Multiple mixed state variable incremental integration for reconstructing extreme multistability in a novel memristive hyperchaotic jerk system with multiple cubic nonlinearity

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.

Memristor hyperchaos in a generalized Kolmogorov-type system with extreme multistability

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.

Stability and multistability of synchronization in networks of coupled phase oscillators

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.

Continuous non-autonomous memristive Rulkov model with extreme multistability

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.

Optical bistability and multistability via double dark resonance in graphene nanostructure

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.

Optical bistability and multistability in a defect slab doped by GaAs/AlGaAs multiple quantum wells

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.

Optical bistability and multistability in a three-level △-type atomic system under the nonresonant condition

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.

Design and multistability analysis of five-value memristor-based chaotic system with hidden attractors

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.

适用可再生能源不确定特性的合成氨多稳态柔性工艺技术

双碳背景下,风光可再生能源发电是能源发展的重要方向,“绿氢”由于其长周期存储和零碳特征,可以有效解决风光电力消纳的难题,有望与电能一同成为未来能源体系的两大支柱。但是由于氢气自身特性和氢脆造成的材料瓶颈,“绿氢”发展遇到制储运多环节安全性与经济性挑战。绿电制氢制氨的“电制绿氨”路径被认为是解决“绿电”“绿氢”技术经济困局的重要途径之一。针对风光资源的不确定性,分析了基于合成氨“哈-博”工艺多种解决方案的优劣,提出了多稳态柔性“电制绿氨”工艺模式以解决“源网氢氨”复杂技术特征耦合下的设计、装置和运行问题;研究了多稳态柔性“电制绿氨”工艺的系统性技术架构、整定经济运行负荷与运行周期的最优化方法;开发了电氢氨一体化数字仿真模型,计及电力约束、资源波动、氢氨需求、系统运行效率和可靠性等因素,对全场景、全流程下的“电制绿氨”进行协同优化,形成了一套面向动态运行的绿电耦合化工的设计方法;研究了催化剂结构性能调优与合成塔内件结构的优化方法,开发了复杂变工况条件的催化剂宏观动力学模型,以及电氢氨一体化协同调度与智能控制技术。多稳态柔性“电制绿氨”工艺实现了合成氨经济运行负荷在30%~110%,负荷调节速率在0.5~1.0%/min,支持日、班,及班内多时域负荷调节要求,30%~110%负荷运行下单位合成氨综合能耗均优于GB 21344—2015《合成氨单位产品能源消耗限额》的标杆值。

多态场景下考虑出行链重构的电动汽车多目标协同优化调度

电动汽车用户日内的充电计划具有规律性,但在突发事件影响下,电动汽车用户的充电行为则具有突发性和主观性。突发事件由用户影响到电动汽车的充放电过程,最终波及电力系统的稳定运行。首先,考虑实际出行中距离变化时用户的充电意愿,提出充电意愿模型,模拟用户的充电意愿区间;然后,基于电动汽车出行时空特性,将影响调度计划的突发事件分为4类,模拟4种事件对既定调度计划的影响,并综合考虑气温和电价等因素,对电动汽车进行充放电调度;最后,提出多态场景下储能站协同电动汽车的能量管理策略,对常态及两种极端条件下的电动汽车进行充放电调度。采用区域电网进行仿真,分析出行链重构在行为场景、事件类型、调度策略、集群规模、用户参与度和风电规模的条件中对电动汽车充放电调度的影响,验证了所提模型的合理性和有效性。

多稳态力学超构材料研究进展

通过人工设计的微结构,力学超构材料能实现天然材料不具备的超常力学性能,如负泊松比、负热膨胀、多稳态、可调刚度等等。其中,多稳态力学超构材料因具有可重复使用、能量存储与吸收、快速变形和放大输出力等优异性能,激发了研究人员的兴趣。多稳态力学超构材料通常是利用双稳态结构单元的串联和/或并联实现的,在外界载荷作用下展示出多个稳定构型且可以互逆切换,具有广阔的应用前景。该文综述了多稳态力学超构材料主要设计策略及最新的研究进展,阐述了双稳态的概念、稳态转换势垒及相应的力学响应特性,分析了双稳态单元的设计原则;根据研究对象的不同,对双稳态单元及其多稳态超构材料研究进展进行了分析;讨论了多稳态构成的力学超构材料在能量吸收、软驱动、机械计算和波调控等领域的应用前景。最后,对多稳态力学超构材料的研究进行了总结,并对未来可能遇到的挑战和机遇进行了展望。

圆弧足被动行走机器人步态多重稳定性研究

目前关于被动行走步态的研究主要是揭示参数变化对其稳定性的影响,而对于步态多重稳定性的研究则较为少见.步态的多重稳定性不仅是行走模式多样化产生的根源,还是引发步态突变的关键因素.尽管当前共存步态的存在性已受到关注,但关于这些步态的产生、演化以及消失机制的系统性研究尚未开展.为此,文章以圆弧足被动行走机器人为研究对象,应用胞映射及点映射算法探索到与周期一步态共存的几种高周期步态,绘制了共存步态的三维吸引盆并对这些步态的行走特性进行了详细的对比分析.此外,基于跳跃矩阵法改进了Poincaré-Newton-Floquet(PNF)算法,对被动行走系统的不稳定轨道及其对应的Floquet乘子进行了求解,并结合吸引盆进一步揭示了步态演化过程中的分岔和激变现象.研究结果表明,共存步态的周期越高,其平均步速越快,但步态稳定性越差;这些共存步态均由极限环的折叠分岔产生,并由倍周期级联路径通向混沌,最终与不稳定轨道在吸引盆边界上产生碰撞而消失.文章的研究结果有助于理解被动行走步态的多重稳定性,并为机器人的优化设计及稳定控制提供理论依据.

Initial-condition-switched boosting extreme multistability and mechanism analysis in a memcapacitive oscillator

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.

A novel variable-order fractional chaotic map and its dynamics

In recent years,fractional-order chaotic maps have been paid more attention in publications because of the memory effect.This paper presents a novel variable-order fractional sine map(VFSM)based on the discrete fractional calculus.Specially,the order is defined as an iterative function that incorporates the current state of the system.By analyzing phase diagrams,time sequences,bifurcations,Lyapunov exponents and fuzzy entropy complexity,the dynamics of the proposed map are investigated comparing with the constant-order fractional sine map.The results reveal that the variable order has a good effect on improving the chaotic performance,and it enlarges the range of available parameter values as well as reduces non-chaotic windows.Multiple coexisting attractors also enrich the dynamics of VFSM and prove its sensitivity to initial values.Moreover,the sequence generated by the proposed map passes the statistical test for pseudorandom number and shows strong robustness to parameter estimation,which proves the potential applications in the field of information security.

Optical bistability and multistability via multi-Raman-channel interference

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.

Multistate transition and coupled solideliquid modeling of motion process of long-runout landslide

The recognition,repetition and prediction of the post-failure motion process of long-runout landslides are key scientific problems in the prevention and mitigation of geological disasters.In this study,a new numerical method involving LPF3D based on a multialgorithm and multiconstitutive model was proposed to simulate long-runout landslides with high precision and efficiency.The following results were obtained:(a)The motion process of landslides showed a steric effect with mobility,including gradual disintegration and spreading.The sliding mass can be divided into three states(dense,dilute and ultradilute)in the motion process,which can be solved by three dynamic regimes(friction,collision,and inertial);(b)Coupling simulation between the solid grain and liquid phases was achieved,focusing on drag force influences;(c)Different algorithms and constitutive models were employed in phase-state simulations.The volume fraction is an important indicator to distinguish different state types and solid‒liquid ratios.The flume experimental results were favorably validated against long-runout landslide case data;and(d)In this method,matched dynamic numerical modeling was developed to better capture the realistic motion process of long-runout landslides,and the advantages of continuum media and discrete media were combined to improve the computational accuracy and efficiency.This new method can reflect the realistic physical and mechanical processes in long-runout landslide motion and provide a suitable method for risk assessment and pre-failure prediction.

Control method based on DRFNN sliding mode for multifunctional flexible multistate switch

To address the low accuracy and stability when applying classical control theory in distribution networks with distributed generation,a control method involving flexible multistate switches(FMSs)is proposed in this study.This approach is based on an improved double-loop recursive fuzzy neural network(DRFNN)sliding mode,which is intended to stably achieve multiterminal power interaction and adaptive arc suppression for single-phase ground faults.First,an improved DRFNN sliding mode control(SMC)method is proposed to overcome the chattering and transient overshoot inherent in the classical SMC and reduce the reliance on a precise mathematical model of the control system.To improve the robustness of the system,an adaptive parameter-adjustment strategy for the DRFNN is designed,where its dynamic mapping capabilities are leveraged to improve the transient compensation control.Additionally,a quasi-continuous second-order sliding mode controller with a calculus-driven sliding mode surface is developed to improve the current monitoring accuracy and enhance the system stability.The stability of the proposed method and the convergence of the network parameters are verified using the Lyapunov theorem.A simulation model of the three-port FMS with its control system is constructed in MATLAB/Simulink.The simulation result confirms the feasibility and effectiveness of the proposed control strategy based on a comparative analysis.

基于分数阶双忆阻器的多稳态混沌系统及其FPGA实现

将分数阶微积分和忆阻器引入混沌系统可以增加混沌系统的复杂性,从而拓宽混沌系统的应用范围。首先在三阶混沌系统中引入了两个分数阶磁控忆阻器构建新型四阶混沌系统,再采用平衡点稳定性分析、分岔图、相图、动力学地图等方法对其进行动力学行为分析。结果表明:分数阶系统产生了无穷多共存吸引子,具有超级多稳态,展现出丰富的动力学行为。阶次的改变会引起忆阻特性曲线不对称改变,系统状态发生改变。最后,搭建了FPGA实验平台,实验结果与数值仿真结果一致。

基于一类新型激活函数的递归神经网络的多稳定性分析

本研究基于一类新型连续锯齿型激活函数研究了递归神经网络(Hopfield神经网络)的多稳定性。首先,通过区间剖分法、Brouwer不动点定理证明了基于该激活函数的n维神经网络模型至少具有7n个平衡点,并运用对角占优矩阵理论、局部稳定性判定定理等方法证明了其中4n个平衡点是局部指数稳定的,剩余的平衡点是不稳定的。其次,通过增加锯齿型激活函数的峰值点将激活函数推广到更一般的情况,得到了n维神经网络在含有k个峰值点的连续锯齿型激活函数中至少具有(2k+1)n个平衡点,其中(k+1)n个平衡点为局部稳定的。本研究设计的激活函数相较于现有的一些激活函数会产生更多的稳定平衡点,并且在增加峰值点的过程中不会增加神经网络的计算复杂度。最后,通过两个具体的数值算例验证了本研究结果的有效性。