A non-local structural derivative model for memristor

Abstract The memristor is of great application and significance in the integrated circuit design, the realization of large-capacity non-volatile memories and the neuromorphic systems. This paper firstly proposes the non-local structural derivative memristor model with two-degree-of-freedom increased to portray the memory effect of memristor. Actually, the developed is a more generalized model that will be reduced to the classical one when the fractal characteristic index α = 1. The proposed model is more flexible than the classical ideal memory model and Riemann Liouville memristor model under the same conditions. In addition, the memory effect described by the present scheme could be adjusted by the position parameter δ. This work provides a new methodology not only to describe the memory effect of the memristor, but also to easily portray the memristor with ultra-weak memory.

[1]  Bo Yu,et al.  Analog Circuit Implementation of Fractional-Order Memristor: Arbitrary-Order Lattice Scaling Fracmemristor , 2018, IEEE Transactions on Circuits and Systems I: Regular Papers.

[2]  J. Hesthaven,et al.  Local discontinuous Galerkin methods for fractional diffusion equations , 2013 .

[3]  Ahmed Gomaa Radwan,et al.  On the analysis of current-controlled fractional-order memristor emulator , 2017, 2017 6th International Conference on Modern Circuits and Systems Technologies (MOCAST).

[4]  F. Mainardi Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models , 2010 .

[5]  Stephen J. Wolf,et al.  The elusive memristor: properties of basic electrical circuits , 2008, 0807.3994.

[6]  D. Stewart,et al.  The missing memristor found , 2008, Nature.

[7]  S. Holm,et al.  A Survey on Fractional Derivative Modeling of Power-Law Frequency-Dependent Viscous Dissipative and Scattering Attenuation in Acoustic Wave Propagation , 2018 .

[8]  K. Miller,et al.  An Introduction to the Fractional Calculus and Fractional Differential Equations , 1993 .

[9]  YangQuan Chen,et al.  A new collection of real world applications of fractional calculus in science and engineering , 2018, Commun. Nonlinear Sci. Numer. Simul..

[10]  Qingsong Hua,et al.  A simple empirical formula of origin intensity factor in singular boundary method for two-dimensional Hausdorff derivative Laplace equations with Dirichlet boundary , 2018, Comput. Math. Appl..

[11]  Cheng We Implicit calculus modeling for simulation of complex scientific and engineering problems , 2014 .

[12]  L. Chua Memristor-The missing circuit element , 1971 .

[13]  Carl B. Boyer,et al.  A History of Mathematics. , 1993 .

[14]  L.O. Chua,et al.  Memristive devices and systems , 1976, Proceedings of the IEEE.

[15]  Dumitru Baleanu,et al.  Relaxation and diffusion models with non-singular kernels , 2017 .

[16]  J. A. Tenreiro Machado,et al.  Fractional generalization of memristor and higher order elements , 2013, Commun. Nonlinear Sci. Numer. Simul..

[17]  Dalibor Biolek,et al.  Computation of the Area of Memristor Pinched Hysteresis Loop , 2012, IEEE Transactions on Circuits and Systems II: Express Briefs.

[18]  Gregory S. Snider,et al.  Spike-timing-dependent learning in memristive nanodevices , 2008, 2008 IEEE International Symposium on Nanoscale Architectures.

[19]  A. Ayatollahi,et al.  Implementation of biologically plausible spiking neural network models on the memristor crossbar-based CMOS/nano circuits , 2009, 2009 European Conference on Circuit Theory and Design.

[20]  Majid Ahmadi,et al.  Optimized implementation of memristor-based full adder by material implication logic , 2014, 2014 21st IEEE International Conference on Electronics, Circuits and Systems (ICECS).

[21]  W. Lu,et al.  High-density Crossbar Arrays Based on a Si Memristive System , 2008 .

[22]  C. Toumazou,et al.  A Versatile Memristor Model With Nonlinear Dopant Kinetics , 2011, IEEE Transactions on Electron Devices.

[23]  J. Trujillo,et al.  A unified approach to fractional derivatives , 2012 .

[24]  Laurent Nottale,et al.  Scale relativity, fractal space-time and quantum mechanics , 1994 .

[25]  Ningning Yang,et al.  Modeling and Analysis of a Fractional-Order Generalized Memristor-Based Chaotic System and Circuit Implementation , 2017, Int. J. Bifurc. Chaos.

[26]  Fernando Corinto,et al.  A Boundary Condition-Based Approach to the Modeling of Memristor Nanostructures , 2012, IEEE Transactions on Circuits and Systems I: Regular Papers.

[27]  R. Williams,et al.  How We Found The Missing Memristor , 2008, IEEE Spectrum.

[28]  Carlos Sánchez-López,et al.  Fractional-Order Memristor Emulator Circuits , 2018, Complex..

[29]  M. Tian,et al.  Diffusive dynamics of polymer chains in an array of nanoposts. , 2016, Physical chemistry chemical physics : PCCP.

[30]  Dalibor Biolek,et al.  SPICE Model of Memristor with Nonlinear Dopant Drift , 2009 .

[31]  Yong Zhang,et al.  A fractal Hilbert microstrip antenna with reconfigurable radiation patterns , 2005, 2005 IEEE Antennas and Propagation Society International Symposium.

[32]  He Huang,et al.  A Novel Window Function for Memristor Model With Application in Programming Analog Circuits , 2016, IEEE Transactions on Circuits and Systems II: Express Briefs.

[33]  Dalibor Biolek,et al.  Interpreting area of pinched memristor hysteresis loop , 2014 .

[34]  Ahmed Gomaa Radwan,et al.  Fractional-order Memristor Response Under DC and Periodic Signals , 2015, Circuits Syst. Signal Process..

[35]  Wen Chen,et al.  Structural derivative based on inverse Mittag-Leffler function for modeling ultraslow diffusion , 2016 .

[36]  W. Chen Time-space fabric underlying anomalous diffusion , 2005, math-ph/0505023.

[37]  Leon O. Chua,et al.  Three Fingerprints of Memristor , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[38]  Wen Chen,et al.  KANSA METHOD BASED ON THE HAUSDORFF FRACTAL DISTANCE FOR HAUSDORFF DERIVATIVE POISSON EQUATIONS , 2018, Fractals.

[39]  Leon O. Chua,et al.  Memfractance: A Mathematical Paradigm for Circuit Elements with Memory , 2014, Int. J. Bifurc. Chaos.

[40]  Richard L. Magin,et al.  A fractal derivative model for the characterization of anomalous diffusion in magnetic resonance imaging , 2016, Commun. Nonlinear Sci. Numer. Simul..

[41]  D. Baleanu,et al.  Discrete fractional logistic map and its chaos , 2014 .

[42]  C. Zheng,et al.  Time fractional derivative model with Mittag-Leffler function kernel for describing anomalous diffusion: Analytical solution in bounded-domain and model comparison , 2018, Chaos, Solitons & Fractals.

[43]  Wen Chen,et al.  A non-local structural derivative model for characterization of ultraslow diffusion in dense colloids , 2018, Commun. Nonlinear Sci. Numer. Simul..

[44]  T. Mareci,et al.  On random walks and entropy in diffusion‐weighted magnetic resonance imaging studies of neural tissue , 2014, Magnetic resonance in medicine.

[45]  Vasily E. Tarasov,et al.  Elasticity for economic processes with memory: Fractional differential calculus approach , 2016 .

[46]  Samiha Mourad,et al.  Digital Logic Implementation in Memristor-Based Crossbars - A Tutorial , 2010, 2010 Fifth IEEE International Symposium on Electronic Design, Test & Applications.

[47]  Dumitru Baleanu,et al.  Discrete fractional differences with nonsingular discrete Mittag-Leffler kernels , 2016 .