Computer assisted proof of chaos in the Muthuswamy-Chua memristor circuit

Galias, Zbigniew

doi:10.1587/nolta.5.309

Cited by 3 publications

(7 citation statements)

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“…[31,40,45,51]), and on complicated behavior of Hénon, Rössler, and other dynamical systems (e.g. [9,10,46,48,49,50]).…”

Section: Computer Assisted Proofs In Dynamical Systemsmentioning

confidence: 99%

On Computer-Assisted Proving The Existence Of Periodic And Bounded Orbits

Srzednicki

2015

Annales Mathematicae Silesianae

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We announce a new result on determining the Conley index of the Poincaré map for a time-periodic non-autonomous ordinary differential equation. The index is computed using some singular cycles related to an index pair of a small-step discretization of the equation. We indicate how the result can be applied to computer-assisted proofs of the existence of bounded and periodic solutions. We provide also some comments on computer-assisted proving in dynamics.

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“…[31,40,45,51]), and on complicated behavior of Hénon, Rössler, and other dynamical systems (e.g. [9,10,46,48,49,50]).…”

Section: Computer Assisted Proofs In Dynamical Systemsmentioning

confidence: 99%

On Computer-Assisted Proving The Existence Of Periodic And Bounded Orbits

Srzednicki

2015

Annales Mathematicae Silesianae

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“…The procedure for the rigorous evaluation of the return map P is written using the CAPD library [CAPD]. For details see [Galias, 2014].…”

Section: The Muthuswamy-chua Memristor Circuitmentioning

confidence: 99%

“…In [Galias, 2014], it has been shown that there exists complex symbolic dynamics defined on four quadrangles Q 1 , Q 2 , Q 3 , and Q 4 . The quadrangles and their images computed nonrigorously are shown in Fig.…”

Section: The Muthuswamy-chua Memristor Circuitmentioning

confidence: 99%

“…As an example of the applicability of this method, we study the existence of symbolic dynamics for a simple third-order memristor circuit [Muthuswamy & Chua, 2010]. In [Galias, 2014], it has been shown that the system is chaotic in the topological sense. More precisely, it was proved that symbolic dynamics defined on four symbols with the topological entropy H ≈ 0.3222 is embedded in the dynamics of the associated return map.…”

Section: Introductionmentioning

confidence: 99%

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Automatized Search for Complex Symbolic Dynamics with Applications in the Analysis of a Simple Memristor Circuit

Galias

2014

Int. J. Bifurcation Chaos

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An automatized method to search for complex symbolic dynamics is proposed. The method can be used to show that a given dynamical system is chaotic in the topological sense. Application of this method in the analysis of a third-order memristor circuit is presented. Several examples of symbolic dynamics are constructed. Positive lower bounds for the topological entropy of an associated return map are found showing that the system is chaotic in the topological sense.

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“…"resistor with memory") and "memristive circuits" became a popular research topic, e.g. [3][4][5][6] and references there. The original purpose of this specific circuit element is to connect electrical charge with magnetic flux, which is, as we stress after [1,5], outside the borders of the use of the resistive "characteristic" given by a single equality v = f(i), with a unique f(.…”

Section: Introductionmentioning

confidence: 99%

On the physical and circuit-theoretic significance of the Memristor

Gluskin

2014

Preprint

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It is noticed that the inductive and capacitive features of the memristor reflect (and are a quintessence of) such features of any resistor. The very presence in the resistive characteristic v = f(i) of the voltage and current state variables, associated, by their electrodynamics sense, with electrical and magnetic fields, forces any resister to cause to accumulate some magnetic and electrostatic fields and energies around itself, i.e. L and C elements are always present. From the circuit-theoretic point of view, the role of the memristor is seen, first of all, in the eliminating of the use of a unique v(i). This makes circuits with hysteretic characteristics relevant, and suggests that the concept of memristor should influence the basic (general) problem of definition of nonlinearity. Since memristor mainly originates from resistor, it was found methodologically necessary to overview some unusual cases of resistive circuits.

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Computer assisted proof of chaos in the Muthuswamy-Chua memristor circuit

Abstract: It is shown that the Muthuswamy Chua memristor circuit is chaotic in the topological sense. A rigorous analysis of the circuit is performed using interval analysis based tools.

Cited by 3 publications

References 20 publications

On Computer-Assisted Proving The Existence Of Periodic And Bounded Orbits

On Computer-Assisted Proving The Existence Of Periodic And Bounded Orbits

Automatized Search for Complex Symbolic Dynamics with Applications in the Analysis of a Simple Memristor Circuit

On the physical and circuit-theoretic significance of the Memristor

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