Mathematical modeling of a memristor device

Elgabra, Hazem; Farhat, Ilyas A. H.; Hosani, Ahmed Saleh Al; Homouz, Dirar; Mohammad, Baker

doi:10.1109/innovations.2012.6207722

Cited by 26 publications

(10 citation statements)

References 8 publications

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“…The seeds of Mimosa pudica L. were soaked in warm water (30 C) for 48 h. They were then grown in well drained peat moss at 21 C with a 12:12 hr light:dark photoperiod. After growing for 2 weeks, the seedlings were transplanted into pots and placed inside a plant growing chamber.…”

Section: Plantsmentioning

confidence: 99%

“…4,10,[19][20][21][22][23][24] They can be divided in 3 groups: linear, nonlinear, and exponential models. [16][17][18][19][20][21][22][23][24][25] Chua et al 11,12 and Adhikari et al 10 found that a memristor has 3 characteristic fingerprints: "When driven by a bipolar periodic signal the device must exhibit a pinched hysteresis loop in the voltage-current plane, assuming the response is periodic; starting from some critical frequency, the hysteresis lobe area should decrease monotonically as the excitation frequency increases; the pinched hysteresis loop should shrink to a single-valued function when the frequency tends to infinity." Voltage gated ion channels in biological tissue are located in membranes, which have capacitance connected in parallel to transmembrane organized ion channels.…”

Section: Introductionmentioning

confidence: 99%

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An analytical model of memristors in plants

Markin

Volkov

Chua

2014

Plant Signaling & Behavior

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Section: Plantsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An analytical model of memristors in plants

Markin

Volkov

Chua

2014

Plant Signaling & Behavior

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“…When the OFF state, the exponential part of the Eq. (20) has the dominant part of the current, which is similar to an ideal PN junction [12,14].…”

Section: Exponential Modelmentioning

confidence: 92%

“…The speed of movement of the boundary between the doped layer and undoped layer is expressed as dx/dt with Eq. (10) [12,13]:…”

Section: Linear Drift Modelmentioning

confidence: 99%

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Mathematical Modeling of Memristors

Oğuz¹

2018

Memristor and Memristive Neural Networks

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The memristor has quite a reputation as a missing circuit element. It is a powerful candidate for next-generation applications after being first implemented in HP's laboratories. At this point, mathematical models were needed for the analysis of the memristor, and a lot of studies were done on this subject. In this chapter, mathematical modeling and simulations of the memristor device have been emphasized. Firstly, linear drift and nonlinear drift models have been described on the basic HP model. The window functions used in the nonlinear drift model have been widely examined. Different from HP model, the Simmons tunnel barrier and the threshold adaptive memristor model (TEAM) have been also mentioned. As a result, the most widely used modeling techniques have been described in detail.

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Globally asymptotic stability analysis for memristor‐based competitive systems of reaction–diffusion delayed neural networks

Gholami

2023

Math Methods in App Sciences

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The main aim of this investigation is to present a mathematical criterion that guarantees the global asymptotic stability of special class of nonlinear neural systems. Indeed, a memristor‐based competitive nonlinear reaction–diffusion Cohen–Grossberg neural network system is chosen to be investigated. Chasing the accuracy and comprehensiveness, our model has to be improved with the following elements: neutrality of the nonlinear part and being effected under time delays in the both of straight and neutral parts of the nonlinearity. Since the proposed neural network is novel, so we need to make use of a novel Lyapunov functional correspondingly to globally asymptotic stabilization of the neural network under investigation. Prior to this process, it is necessary to present a uniqueness criterion for solutions of the proposed neural network. To this aim, the well‐known M‐matrix technique of the linear algebra is applied that guarantees existence of a unique equilibrium point of the considered Cohen–Grossberg neural network. Numerical perspective of this investigation leads us to some numerical prototypes that justify our stability criterion is applicable. This investigation will be finalized with interesting discussion on the nature of time delays that are characterized as fundamental elements in modeling of the neural networks.

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Mathematical modeling of a memristor device

Cited by 26 publications

References 8 publications

An analytical model of memristors in plants

An analytical model of memristors in plants

Mathematical Modeling of Memristors

Globally asymptotic stability analysis for memristor‐based competitive systems of reaction–diffusion delayed neural networks

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