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”.
Highlights
Michael Faraday (1791-1867) is generally well known for his contributions to the study of electromagnetism and electrochemistry
Mathematical analysis and detailed numerical investigations have enabled to establish that such a transition corresponds to the route to Shilnikov spiral chaos originally described by L.P
S hilnikov[20] and Shilnikov et al 27) but gives rise to a “double spiral attractor”. Another scenario leading to spiral chaos, as well as double spiral chaos, and triple spiral chaos has been proposed by B. Deng[18] twenty-five years ago
Summary
Jean‐Marc Ginoux1*, Bharathwaj Muthuswamy[2], Riccardo Meucci[3,4], Stefano Euzzor[3], Angelo Di Garbo5 & Kaliyaperumal Ganesan[6]. In 1976, five years after Chua[4] had postulated a missing circuit element that he called memristor, Chua published a paper with Sun Kang[5] in which they recalled that: Thermistors have been widely used as a linear resistor whose resistance varies with the ambient temperature. Their work triggered a renewed interest in memristors and their applications across widely different fields which has consistently grown since During these last five years, Rajamani et al.[7] analyzed an electronic oscillator circuit designed by connecting an inductor in series with a “locally-active” Positive Temperature Coefficient (PTC) memristor and a battery. The aim of this work is to investigate a circuit consisting of a linear passive capacitor, a linear passive inductor, a nonlinear resistor and a Negative Temperature Coefficient thermistor, that is, a nonlinear “locally active” volatile memristor. The memristive model for thermistors is well established and the device can be bought as an off-the-shelf component with a variety of parameter o ptions[13]
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