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1.
Wu-Yang Zhu 《中国物理 B》2022,31(6):60204-060204
The memristor is also a basic electronic component, just like resistors, capacitors and inductors. It is a nonlinear device with memory characteristics. In 2008, with HP's announcement of the discovery of the TiO2 memristor, the new memristor system, memory capacitor (memcapacitor) and memory inductor (meminductor) were derived. Fractional-order calculus has the characteristics of non-locality, weak singularity and long term memory which traditional integer-order calculus does not have, and can accurately portray or model real-world problems better than the classic integer-order calculus. In recent years, researchers have extended the modeling method of memristor by fractional calculus, and proposed the fractional-order memristor, but its concept is not unified. This paper reviews the existing memristive elements, including integer-order memristor systems and fractional-order memristor systems. We analyze their similarities and differences, give the derivation process, circuit schematic diagrams, and an outlook on the development direction of fractional-order memristive elements. 相似文献
2.
Zhi-Jun Li 《中国物理 B》2023,32(1):10503-010503
Considering the fact that memristors have the characteristics similar to biological synapses, a fractional-order multistable memristor is proposed in this paper. It is verified that the fractional-order memristor has multiple local active regions and multiple stable hysteresis loops, and the influence of fractional-order on its nonvolatility is also revealed. Then by considering the fractional-order memristor as an autapse of Hindmarsh-Rose (HR) neuron model, a fractional-order memristive neuron model is developed. The effects of the initial value, external excitation current, coupling strength and fractional-order on the firing behavior are discussed by time series, phase diagram, Lyapunov exponent and inter spike interval (ISI) bifurcation diagram. Three coexisting firing patterns, including irregular asymptotically periodic (A-periodic) bursting, A-periodic bursting and chaotic bursting, dependent on the memristor initial values, are observed. It is also revealed that the fractional-order can not only induce the transition of firing patterns, but also change the firing frequency of the neuron. Finally, a neuron circuit with variable fractional-order is designed to verify the numerical simulations. 相似文献
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Fractional Euler-Lagrange equations are investigated in the presence of Grassmann variables. The fractional Hamiltonian and
the path integral of the fractional supersymmetric classical model are constructed.
Presented at the 3rd International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, Istanbul, Turkey, June 20–22,
2005. 相似文献
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6.
Our comments point out some mistakes in the main theorem given by Yang and Qi in Ref. [1] concerning the equivalent passivity method to design a nonlinear controller for the stabilizing fractional order unified chaotic system. The proof of this theorem is not reliable, since the mathematical basis of the fractional order calculus is not considered. Moreover, there are some algebraic mistakes in the inequalities used, thus making the proof invalid. We propose a proper Lyapunov function and the stability of Yang and Qi's Controller is investigated based on the fractional order Lyapunov theorem. 相似文献
7.
The Hamiltonian formulation for mechanical systems containing Riemman-Liouville fractional derivatives are investigated in
fractional time. The fractional Hamilton’s equations are obtained and two examples are investigated in detail.
相似文献
8.
We introduce conformable fractional Nikiforov-Uvarov (NU) method by means of conformable fractional derivative which is the most natural definition in non-integer calculus. Since, NU method gives exact eigenstate solutions of Schrödinger equation (SE) for certain potentials in quantum mechanics, this method is carried into the domain of fractional calculus to obtain the solutions of fractional SE. In order to demonstrate the applicability of the conformable fractional NU method, we solve fractional SE for harmonic oscillator potential, Woods-Saxon potential, and Hulthen potential. 相似文献
9.
赵晓龙 《原子与分子物理学报》2014,31(6)
基于分数阶微积分理论和介电分数单元,建立了分数Poynting-Thomson模型,给出了复介电常数的表达式.利用遗传算法结合共轭梯度法,分别求得复介电常数实部和虚部的最优参数,并对E7（主要是氰基联苯化合物）复介电常数实部和虚部的实验数据进行拟合.结果表明能对E7的复介电常数给出很好的描述.另外,由于该法对研究聚合物的复介电常数有广泛的适用性,故该法对研究与E7性质相差很大的聚合物同样适用. 相似文献
10.
基于分数阶微积分理论和介电分数单元,建立了分数Poynting-Thomson模型,给出了复介电常数的表达式.利用遗传算法结合共轭梯度法,分别求得复介电常数实部和虚部的最优参数,并对E7（主要是氰基联苯化合物）复介电常数实部和虚部的实验数据进行拟合.结果表明能对E7的复介电常数给出很好的描述.另外,由于该法对研究聚合物的复介电常数有广泛的适用性,故该法对研究与E7性质相差很大的聚合物同样适用. 相似文献
11.
Fractional calculus (FC) is the area of calculus that generalizes the operations of differentiation and integration. FC operators are non-local and capture the history of dynamical effects present in many natural and artificial phenomena. Entropy is a measure of uncertainty, diversity and randomness often adopted for characterizing complex dynamical systems. Stemming from the synergies between the two areas, this paper reviews the concept of entropy in the framework of FC. Several new entropy definitions have been proposed in recent decades, expanding the scope of applicability of this seminal tool. However, FC is not yet well disseminated in the community of entropy. Therefore, new definitions based on FC can generalize both concepts in the theoretical and applied points of view. The time to come will prove to what extend the new formulations will be useful. 相似文献
12.
The complex dynamics of a variable viscoelasticity oscillator is studied using the novel concept of Variable‐Order (VO) Calculus. The damping force in the oscillator varies continuously between the elastic and viscous regimes depending on the position of the mass. The oscillator considered here is composed of a linear spring of stiffness k that inputs a restitutive force Fk = ‐k x, a VO damper of order q(x(t)) that generates a damping force Fq = ‐cq ??q(x(t)) x, and a mass m. A modified Runge‐Kutta method is used in conjunction with a trapezoidal numerical integration technique to yield a second‐order accurate method for the solution of the resulting VO Differential Equation (VODE). The VO oscillator is also modelled using a Constant Order (CO) formulation where a number of CO fractional order differentials are weighted to simulate the VO behavior. The CO formulation asymptotically approaches the VO results when a relatively large number of weights is used. For the viscoelastic range of 0 ≤ q ≤ 1, the dynamics of the oscillator is well approximated by the CO formulation when 5 or more fractional terms are included (e.g., 0, 1/4, 1/2, 3/4, and 1). 相似文献
13.
D. Băleanu 《Czechoslovak Journal of Physics》2004,54(11):1165-1170
The analog of Maxwell electromagnetism for hydrodynamic turbulence, the metafluid dynamics, is investigated as a constrained system within fractional Riemann-Liouville derivatives. 相似文献
14.
A general approach to the construction of non-Markovian quantum theory is proposed. Non-Markovian equations for quantum observables and states are suggested by using general fractional calculus. In the proposed approach, the non-locality in time is represented by operator kernels of the Sonin type. A wide class of the exactly solvable models of non-Markovian quantum dynamics is suggested. These models describe open (non-Hamiltonian) quantum systems with general form of nonlocality in time. To describe these systems, the Lindblad equations for quantum observable and states are generalized by taking into account a general form of nonlocality. The non-Markovian quantum dynamics is described by using integro-differential equations with general fractional derivatives and integrals with respect to time. The exact solutions of these equations are derived by using the operational calculus that is proposed by Yu. Luchko for general fractional differential equations. Properties of bi-positivity, complete positivity, dissipativity, and generalized dissipativity in general non-Markovian quantum dynamics are discussed. Examples of a quantum oscillator and two-level quantum system with a general form of nonlocality in time are suggested. 相似文献
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通过在蔡氏电路的耦合电阻支路中串联一个电感,采用压控忆阻替换蔡氏电路中的蔡氏二极管,提出了一种新颖的五阶压控忆阻蔡氏混沌电路.建立该电路的数学模型,从理论上分析了平衡点及其稳定性的演化过程.特别地,该电路在给定参数下只有一个不稳定的零平衡点,却形成了混沌与周期的非对称吸引子共存的吸引盆,意味着双稳定性的存在.进而利用数值仿真与PSIM电路仿真着重研究了本文电路在不同初始状态下产生的双稳定性现象及其形成机理.PSIM电路仿真结果与数值仿真结果一致,较好地验证了理论分析.借助分岔图、李雅普诺夫指数、相轨图和吸引盆进一步深入探讨了归一化五阶压控忆阻蔡氏系统依赖于系统初始条件的动力学行为.结果表明,该忆阻蔡氏系统在不同的初始条件下能够呈现出混沌吸引子与周期极限环共存的双稳定性现象. 相似文献
17.
Mohammad Pourmahmood Aghababa 《中国物理 B》2012,21(10):100505-100505
The present paper investigates the existence of chaos in a non-autonomous fractional-order micro-electromechanical resonator system(FOMEMRS).Using the maximal Lyapunov exponent criterion,we show that the FOMEMRS exhibits chaos.Strange attractors of the system are plotted to validate its chaotic behavior.Afterward,a novel fractional finite-time controller is introduced to suppress the chaos of the FOMEMRS with model uncertainties and external disturbances in a given finite time.Using the latest version of the fractional Lyapunov theory,the finite time stability and robustness of the proposed scheme are proved.Finally,we present some computer simulations to illustrate the usefulness and applicability of the proposed method. 相似文献
18.
This paper presents a new smooth memristor oscillator,
which is derived from Chua's oscillator by replacing Chua's diode
with a flux-controlled memristor and a negative conductance. Novel
parameters and initial conditions are dependent upon dynamical behaviours
such as transient chaos and stable chaos with an intermittence
period and are found in the smooth memristor oscillator. By using
dynamical analysis approaches including time series, phase portraits
and bifurcation diagrams, the dynamical behaviours of the proposed
memristor oscillator are effectively investigated in this paper. 相似文献
19.
局部有源忆阻器(locally-active memristor,LAM)凭借其高集成度、低功耗和局部有源特性等优点,在神经形态计算领域显示出巨大的潜力.本文提出了一种简单的N型LAM数学模型,通过揭示其非线性动力特性,设计了N型LAM神经元电路.采用Hopf分岔、数值分析等方法定量研究了该电路的动力学行为,成功模拟了多种神经形态行为,包括全或无行为、尖峰、簇发、周期振荡等.并利用该神经元电路结构模拟了生物触觉神经元的频率特性.仿真结果表明:当输入信号幅值低于阈值时,神经元电路输出信号的振荡频率与输入信号强度呈正相关(即兴奋状态),并在阈值处达到最大值.随后,继续增大激励强度,振荡频率则逐渐降低(即保护性抑制状态).最后,设计了N型LAM硬件仿真器,并完成了人工神经元电路的硬件实现,实验结果与仿真结果、理论分析相一致,验证了该N型LAM具备的神经形态行为. 相似文献
20.
忆阻混沌振荡器的动力学分析 总被引：4，自引：0，他引：4
忆阻器(memristor)是一种有记忆功能的非线性电阻器,它是除电阻器、电容器和电感器之外的第四种基本电路元件.采用一个具有光滑磁控特性曲线的忆阻器和一个负电导替换蔡氏振荡器中的蔡氏二极管,导出了一个基于忆阻器的振荡器电路.采用常规的动力学分析手段研究了电路参数和初始条件变化时该光滑忆阻振荡器的动力学特性.研究结果表明,光滑忆阻振荡器与一般的混沌系统完全不同,它的动力学行为除了与电路参数有关外,还极端依赖于电路的初始条件,存在瞬态混沌和状态转移等奇异的非线性物理现象. 相似文献