OM behavior are investigated. The transition from OB to OM or vice versa is found by varying the detuning of the coherent coupling field or by adjusting the intensity of the coupling field. The influence of the atomic cooperation parameter on the OM behavior is also discussed.展开更多
Extreme multistability has seized scientists’ attention due to its rich diversity of dynamical behaviors and great flexibility in engineering applications. In this paper, a four-dimensional(4D) memcapacitive oscillat...Extreme multistability has seized scientists’ attention due to its rich diversity of dynamical behaviors and great flexibility in engineering applications. In this paper, a four-dimensional(4D) memcapacitive oscillator is built using four linear circuit elements and one nonlinear charge-controlled memcapacitor with a cosine inverse memcapacitance. The 4D memcapacitive oscillator possesses a line equilibrium set, and its stability periodically evolves with the initial condition of the memcapacitor. The 4D memcapacitive oscillator exhibits initial-condition-switched boosting extreme multistability due to the periodically evolving stability. Complex dynamical behaviors of period doubling/halving bifurcations, chaos crisis, and initial-condition-switched coexisting attractors are revealed by bifurcation diagrams, Lyapunov exponents, and phase portraits. Thereafter, a reconstructed system is derived via integral transformation to reveal the forming mechanism of the initial-condition-switched boosting extreme multistability in the memcapacitive oscillator. Finally, an implementation circuit is designed for the reconstructed system, and Power SIMulation(PSIM) simulations are executed to confirm the validity of the numerical analysis.展开更多
We investigate the optical bistability and multistability behaviors in a closed three-level A-type atomic system. By adding a sideband on either hand of the transitions which are originally coupled by a coherent contr...We investigate the optical bistability and multistability behaviors in a closed three-level A-type atomic system. By adding a sideband on either hand of the transitions which are originally coupled by a coherent control field and a coherent probe field to disturb the two-photon resonance, bistability occurs due to two-channel interference. Increasing the sideband Rabi frequency leads to the switching from bistability to tristability. When the sideband simultaneously couples with both hands, we can easily obtain quadrastability.展开更多
We theoretically investigate the multistable behavior of a hybrid optomechanical system,in which a charged mechanical resonator is coupled via Coulomb interaction to an optomechanical cavity containing an optical para...We theoretically investigate the multistable behavior of a hybrid optomechanical system,in which a charged mechanical resonator is coupled via Coulomb interaction to an optomechanical cavity containing an optical parametric amplifier(OPA).It is shown that the multistable behavior of the mean intracavity photon number can be controlled flexibly by adjusting the nonlinear gain parameter of the OPA,the phase of the field pumping the OPA,the power and frequency of the field driving the cavity,and the Coulomb coupling strength between the two charged mechanical resonators.In particular,the increase of the nonlinear gain parameter can result in a transition from bistability to tristability.Moreover,the effect of the Coulomb coupling strength on the bistable behavior of the steady-state positions of the two mechanical resonators is discussed.展开更多
Metamaterials with multistability have attracted much attention due to their extraordinary physical properties. In this paper, we report a novel multistable strategy that is reversible under external forces, based on ...Metamaterials with multistability have attracted much attention due to their extraordinary physical properties. In this paper, we report a novel multistable strategy that is reversible under external forces, based on the fact that a variational reversible locally resonant elastic metamaterial(LREM) with four configurations is proposed. Through a combination of theoretical analysis and numerical simulations, this newly designed metamaterial is proven to exhibit different bandgap ranges and vibration attenuation properties in each configuration. Especially, there is tunable anisotropy shown in these configurations, which enables the bandgaps in two directions to be separated or overlapped. A model with a bandgap shifting ratio(BSR) of 100% and an overlap ratio of 25% is set to validate the multistable strategy feasibility. The proposed design strategy demonstrates significant potentials for applications in versatile scenarios.展开更多
We investigate the optical bistabiiity （OB） in a duplicated two-level system contained in a ring cavity. The atoms are driven by two orthogonally polarized fields with a relative phase. The OB behavior of such a sys...We investigate the optical bistabiiity （OB） in a duplicated two-level system contained in a ring cavity. The atoms are driven by two orthogonally polarized fields with a relative phase. The OB behavior of such a system can be controlled by the amplitude and the relative phase of the coupling field, and it is possible to switch between bistabilitv and multistability by adjusting the relative phase.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.62061014)Technological Innovation Projects in the Field of Artificial Intelligence in Liaoning province(Grant No.2023JH26/10300011)Basic Scientific Research Projects in Department of Education of Liaoning Province(Grant No.JYTZD2023021).
文摘Memristors are extensively used to estimate the external electromagnetic stimulation and synapses for neurons.In this paper,two distinct scenarios,i.e.,an ideal memristor serves as external electromagnetic stimulation and a locally active memristor serves as a synapse,are formulated to investigate the impact of a memristor on a two-dimensional Hindmarsh-Rose neuron model.Numerical simulations show that the neuronal models in different scenarios have multiple burst firing patterns.The introduction of the memristor makes the neuronal model exhibit complex dynamical behaviors.Finally,the simulation circuit and DSP hardware implementation results validate the physical mechanism,as well as the reliability of the biological neuron model.
基金Project supported by the National Natural Science Foundation of China(Grant No.62071411)the Research Foundation of Education Department of Hunan Province,China(Grant No.20B567).
文摘Memristor-based chaotic systems with infinite equilibria are interesting because they generate extreme multistability.Their initial state-dependent dynamics can be explained in a reduced-dimension model by converting the incremental integration of the state variables into system parameters.However,this approach cannot solve memristive systems in the presence of nonlinear terms other than the memristor term.In addition,the converted state variables may suffer from a degree of divergence.To allow simpler mechanistic analysis and physical implementation of extreme multistability phenomena,this paper uses a multiple mixed state variable incremental integration(MMSVII)method,which successfully reconstructs a four-dimensional hyperchaotic jerk system with multiple cubic nonlinearities except for the memristor term in a three-dimensional model using a clever linear state variable mapping that eliminates the divergence of the state variables.Finally,the simulation circuit of the reduced-dimension system is constructed using Multisim simulation software and the simulation results are consistent with the MATLAB numerical simulation results.The results show that the method of MMSVII proposed in this paper is useful for analyzing extreme multistable systems with multiple higher-order nonlinear terms.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12172066,61801054,and 51777016)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK20160282)the Postgraduate Research and Practice Innovation Program of Jiangsu Province,China(Grant No.KYCX212823)。
文摘Based on the two-dimensional(2D)discrete Rulkov model that is used to describe neuron dynamics,this paper presents a continuous non-autonomous memristive Rulkov model.The effects of electromagnetic induction and external stimulus are simultaneously considered herein.The electromagnetic induction flow is imitated by the generated current from a flux-controlled memristor and the external stimulus is injected using a sinusoidal current.Thus,the presented model possesses a line equilibrium set evolving over the time.The equilibrium set and their stability distributions are numerically simulated and qualitatively analyzed.Afterwards,numerical simulations are executed to explore the dynamical behaviors associated to the electromagnetic induction,external stimulus,and initial conditions.Interestingly,the initial conditions dependent extreme multistability is elaborately disclosed in the continuous non-autonomous memristive Rulkov model.Furthermore,an analog circuit of the proposed model is implemented,upon which the hardware experiment is executed to verify the numerically simulated extreme multistability.The extreme multistability is numerically revealed and experimentally confirmed in this paper,which can widen the future engineering employment of the Rulkov model.
基金Project supported by the National Natural Science Foundation of China(Grant No.51377124)the Science Fund for New Star of Youth Science and Technology of Shaanxi Province,China(Grant No.2016KJXX-40).
文摘The self-excited attractors and hidden attractors in a memcapacitive system which has three elements are studied in this paper.The critical parameter of stable and unstable states is calculated by identifying the eigenvalues of Jacobian matrix.Besides,complex dynamical behaviors are investigated in the system,such as coexisting attractors,hidden attractors,coexisting bifurcation modes,intermittent chaos,and multistability.From the theoretical analyses and numerical simulations,it is found that there are four different kinds of transient transition behaviors in the memcapacitive system.Finally,field programmable gate array(FPGA)is used to implement the proposed chaotic system.
基金supported by Natural Science Foundation of Jiangxi,China (Grant Nos 2007GZW0819 and 2008GQW0017)the Scientific Research Foundation of Jiangxi Provincial Department of Education,China (Grant Nos [2007]191 and GJJ09504)+1 种基金the Science Foundation of East China Jiaotong University of China (Grant No 06ZKJC01)the Foundation of Talent of Jinggang of Jiangxi Province of China
文摘Under a nonresonant condition, we theoretically investigate hybrid absorptive-dispersive optical bistability and multistability behaviours in a three-level △-type system by using a microwave field to drive a hyperfine transition between two upper excited states inside a unidirectional ring cavity. We find that the optical bistability and multistability behaviours can be controlled by adjusting the intensity of the microwave field or the intensity of the coherent coupling field. Furthermore, our studies show an interesting phenomenon of the transition from the optical bistability to the optical multistability only by changing the negative detuning of the coupling field into the positive detuning of the coupling field.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61971228 and 61871230)the Natural Science Foundations of Jiangsu Higher Education Institutions,China(Grant No.19KJB520042)the Postgraduate Research&Practice Innovation Program of Jiangsu Province,China(Grant No.SJCX210564)。
文摘An improved heterogeneous dual memristive circuit(DMC)is proposed based on Chua's circuit,which shows good symmetry and multistablility.For the difficulty in controlling the initial conditions,which restricts the engineering applications,the 3 rd-order model(3 OM)in flux-charge domain is derived from the 5 th-order model(5 OM)in volt-ampere domain by using the flux-charge analysis method(FCAM).The consistence of symmetry and multistability before and after dimensionality decreasing is meticulously investigated via bifurcation diagram,Lyapunov exponents,and especially attraction basins.The comparative analysis validates the effectiveness of reduction model and improves the controllability of the circuit.To avoid the noise in the analog circuit,a field-programmable gate array(FPGA)is utilized to realize the reduction model,which is rarely reported and valuable for relevant research and application.
基金supported by the National Natural Science Foundation of China(Grant No.61203004)the Natural Science Foundation of Heilongjiang Province,China(Grant No.F201220)the Heilongjiang Provincial Natural Science Foundation of Joint Guidance Project(Grant No.LH2020F022).
文摘A five-value memristor model is proposed,it is proved that the model has a typical hysteresis loop by analyzing the relationship between voltage and current.Then,based on the classical Liu-Chen system,a new memristor-based fourdimensional(4D)chaotic system is designed by using the five-value memristor.The trajectory phase diagram,Poincare mapping,bifurcation diagram,and Lyapunov exponent spectrum are drawn by numerical simulation.It is found that,in addition to the general chaos characteristics,the system has some special phenomena,such as hidden homogenous multistabilities,hidden heterogeneous multistabilities,and hidden super-multistabilities.Finally,according to the dimensionless equation of the system,the circuit model of the system is built and simulated.The results are consistent with the numerical simulation results,which proves the physical realizability of the five-value memristor-based chaotic system proposed in this paper.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.62003177,61973172,61973175,and 62073177)the key Technologies Research and Tianjin Natural Science Foundation (Grant No.19JCZDJC32800)+1 种基金China Postdoctoral Science Foundation (Grant Nos.2020M670633 and 2020M670045)Academy of Finland (Grant No.315660)。
文摘Memristor chaotic systems have aroused great attention in recent years with their potentials expected in engineering applications.In this paper,a five-dimension(5D)double-memristor hyperchaotic system(DMHS)is modeled by introducing two active magnetron memristor models into the Kolmogorov-type formula.The boundness condition of the proposed hyperchaotic system is proved.Coexisting bifurcation diagram and numerical verification explain the bistability.The rich dynamics of the system are demonstrated by the dynamic evolution map and the basin.The simulation results reveal the existence of transient hyperchaos and hidden extreme multistability in the presented DMHS.The NIST tests show that the generated signal sequence is highly random,which is feasible for encryption purposes.Furthermore,the system is implemented based on a FPGA experimental platform,which benefits the further applications of the proposed hyperchaos.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11875135)。
文摘Coupled phase oscillators usually achieve synchronization as the coupling strength among oscillators is increased beyond a critical value. The stability of synchronous state remains an open issue. In this paper, we study the stability of the synchronous state in coupled phase oscillators. It is found that numerical integration of differential equations of coupled phase oscillators with a finite time step may induce desynchronization at strong couplings. The mechanism behind this instability is that numerical accumulated errors in simulations may trigger the loss of stability of the synchronous state.Desynchronization critical couplings are found to increase and diverge as a power law with decreasing the integral time step. Theoretical analysis supports the local stability of the synchronized state. Globally the emergence of synchronous state depends on the initial conditions. Other metastable ordered states such as twisted states can coexist with the synchronous mode. These twisted states keep locally stable on a sparse network but lose their stability when the network becomes dense.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61374094 and 61503338)the Natural Science Foundation of Zhejiang Province,China(Grant No.LQ15F030005)
文摘In this paper, the multistability issue is discussed for delayed complex-valued recurrent neural networks with discontinuous real-imaginary-type activation functions. Based on a fixed theorem and stability definition, sufficient criteria are established for the existence and stability of multiple equilibria of complex-valued recurrent neural networks. The number of stable equilibria is larger than that of real-valued recurrent neural networks, which can be used to achieve high-capacity associative memories. One numerical example is provided to show the effectiveness and superiority of the presented results.
文摘Electrons in graphene nanoribbons can lead to exceptionally strong optical responses in the infrared and terahertz regions owing to their unusual dispersion relation.Therefore,on the basis of quantum optics and solid-material scientific principles,we show that optical bistability and multistability can be generated in graphene nanostructure under strong magnetic field.We also show that by adjusting the intensity and detuning of infrared laser field,the threshold intensity and hysteresis loop can be manipulated efficiently.The effects of the electronic cooperation parameter which are directly proportional to the electronic number density and the length of the graphene sample are discussed.Our proposed model may be useful for the nextgeneration all-optical systems and information processing based on nano scale devices.
文摘We proposed a new model for controlling the optical bistability（OB） and optical multistability（OM） in a defect slab doped with four-level GaAs/AlGaAs multiple quantum wells with 15 periods of 17.5 nm GaAs wells and 15-nm Al_（0.3）Ga_（0.7）As barriers. The effects of biexciton energy renormalization, exciton spin relaxation, and thickness of the slab on the OB and OM properties of the defect slab were theoretically investigated. We found that the transition from OB to OM or vice versa is possible by adjusting the controllable parameters in a lab. Moreover, the transmission, reflection, and absorption properties of the weak probe light through the slab were also discussed in detail.
基金the National Basic Research Program of China，the National Natural Science Foundation of China，the Fundamental Research Funds for the Central Universities
基金Project supported by the Natural Science Foundation of Hubei Province(Grant No.2024AFD068).
文摘In recent years,the phenomenon of multistability has attracted wide attention.In this paper,a memristive chaotic system with extreme multistability is constructed by using a memristor.The dynamic behavior of the system is analyzed by Poincar´e mapping,a time series diagram,and a bifurcation diagram.The results show that the new system has several significant characteristics.First,the new system has a constant Lyapunov exponent,transient chaos and one complete Feigenbaum tree.Second,the system has the phenomenon of bifurcation map shifts that depend on the initial conditions.In addition,we find periodic bursting oscillations,chaotic bursting oscillations,and the transition of chaotic bursting oscillations to periodic bursting oscillations.In particular,when the system parameters take different discrete values,the system generates a bubble phenomenon that varies with the initial conditions,and this bubble can be shifted with the initial values,which has rarely been seen in the previous literature.The implementation by field-programmable gate array(FPGA)and analog circuit simulation show close alignment with the MATLAB numerical simulation results,validating the system’s realizability.Additionally,the image encryption algorithm integrating DNA-based encoding and chaotic systems further demonstrates its practical applicability.
基金Supported by the Natural Science Foundation of Jiangxi of China (Grant No. 2007GZW0819)the National Basic Research Program of China (Grant No. 2005CB724508)the Foundation of Talent of Jinggang of Jiangxi Province (Grant No. 2008DQ00400)
文摘The steady-state optical bistability(OB) and optical multistability(OM) behavior in the quasi——type atomic system driven by a probe field and a coherent coupling field inside a unidirectional ring cavity are shown,and the effects of coupling-field detuning and coupling-field intensity on the OB and OM behavior are investigated. The transition from OB to OM or vice versa is found by varying the detuning of the coherent coupling field or by adjusting the intensity of the coupling field. The influence of the atomic cooperation parameter on the OM behavior is also discussed.
基金Project supported by the National Natural Science Foundation of China (Nos. 51777016 and 61801054)the Natural Science Foundation of Jiangsu Province,China (No. BK20191451)+2 种基金the Natural Science Foundation of Changzhou,Jiangsu Province,China (No. CJ20190037)the Open Research Fund of Key Laboratory of MEMS of Ministry of EducationSoutheast University,China。
文摘Extreme multistability has seized scientists’ attention due to its rich diversity of dynamical behaviors and great flexibility in engineering applications. In this paper, a four-dimensional(4D) memcapacitive oscillator is built using four linear circuit elements and one nonlinear charge-controlled memcapacitor with a cosine inverse memcapacitance. The 4D memcapacitive oscillator possesses a line equilibrium set, and its stability periodically evolves with the initial condition of the memcapacitor. The 4D memcapacitive oscillator exhibits initial-condition-switched boosting extreme multistability due to the periodically evolving stability. Complex dynamical behaviors of period doubling/halving bifurcations, chaos crisis, and initial-condition-switched coexisting attractors are revealed by bifurcation diagrams, Lyapunov exponents, and phase portraits. Thereafter, a reconstructed system is derived via integral transformation to reveal the forming mechanism of the initial-condition-switched boosting extreme multistability in the memcapacitive oscillator. Finally, an implementation circuit is designed for the reconstructed system, and Power SIMulation(PSIM) simulations are executed to confirm the validity of the numerical analysis.
基金supported by the National Natural Science Foundation of China(No.60708008)the Project of Academic Leaders in Shanghai (No. 07XD14030)the Knowledge Innovation Program of the Chinese Academy of Sciences
文摘We investigate the optical bistability and multistability behaviors in a closed three-level A-type atomic system. By adding a sideband on either hand of the transitions which are originally coupled by a coherent control field and a coherent probe field to disturb the two-photon resonance, bistability occurs due to two-channel interference. Increasing the sideband Rabi frequency leads to the switching from bistability to tristability. When the sideband simultaneously couples with both hands, we can easily obtain quadrastability.
基金supported by the National Natural Science Foundation of China(Grant No.11304110)the Natural Science Foundation of Jiangsu Province(Grant Nos.BK20130413 and BK20140450)the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No.13KJB140002)
文摘We theoretically investigate the multistable behavior of a hybrid optomechanical system,in which a charged mechanical resonator is coupled via Coulomb interaction to an optomechanical cavity containing an optical parametric amplifier(OPA).It is shown that the multistable behavior of the mean intracavity photon number can be controlled flexibly by adjusting the nonlinear gain parameter of the OPA,the phase of the field pumping the OPA,the power and frequency of the field driving the cavity,and the Coulomb coupling strength between the two charged mechanical resonators.In particular,the increase of the nonlinear gain parameter can result in a transition from bistability to tristability.Moreover,the effect of the Coulomb coupling strength on the bistable behavior of the steady-state positions of the two mechanical resonators is discussed.
基金supported by the National Natural Science Foundation of China(No.52192633)the Natural Science Basic Research Plan in Shaanxi Province of China(No.2025JC-YBMS-050)。
文摘Metamaterials with multistability have attracted much attention due to their extraordinary physical properties. In this paper, we report a novel multistable strategy that is reversible under external forces, based on the fact that a variational reversible locally resonant elastic metamaterial(LREM) with four configurations is proposed. Through a combination of theoretical analysis and numerical simulations, this newly designed metamaterial is proven to exhibit different bandgap ranges and vibration attenuation properties in each configuration. Especially, there is tunable anisotropy shown in these configurations, which enables the bandgaps in two directions to be separated or overlapped. A model with a bandgap shifting ratio(BSR) of 100% and an overlap ratio of 25% is set to validate the multistable strategy feasibility. The proposed design strategy demonstrates significant potentials for applications in versatile scenarios.
基金supported by the National Natural Science Foundation of China(Nos.61108006 and 11104221)the Scientific Research Program Funded by Shaanxi Provincial Education Department(No.11JK0529)+2 种基金the Natural Science Basis Research Plan in Shaanxi Province of China(No.2010JQ1002)the Doctoral Program Foundation of Institutions of Higher Education of China(No.20106101120020)the support from the Science Foundation of Northwest University(No.10NW14)
文摘We investigate the optical bistabiiity （OB） in a duplicated two-level system contained in a ring cavity. The atoms are driven by two orthogonally polarized fields with a relative phase. The OB behavior of such a system can be controlled by the amplitude and the relative phase of the coupling field, and it is possible to switch between bistabilitv and multistability by adjusting the relative phase.
