Stability analysis of fractional order memristor synapse-coupled hopfield neural network with ring structure

Aguilar CZ, Gómez-Aguilar J, Alvarado-Martínez V, Romero-Ugalde H (2020) Fractional order neural networks for system identification. Chaos Solitons Fractals 130:109444

Article  Google Scholar 

Amirian MM, Towers I, Jovanoski Z, Irwin AJ (2020) Memory and mutualism in species sustainability: a time-fractional lotka-volterra model with harvesting. Heliyon 6(9):e04816

Article  Google Scholar 

Amirian MM, Irwin AJ, Finkel ZV (2022) Extending the monod model of microbial growth with memory. arXiv preprint arXiv:2207.02028

Bao H, Hu A, Liu W, Bao B (2019) Hidden bursting firings and bifurcation mechanisms in memristive neuron model with threshold electromagnetic induction. IEEE Trans Neural Netw Learn Syst 31(2):502–511

Article  Google Scholar 

Chen Y-S, Lin T-H, Lin S-M (2007) Raa: a ring-based address autoconfiguration protocol in mobile ad hoc networks. Wirel pers commun 43(2):549–571

Article  Google Scholar 

Chen J, Zeng Z, Jiang P (2014) Global Mittag-Leffler stability and synchronization of memristor-based fractional-order neural networks. Neural Netw 51:1–8

Article  Google Scholar 

Chen C, Chen J, Bao H, Chen M, Bao B (2019) Coexisting multi-stable patterns in memristor synapse-coupled Hopfield neural network with two neurons. Nonlinear Dyn 95(4):3385–3399

Article  Google Scholar 

Garrappa R (2018) Numerical solution of fractional differential equations: a survey and a software tutorial. Math 6(2):16

Article  Google Scholar 

Gaurav G, Anand RS, Kumar V (2021) Eeg based cognitive task classification using multifractal detrended fluctuation analysis. Cogn Neurodyn 15(6):999–1013

CAS  Article  Google Scholar 

He S (2020) Complexity and chimera states in a ring-coupled fractional-order memristor neural network. Front Appl Math Stat 6:24. https://doi.org/10.3389/fams

Article  Google Scholar 

Hu X, Liu C (2019) Dynamic property analysis and circuit implementation of simplified memristive Hodgkin-Huxley neuron model. Nonlinear Dyn 97(2):1721–1733

Article  Google Scholar 

Jiang C, Zhang F, Li T (2018) Synchronization and antisynchronization of N-coupled fractional-order complex chaotic systems with ring connection. Math Methods Appl Sci 41(7):2625–2638

Article  Google Scholar 

Joya G, Atencia M, Sandoval F (2002) Hopfield neural networks for optimization: study of the different dynamics. Neurocomputing 43(1–4):219–237

Article  Google Scholar 

Kaslik E, Sivasundaram S (2012) Nonlinear dynamics and chaos in fractional-order neural networks. Neural Netw 32:245–256

Article  Google Scholar 

Kaveh A, Rahami H (2011) Block circulant matrices and applications in free vibration analysis of cyclically repetitive structures. Acta Mech 217(1):51–62

Article  Google Scholar 

Kazemi S, Jamali Y (2022) Phase synchronization and measure of criticality in a network of neural mass models. Sci Rep 12(1):1–18

Article  Google Scholar 

Khalighi M, Eftekhari L, Hosseinpour S, Lahti L (2021) Three-species Lotka-Volterra model with respect to Caputo and Caputo-Fabrizio fractional operators. Symmetry 13(3):368

Article  Google Scholar 

Khalighi M, Amirianmatlob M, Malek A (2021) A new approach to solving multiorder time-fractional advection-diffusion-reaction equations using BEM and Chebyshev matrix. Math Methods Appl Sci 44(4):2964–2984

Article  Google Scholar 

Khalighi M, Gonze D, Faust K, Sommeria-Klein G, Lahti L (2021) Quantifying the impact of ecological memory on the dynamics of interacting communities. bioRxiv

Korn H, Faure P (2003) Is there chaos in the brain? II. Experimental evidence and related models. Compt rendus biol 326(9):787–840

Article  Google Scholar 

Li Q, Yang X-S, Yang F (2005) Hyperchaos in Hopfield-type neural networks. Neurocomputing 67:275–280

Article  Google Scholar 

Li K, Bao H, Li H, Ma J, Hua Z, Bao B (2021) Memristive Rulkov neuron model with magnetic induction effects. IEEE Trans Ind Inf 18(3):1726–1736

Article  Google Scholar 

Li Q, Yang X (2005) Complex dynamics in a simple Hopfield-type neural network. In: International symposium on neural networks, Springer, pp. 357–362

Matignon D (1996) Stability results for fractional differential equations with applications to control processing. In: Computational engineering in systems applications, vol. 2, Lille, France, pp. 963–968

Matlob MA, Jamali Y (2019) The concepts and applications of fractional order differential calculus in modeling of viscoelastic systems: a primer. Crit Rev\(^TM\) in Biomed Eng, 47(4)

Mazarei A, Matlob MA, Riazi G, Jamali Y (2018) The role of topology in the synchronization of neuronal networks based on the Hodgkin-Huxley model. arXiv preprint arXiv:1812.02297

Mêwanou R, Pierre S (2006) Link-state-based algorithms for dynamic routing in all-optical networks with ring topologies. Photonic Netw Commun 11(1):5–14

Article  Google Scholar 

Morris C, Lecar H (1981) Voltage oscillations in the barnacle giant muscle fiber. Biophys J 35(1):193–213

CAS  Article  Google Scholar 

Njitacke Z, Kengne J, Fotsin H (2019) A plethora of behaviors in a memristor based Hopfield neural networks (hnns). Int J Dyn Control 7(1):36–52

Article  Google Scholar 

Nobukawa S, Yamanishi T, Nishimura H, Wada Y, Kikuchi M, Takahashi T (2019) Atypical temporal-scale-specific fractal changes in Alzheimer’s disease eeg and their relevance to cognitive decline. Cogn Neurodyn 13(1):1–11

Article  Google Scholar 

Nobukawa S, Wagatsuma N, Nishimura H (2020) Deterministic characteristics of spontaneous activity detected by multi-fractal analysis in a spiking neural network with long-tailed distributions of synaptic weights. Cogn Neurodyn 14(6):829–836

Article  Google Scholar 

Podlubny I (1998) Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. Elsevier

Rech PC (2015) Period-adding and spiral organization of the periodicity in a Hopfield neural network. Int J Mach Learn Cybern 6(1):1–6

Article  Google Scholar 

Saeedian M, Khalighi M, Azimi-Tafreshi N, Jafari G, Ausloos M (2017) Memory effects on epidemic evolution: the susceptible-infected-recovered epidemic model. Phys Rev E 95(2):022409

CAS  Article  Google Scholar 

Srinivasulu A (2012) Digital very-large-scale integration (VLSI) hopfield neural network implementation on field programmable gate arrays (FPGA) for solving constraint satisfaction problems. J Eng Technol Res 4(1):11–21

Google Scholar 

Tang Y, Wang Z, Fang J-a (2009) Pinning control of fractional-order weighted complex networks. Chaos Interdiscip J Nonlinear Sci 19(1):013112

Article  Google Scholar 

Tee GJ (2007) Eigenvectors of block circulant and alternating circulant matrices. N Z J Math 36(8):195–211

Google Scholar 

Thomas A (2013) Memristor-based neural networks. J Phys D Appl Phys 46(9):093001

CAS  Article  Google Scholar 

Usha K, Subha P (2019) Hindmarsh-rose neuron model with memristors. Biosystems 178:1–9

Google Scholar 

Wang XF, Chen G (2003) Complex networks: small-world, scale-free and beyond. IEEE circuits syst mag 3(1):6–20

Article  Google Scholar 

Wen X-J, Wu Z-M, Lu J-G (2008) Stability analysis of a class of nonlinear fractional-order systems. IEEE Trans circuits syst II Express Briefs 55(11):1178–1182

Article  Google Scholar 

Xiong P-Y, Jahanshahi H, Alcaraz R, Chu Y-M, Gómez-Aguilar J, Alsaadi FE (2021) Spectral entropy analysis and synchronization of a multi-stable fractional-order chaotic system using a novel neural network-based chattering-free sliding mode technique. Chaos, Solitons Fractals 144:110576

Article  Google Scholar 

Xu Q, Ding S, Bao H, Chen M, Bao B (2021) Piecewise-linear simplification for adaptive synaptic neuron model. Express Briefs, IEEE Trans Circuits Syst II

Xu Q, Ju Z, Ding S, Feng C, Chen M, Bao B (2022) Electromagnetic induction effects on electrical activity within a memristive Wilson neuron model. Cogn Neurodyn 1–11

Yang Y, Ma J, Xu Y, Jia Y (2021) Energy dependence on discharge mode of Izhikevich neuron driven by external stimulus under electromagnetic induction. Cogn Neurodyn 15(2):265–277

Article  Google Scholar 

Zúñiga-Aguilar C, Romero-Ugalde H, Gómez-Aguilar J, Escobar-Jiménez R, Valtierra-Rodríguez M (2017) Solving fractional differential equations of variable-order involving operators with Mittag-Leffler kernel using artificial neural networks. Chaos Solitons Fractals 103:382–403

Article  Google Scholar 

Zúñiga-Aguilar C, Coronel-Escamilla A, Gómez-Aguilar J, Alvarado-Martínez V, Romero-Ugalde H (2018) New numerical approximation for solving fractional delay differential equations of variable order using artificial neural networks. European Phys J Plus 133(2):1–16

Article  Google Scholar 

Zúñiga-Aguilar C, Gómez-Aguilar J, Romero-Ugalde H, Escobar-Jiménez R, Fernández-Anaya G, Alsaadi FE (2021) Numerical solution of fractal-fractional Mittag–Leffler differential equations with variable-order using artificial neural networks. Eng Comput 1–14

Zúñiga-Aguilar C, Gómez-Aguilar J, Romero-Ugalde H, Jahanshahi H, Alsaadi FE (2021) Fractal-fractional neuro-adaptive method for system identification. Eng Comput 1–24

留言 (0)

沒有登入
gif