Effects of Variable-Order Passive Circuit Element in Chua Circuit

2019 ◽  
Vol 39 (5) ◽  
pp. 2293-2306
Author(s):  
Özkan Atan
Keyword(s):  
Variable Order ◽  
Circuit Element ◽  
Chua Circuit ◽  
Passive Circuit

Impulsive Control and Synchronization of Memristor-Based Chaotic Circuits

2014 ◽  
Vol 24 (12) ◽  
pp. 1450162 ◽  
Author(s):  
Shiju Yang ◽  
Chuandong Li ◽  
Tingwen Huang
Keyword(s):  
Chaotic System ◽  
Impulsive Control ◽  
Chaotic Behavior ◽  
Memory Function ◽  
Sufficient Conditions ◽  
Impulsive System ◽  
Circuit Element ◽  
Chaotic Circuits ◽  
Control And Synchronization ◽  
Passive Circuit

The memristor is a novel nonlinear passive circuit element which has the memory function, and the circuits based on the memristors might exhibit chaotic behavior. In this paper, we revisit a memristor-based chaotic circuit, and then investigate its stabilization and synchronization via impulsive control. By impulsive system theory, some sufficient conditions for the stabilization and synchronization of the memristor-based chaotic system are established. Moreover, an estimation of the upper bound of the impulse interval is proposed under the condition that the parameters of the chaotic system and the impulsive control law are well defined. To show the effectiveness of the theoretical results, numerical simulations are also presented.

scholarly journals A Chaotic Attractor in Delayed Memristive System

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Lidan Wang ◽  
Shukai Duan
Keyword(s):  
Chaotic Attractor ◽  
Nonlinear Function ◽  
Successful Development ◽  
Circuit Element ◽  
Nonlinear Characteristics ◽  
Theoretical Design ◽  
Memristive System ◽  
Delayed System ◽  
Passive Circuit ◽  
First Time

Over the last three decades, theoretical design and circuitry implementation of various chaotic generators by simple electronic circuits have been a key subject of nonlinear science. In 2008, the successful development of memristor brings new activity for this research. Memristor is a new nanometre-scale passive circuit element, which possesses memory and nonlinear characteristics. This makes it have a unique charm to attract many researchers’ interests. In this paper, memristor, for the first time, is introduced in a delayed system to design a signal generator to produce chaotic behaviour. By replacing the nonlinear function with memristors in parallel, the memristor oscillator exhibits a chaotic attractor. The simulated results demonstrate that the performance is well predicted by the mathematical analysis and supports the viability of the design.

scholarly journals Memfractance: A Mathematical Paradigm for Circuit Elements with Memory

2014 ◽  
Vol 24 (09) ◽  
pp. 1430023 ◽  
Author(s):  
Mohammed-Salah Abdelouahab ◽  
René Lozi ◽  
Leon Chua
Keyword(s):  
Fractional Calculus ◽  
Nanoscale Device ◽  
Circuit Element ◽  
Ohm’S Law ◽  
History Of ◽  
Memristive Systems ◽  
Ohm's Law ◽  
Inductive Elements ◽  
Passive Circuit ◽  
With Memory

Memristor, the missing fourth passive circuit element predicted forty years ago by Chua was recognized as a nanoscale device in 2008 by researchers of a H. P. Laboratory. Recently the notion of memristive systems was extended to capacitive and inductive elements, namely, memcapacitor and meminductor whose properties depend on the state and history of the system. In this paper, we use fractional calculus to generalize and provide a mathematical paradigm for describing the behavior of such elements with memory. In this framework, we extend Ohm's law to the generalized Ohm's law and prove it.

scholarly journals Memristor Equations: Incomplete Physics and Undefined Passivity/Activity

2017 ◽  
Vol 16 (04) ◽  
pp. 1771001 ◽  
Author(s):  
Kyle M. Sundqvist ◽  
David K. Ferry ◽  
Laszlo B. Kish
Keyword(s):  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Passive System ◽  
Circuit Element ◽  
Fundamental Physics ◽  
Seminal Paper ◽  
Passive Device ◽  
Fluctuation Dissipation ◽  
Passive Circuit ◽  
Fundamental Physical

In his seminal paper, Chua presented a fundamental physical claim by introducing the memristor, “The missing circuit element”. The memristor equations were originally supposed to represent a passive circuit element because, with active circuitry, arbitrary elements can be realized without limitations. Therefore, if the memristor equations do not guarantee that the circuit element can be realized by a passive system, the fundamental physics claims about the memristor as “missing circuit element” loses all its weight. The question of passivity/activity belongs to physics thus we incorporate thermodynamics into the study of this problem. We show that the memristor equations are physically incomplete regarding the problem of passivity/activity. As a consequence, the claim that the present memristor functions describe a passive device lead to unphysical results, such as violating the Second Law of thermodynamics, in infinitely large number of cases. The seminal memristor equations cannot introduce a new physical circuit element without making the model more physical such as providing the Fluctuation–Dissipation Theory of memristors.

Memristor Based van der Pol Oscillation Circuit

2014 ◽  
Vol 24 (12) ◽  
pp. 1450154 ◽  
Author(s):  
Yimin Lu ◽  
Xianfeng Huang ◽  
Shaobin He ◽  
Dongdong Wang ◽  
Bo Zhang
Keyword(s):  
Analog Circuit ◽  
Van Der Pol Oscillator ◽  
Van Der Pol ◽  
Circuit Element ◽  
Nonlinear Properties ◽  
Oscillation Circuit ◽  
Excited Oscillation ◽  
Exciting Source ◽  
The Stability ◽  
Passive Circuit

The memristor is referred to as the fourth fundamental passive circuit element of which inherent nonlinear properties offer to construct the chaos circuits. In this paper, a flux-controlled memristor circuit is developed, and then a van der Pol oscillator is implemented based on this new memristor circuit. The stability of the circuit, the occurring conditions of Hopf bifurcation and limit circle of the self-excited oscillation are analyzed; meanwhile, under the condition of the circuit with an external exciting source, the circuit exhibits a complicated nonlinear dynamic behavior, and chaos occurs within a certain parameter set. The memristor based van der Pol oscillator, furthermore, has been created by an analog circuit utilizing active elements, and there is a good agreement between the circuit responses and numerical simulations of the van der Pol equation. In the consequence, a new approach has been proposed to generate chaos within a nonautonomous circuit system.

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