Synchronization conditions in simple memristor neural networks

Ascoli, Alon; Lanza, Valentina; Corinto, Fernando; Tetzlaff, Ronald

doi:10.1016/j.jfranklin.2015.06.003

Cited by 31 publications

(13 citation statements)

References 28 publications

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“…As an example, in [28] dynamic memristors are used for synchronizing memristor-coupled oscillatory neural cells, whereas in [39,58] they are used within circuits displaying chaotic dynamics. As an example, in [28] dynamic memristors are used for synchronizing memristor-coupled oscillatory neural cells, whereas in [39,58] they are used within circuits displaying chaotic dynamics.…”

Section: Discussion and Comparisonmentioning

confidence: 99%

“…Indeed, if one turns off the power, that is it opens or short circuits a memristor, when the memristor charge is q (or the memristor flux is φ), both voltage and current become zero, yet the memristor can hold the value of the charge unchanged at q (or the flux unchanged at φ), for subsequent times [21][22][23].During recent years there has been a widespread interest in the scientific community in memristor modelling and simulation, applications, and the dynamic analysis of nonlinear circuits containing memristors, see, for example [20,[24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42]. It is supposed that during the analogue computation of the CNN the memristors behave as dynamic elements, so that each dynamic memristor (DM)-CNN cell is described by a second-order differential system in the state variables given by the capacitor voltage and the memristor flux.…”

mentioning

confidence: 99%

“…During recent years there has been a widespread interest in the scientific community in memristor modelling and simulation, applications, and the dynamic analysis of nonlinear circuits containing memristors, see, for example [20,[24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42]. Memristors have found promising potential applications in developing nonvolatile random access memories, where they are used in binary mode of operation as resistances that switch between on and off states [43].…”

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confidence: 99%

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Complete stability of feedback CNNs with dynamic memristors and second‐order cells

Marco

Forti

Pancioni

2016

Circuit Theory & Apps

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The paper considers a feedback cellular neural network (CNN) obtained by interconnecting elementary cells with an ideal capacitor and an ideal flux-controlled memristor. It is supposed that during the analogue computation of the CNN the memristors behave as dynamic elements, so that each dynamic memristor (DM)-CNN cell is described by a second-order differential system in the state variables given by the capacitor voltage and the memristor flux. The proposed networks are called DM-CNNs, that is CNNs using a dynamic (D) memristor (M). After giving a foundation to the DM-CNN model, the paper establishes a fundamental result on complete stability, that is convergence of solutions toward equilibrium points, when the DM-CNN has symmetric interconnections. Because of the presence of dynamic memristors, a DM-CNN displays peculiar and basically different dynamic properties with respect to standard CNNs. First of all a DM-CNN computes during the time evolution of the memristor fluxes, instead of the capacitor voltages as for a standard CNN. Furthermore, when a steady state is reached, the memristors keep in memory the result of the computation, that is the limiting values of the fluxes, while all memristor currents and voltages, as well as all currents, voltages, and power in the DM-CNN vanish. Instead, for standard CNNs, currents, voltages, and power do not drop off when a steady state is reached. voltage applied to it. A crucial feature is that an ideal memristor can exhibit nonvolatile memory. Indeed, if one turns off the power, that is it opens or short circuits a memristor, when the memristor charge is q (or the memristor flux is φ), both voltage and current become zero, yet the memristor can hold the value of the charge unchanged at q (or the flux unchanged at φ), for subsequent times [21][22][23].During recent years there has been a widespread interest in the scientific community in memristor modelling and simulation, applications, and the dynamic analysis of nonlinear circuits containing memristors, see, for example [20,[24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42]. Memristors have found promising potential applications in developing nonvolatile random access memories, where they are used in binary mode of operation as resistances that switch between on and off states [43]. They are also important in neuromorphic architectures, because of the possibility to implement CNN cells and interconnections in nanotechnology by means of memristors, with significantly reduced power dissipation and area consumption [34,44,45]. In particular, [34,46] developed a number of effective memristor bridge circuits for implementing the synaptic connections in CNN architectures. A time sharing protocol is used where during the programming phase, strong (large and wide) voltage pulses are used for programming the synaptic weights, while weak (small or narrow) pulses having negligible effects on the memristor resistance are used during the analogue processing of input signals. Applications to implement lear...

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Section: Discussion and Comparisonmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Complete stability of feedback CNNs with dynamic memristors and second‐order cells

Marco

Forti

Pancioni

2016

Circuit Theory & Apps

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“…where, as stated earlier, k conv,8 represents a unitary constant with units V −1 . Using Equations 27 and 28 into Equation 30, and letting…”

Section: Ideal Memristor-based Circuit-theoretic Model Of the Kick-flmentioning

confidence: 99%

“…which may also be obtained by inserting Equation 30 into Equation 29 from the part I paper [12]. Noting that v int2 (t (0) 0,g ) = 0 V, using Equation 33, Equation 32 may be finally cast as…”

Section: Ideal Memristor-based Circuit-theoretic Model Of the Kick-flmentioning

confidence: 99%

Memristor‐enhanced humanoid robot control system – Part II: Circuit theoretic model and performance analysis

Baumann

Ascoli

Tetzlaff

et al. 2017

Circuit Theory & Apps

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Summary Neuromorphic circuits shall be considered in electronics to perform complex computing tasks in a time‐efficient and energy‐efficient fashion and to adapt their problem‐solving methodologies to changes in initial conditions and parameters. One of the key biological paradigms at the basis of their operation, allowing them to exhibit higher performance levels as compared with state‐of‐the‐art electronic systems, is the mem‐computing functionality, i.e. the capability to process and store data in the same physical location, which represents the core principle to overcome the time inefficiency of von Neumann machine architectures. With the advent of memristors, the interest in the exploitation of this principle to develop dynamic circuits for the implementation of innovative signal processing strategies has grown considerably. Here, we leverage the mem‐computing capability inherent in these devices to propose an innovative control system for motion control in a humanoid robot. In the part I paper, we introduced the paradigm theoretic foundations. In this part II manuscript, we propose circuit‐theoretic models for the new control system based upon an ideal and upon a physical memristor model and demonstrate through numerical simulations how it outperforms the old approach in terms of time‐efficiency and energy‐efficiency, maintaining a good degree of adaptability to changes in environmental conditions.

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Complex Dynamics and Synchronization Phenomena in Arrays of Memristor Oscillators

Corinto

Forti

Chua

2020

Nonlinear Circuits and Systems With Memristors

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Synchronization conditions in simple memristor neural networks

Cited by 31 publications

References 28 publications

Complete stability of feedback CNNs with dynamic memristors and second‐order cells

Complete stability of feedback CNNs with dynamic memristors and second‐order cells

Memristor‐enhanced humanoid robot control system – Part II: Circuit theoretic model and performance analysis

Complex Dynamics and Synchronization Phenomena in Arrays of Memristor Oscillators

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