A physical memristor based Muthuswamy–Chua–Ginoux system

Abstract

In 1976, Leon Chua showed that a thermistor can be modeled as a memristive device. Starting from this statement we designed a circuit that has four circuit elements: a linear passive inductor, a linear passive capacitor, a nonlinear resistor and a thermistor, that is, a nonlinear “locally active” memristor. Thus, the purpose of this work was to use a physical memristor, the thermistor, in a Muthuswamy–Chua chaotic system (circuit) instead of memristor emulators. Such circuit has been modeled by a new three-dimensional autonomous dynamical system exhibiting very particular properties such as the transition from torus breakdown to chaos. Then, mathematical analysis and detailed numerical investigations have enabled to establish that such a transition corresponds to the so-called route to Shilnikov spiral chaos but gives rise to a “double spiral attractor”.

Oscillatory Circuits With a Real Non-Volatile Stanford Memristor Model

“…Moreover, it can be shown that for all g satisfying ( 11) the EP at the origin has unique unstable eigenvalue (see Appendix). This implies that for each fixed gap g ∈ (g a , g b ), and hence for the value of G a given by (10), there exists a range of g defined by condition (11) where SMCC possesses three EPs and the EP at the origin has a unique unstable eigenvalue. It is worth to remark that this scenario is quite similar to that displayed by the double-scroll family [44].…”

“…In the volatile case, to obtain oscillations, a passive memristor with an S-type locally active quasi-static i − v characteristic is used. As in a typical Hanson-Pearson oscillator, the memristor is biased via a suitable network in the locally-active region, i.e., in a branch of the characteristic with a negative differential resistance (NDR) [5], [6], [11], [12], [33]. It is worth to remark that NDR is observed in thermistors and other specific types of passive nanoscale devices, as NbO x , VO 2 , and TaO x devices [34].…”

A S-Type Bistable Locally-Active Memristor and Its Application in Oscillator Circuit

“…As a nonlinear locally-active device, S-type LAM is conceptually simple for building oscillating circuit without pure negative resistor, and the local active region renders the oscillating system capable to amplify extermely small fluctuation in energy. Therefore, S-type LAM is preferred over other memristor in the design of chaotic oscillator [35][36][37]. In Ref [30], Wang designed a S-type LAM-based chaotic oscillator by using a resistor, a capacitor and an inductor.…”

A Dynamic AES Encryption Based on Memristive Chaos Neural Network

“…14 There is also a lot of research on building chaotic systems and neural networks based on memristors. [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] For example, in 2008, it was derived that several nonlinear oscillators from Chua's oscillators by replacing Chua's diodes with memristors. 15 In 2012, delayed switching effect was used to control the switching of a memristor synapse between two neurons.…”

“…25 A physical memristor based on the Muthuswamy-Chua chaotic system (circuit) was provided. 27 In this paper, based on the memristor-based transient chaotic neural network (MTCNN), 31 the chaotic state for a long time is realized by the MTCNN. By MTCNN, AES initial key is dynamically generated to realize "one time one secret."…”