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
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
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
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
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
Inspired by basic circuit connection methods,memristors can also be utilized in the construction of complex discrete chaotic systems.To investigate the dynamical effects of hybrid memristors,we propose two hybrid tri-...Inspired by basic circuit connection methods,memristors can also be utilized in the construction of complex discrete chaotic systems.To investigate the dynamical effects of hybrid memristors,we propose two hybrid tri-memristor hyperchaotic(HTMH)mapping structures based on the hybrid parallel/cascade and cascade/parallel operations,respectively.Taking the HTMH mapping structure with hybrid parallel/cascade operation as an example,this map possesses a spatial invariant set whose stability is closely related to the initial states of the memristors.Dynamics distributions and bifurcation behaviours dependent on the control parameters are explored with numerical tools.Specifically,the memristor initial offset-boosting mechanism is theoretically demonstrated,and memristor initial offset-boosting behaviours are numerically verified.The results clarify that the HTMH map can exhibit hyperchaotic behaviours and extreme multistability with homogeneous coexisting infinite attractors.In addition,an FPGA hardware platform is fabricated to implement the HTMH map and generate pseudorandom numbers(PRNs)with high randomness.Notably,the generated PRNs can be applied in Wasserstein generative adversarial nets(WGANs)to enhance training stability and generation capability.展开更多
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 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.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 (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 National Natural Science Foundation of China(Grant Nos.62271088,62201094,and 62071142)the Scientific Research Foundation of Jiangsu Provincial Education Department of China(Grant No.22KJB510001)。
文摘Inspired by basic circuit connection methods,memristors can also be utilized in the construction of complex discrete chaotic systems.To investigate the dynamical effects of hybrid memristors,we propose two hybrid tri-memristor hyperchaotic(HTMH)mapping structures based on the hybrid parallel/cascade and cascade/parallel operations,respectively.Taking the HTMH mapping structure with hybrid parallel/cascade operation as an example,this map possesses a spatial invariant set whose stability is closely related to the initial states of the memristors.Dynamics distributions and bifurcation behaviours dependent on the control parameters are explored with numerical tools.Specifically,the memristor initial offset-boosting mechanism is theoretically demonstrated,and memristor initial offset-boosting behaviours are numerically verified.The results clarify that the HTMH map can exhibit hyperchaotic behaviours and extreme multistability with homogeneous coexisting infinite attractors.In addition,an FPGA hardware platform is fabricated to implement the HTMH map and generate pseudorandom numbers(PRNs)with high randomness.Notably,the generated PRNs can be applied in Wasserstein generative adversarial nets(WGANs)to enhance training stability and generation capability.
