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

Innocenti, Gabbriella; Marco, Mauro Di; Tesi, A.; Forti, Mauro

doi:10.1142/s0218127420501102

Cited by 8 publications

(6 citation statements)

References 57 publications

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“…Memristor circuit capable to reproduce the dynamics of the FitzHugh-Nagumo neuron model: the passive two-terminal elementi L (blue box) with Rm, Lm, and Cm as in (32), and the flux-controlled memristor (red box) with the nonlinear characteristic (30).…”

Section: A the Case Of Singular Matrix Amentioning

confidence: 99%

“…For ideal memristors, it has been shown that multistability is connected to the fact that the state space of memristor circuits is decomposed into a continuum of invariant manifolds [11]. Since on each manifold either convergent or oscillatory and more complex behaviors can be displayed, the coexistence of infinitely many attractors is a natural scenario for circuits with ideal memristors [26], [27], [28], [29], [30], [31], [32]. Moreover, each invariant manifold can be uniquely identified via some parameters referred to as manifold indexes, whose values depend on the initial conditions of the circuit.…”

Section: Introductionmentioning

confidence: 99%

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Embedding the Dynamics of Forced Nonlinear Systems in Multistable Memristor Circuits

Innocenti

Tesi

Marco

et al. 2022

IEEE J. Emerg. Sel. Topics Circuits Syst.

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A well-known feature of memristors is that they makes the circuit dynamics much richer than that generated by classical RLC circuits containing nonlinear resistors. In the case of circuits with ideal memristors, such a multistability property, i.e., the coexistence of many different attractors for a fixed set of parameters, is connected to the fact that the state space is composed of a continuum of invariant manifolds where either convergent or oscillatory and more complex behaviors can be displayed. In this paper we investigate the possibility of designing memristor circuits where known attractors are embedded into the invariant manifolds. We consider a class of forced nonlinear systems containing several systems which are known to display complex dynamics, and we investigate under which conditions the dynamics of any given system of the class can be reproduced by a circuit composed of a two-terminal (one port) element connected to a flux-controlled memristor. It is shown that an input-less circuit is capable to replicate the system attractors generated by varying the constant forcing input, once the parameters of the two-terminal element and the memristor nonlinear characteristic are suitably selected. Indeed, there is a one-one correspondence between the dynamics generated by the nonlinear system for a constant value of the input and that displayed on one of the invariant manifolds of the input-less memristor circuit. Some extensions concerning the case of non-constant forcing terms and the use of charge-controlled memristors are also provided. The results are illustrated via FitzHugh-Nagumo model and Duffing oscillator.

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Section: A the Case Of Singular Matrix Amentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Embedding the Dynamics of Forced Nonlinear Systems in Multistable Memristor Circuits

Innocenti

Tesi

Marco

et al. 2022

IEEE J. Emerg. Sel. Topics Circuits Syst.

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“…Moreover, structural changes of the attractors are observed when the initial conditions are varied while keeping constant the values of the circuit parameters, a peculiar phenomenon which is referred to as bifurcations without parameters (Corinto and Forti, 2017 ; Di Marco et al, 2018 ; Innocenti et al, 2019b ). In particular, Di Marco et al ( 2018 ), Innocenti et al ( 2019b ) have employed techniques within the Harmonic Balance (HB) context for predicting limit cycles and their bifurcations by first showing that the dynamics of the memristor circuit admits an equivalent input-output representation, which has been recently extended also to circuits containing memory elements (Innocenti et al, 2020 ).…”

Section: Introductionmentioning

confidence: 99%

Memristor Circuits for Simulating Neuron Spiking and Burst Phenomena

et al. 2021

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Since the introduction of memristors, it has been widely recognized that they can be successfully employed as synapses in neuromorphic circuits. This paper focuses on showing that memristor circuits can be also used for mimicking some features of the dynamics exhibited by neurons in response to an external stimulus. The proposed approach relies on exploiting multistability of memristor circuits, i.e., the coexistence of infinitely many attractors, and employing a suitable pulse-programmed input for switching among the different attractors. Specifically, it is first shown that a circuit composed of a resistor, an inductor, a capacitor and an ideal charge-controlled memristor displays infinitely many stable equilibrium points and limit cycles, each one pertaining to a planar invariant manifold. Moreover, each limit cycle is approximated via a first-order periodic approximation analytically obtained via the Describing Function (DF) method, a well-known technique in the Harmonic Balance (HB) context. Then, it is shown that the memristor charge is capable to mimic some simplified models of the neuron response when an external independent pulse-programmed current source is introduced in the circuit. The memristor charge behavior is generated via the concatenation of convergent and oscillatory behaviors which are obtained by switching between equilibrium points and limit cycles via a properly designed pulse timing of the current source. The design procedure takes also into account some relationships between the pulse features and the circuit parameters which are derived exploiting the analytic approximation of the limit cycles obtained via the DF method.

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“…More recently, the flux-charge approach has been extended to much broader classes of circuits containing more than one memristor as well as memcapacitors and meminductors (see, e.g., [8,9,[36][37][38][39][40][41] and references therein). Finally, [42] provides a systematic input-output approach to characterize the dynamical properties of a class of circuits composed of a linear time-invariant two-terminal element coupled with one of the ideal mem-elements. Such an approach can be fruitfully used to predict limit cycles and their bifurcations via the Harmonic balance method (HBM) [43][44][45], as shown in [46,47].…”

Section: Introductionmentioning

confidence: 99%

“…Specifically, the linear two-terminal element can contain linear R, L, C components and ideal operational amplifiers, while the mem-element can be a flux-or charge-controlled memristor, a flux-or σ -controlled capacitor, a ρor charge-controlled inductor. Then, on the basis of the approach developed in [42], it is shown that each circuit of the class admits a suitable feedback system representation. Exploiting the structural properties of such a representation, Sect.…”

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

Cited by 8 publications

References 57 publications

Embedding the Dynamics of Forced Nonlinear Systems in Multistable Memristor Circuits

Embedding the Dynamics of Forced Nonlinear Systems in Multistable Memristor Circuits

Memristor Circuits for Simulating Neuron Spiking and Burst Phenomena

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

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