Unravelling the dynamical richness of 3D canonical memristor oscillators

Ponce, Enrique; Ros, Javier; Freire, Emilio; Amador, Andrés

doi:10.1016/j.mee.2017.08.004

Cited by 10 publications

(11 citation statements)

References 11 publications

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“…Later, it became clear that the state space of circuits containing ideal memristors can be decomposed into a continuum of invariant manifolds (foliation property of the state space), which are indexed by some constant parameter whose value depends on the initial conditions of the circuit. Specifically, in [22,23] a third-order memristor circuit is investigated in the voltage-current domain, while quite general classes of memristor circuits are analyzed in the flux-charge domain (see [24][25][26][27] and references therein). In particular, the flux-charge analysis method (FCAM), introduced in [24,25], makes it clear that the rich dynamics displayed by memristor circuits is due to the fact that the state space contains infinitely many invariant manifolds.…”

Section: Introductionmentioning

confidence: 99%

Circuits with a mem-element: invariant manifolds control via pulse programmed sources

et al. 2021

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The paper considers the problem of controlling multistability in a general class of circuits composed of a linear time-invariant two-terminal (one port) element, containing linear R, L, C components and ideal operational amplifiers, coupled with one of the mem-elements (memory elements) introduced by Prof. L.O. Chua, i.e., memristors, memcapacitors, and meminductors. First, explicit expressions of the invariant manifolds of the circuit are directly given in terms of the state variables of the two-terminal element and the mem-element. Then, the problem of steering the circuit dynamics from an initial invariant manifold to a final one, and hence to potentially switch among different attractors of the circuit, is addressed by designing pulse shaped control inputs. The control inputs ensure that the transition between the initial and final manifolds is accomplished within a given finite time interval. Moreover, it is shown how the designed control inputs can be implemented by introducing independent voltage and current sources in the two-terminal element. Notably, it turns out that it is always possible to solve the considered control problem by using a unique independent source. Several examples are provided to illustrate how the proposed approach can be applied to different circuits with mem-elements and to highlight the influence of the features of the designed sources on the behavior of the controlled dynamics.

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Section: Introductionmentioning

confidence: 99%

Circuits with a mem-element: invariant manifolds control via pulse programmed sources

et al. 2021

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“…The properties of memristors [3,9] open up new possibilities of constructing the memristor based oscillators (MBO) of different types [10][11][12][13][14]. The complex behavior of MBOs is analyzed in some papers (see for instance [15][16][17][18]). The inertial property of memristors provides the elimination from oscillator circuits the reactive elements (inductors and capacitors) which are poorly compatible with the requirements of the integrated implementation of neuromorphic systems.…”

Section: Introductionmentioning

confidence: 99%

Functional Capabilities of Coupled Memristor-Based Reactance-Less Oscillators

Rakitin¹,

Русаков²

2021

Memristor - An Emerging Device for Post-Moore’s Computing and Applications

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New functionalities of reactance-less memristor based oscillators are discussed which arise when two elementary oscillators are connected. It is shown that the system of coupled memristor based oscillators can be used for converting analog and analog-digital signals into binary pulse sequences. The approach to control the thresholds in memristor based oscillators is discussed. Standard control approach in memristor based oscillators is the exploitation of input signal to drive the rate of change in the state of the memristor. In contrast, the main idea of the considered controlling approach is to send the input signal not directly to the memristor device but to the comparator circuit and as result to control oscillator circuit behavior by change of interval of memristor resistor variation. The capabilities of coupled memristor based oscillators with control thresholds are sufficient for constructing the simple circuit elements of oscillatory computing architectures.

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“…it can be decomposed in a continuum of invariant manifolds where the circuit dynamics is described by a reduced order system. Specifically, in [Amador et al, 2017;Ponce et al, 2017] it is shown that the dynamics of a third order memristor circuit admits a first integral in the current-voltage domain and hence it can be equivalently described by a family of second order systems indexed by an additional constant parameter. Notably, the existence of a first integral implies that the second order systems have a smoother vector field, which is a useful property when the memristor has a piecewise linear characteristic.…”

Section: Introductionmentioning

confidence: 99%

Input–Output Characterization of the Dynamical Properties of Circuits with a Memelement

Innocenti

Marco

Tesi

et al. 2020

Int. J. Bifurcation Chaos

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The paper proposes a novel input–output approach to characterize the dynamical properties of a class of circuits composed by a linear time-invariant two-terminal element coupled with one of the ideal memelements (memory elements) introduced by Prof. L. O. Chua, i.e. memristors, memcapacitors, and meminductors. The developed approach permits to readily determine the conditions under which the dynamics of any circuit of the class admits a first integral. It is also shown that the circuit dynamics can be obtained by collecting the dynamical behaviors displayed by a canonical reduced-order input–output system subject to a constant input of any amplitude. Notably, the reduced-order system exactly describes the dynamics of a circuit forced by a constant generator and with a nonlinear memoryless element in place of the memelement. The relation between the proposed input–output approach and the available state space ones (e.g. Flux-Charge Analysis Method (FCAM)) is also addressed. The main result is that explicit expressions of the invariant manifolds can be directly obtained in the voltage–current state space. Finally, it is shown how the approach also applies to circuits which contain forcing generators. It is believed that the proposed input–output approach can be a useful alternative to state space methods for studying multistability and control issues.

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Unravelling the dynamical richness of 3D canonical memristor oscillators

Cited by 10 publications

References 11 publications

Circuits with a mem-element: invariant manifolds control via pulse programmed sources

Circuits with a mem-element: invariant manifolds control via pulse programmed sources

Functional Capabilities of Coupled Memristor-Based Reactance-Less Oscillators

Input–Output Characterization of the Dynamical Properties of Circuits with a Memelement

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