Fractional-order simplest memristor-based chaotic circuit with new derivative

Ruan, Jingya; Sun, Kehui; Mou, Jun; He, Shaobo; Zhang, Limin

doi:10.1140/epjp/i2018-11828-0

Cited by 104 publications

(35 citation statements)

References 22 publications

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“…He et al [29] firstly solved the nonlinear CF equations by the conformable Adomian decomposition method (CADM) and found chaos in the CF simplified Lorenz system. Later, Ruan et al [30] investigated dynamics of a CF memristor system based on CADM, and rich dynamical behaviors were found. It shows that the CF nonlinear systems also generate chaos, and it is an interesting topic to explore complexity in these systems.…”

Section: Introductionmentioning

confidence: 99%

Chaos and Symbol Complexity in a Conformable Fractional‐Order Memcapacitor System

Banerjee

2018

Complexity

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Application of conformable fractional calculus in nonlinear dynamics is a new topic, and it has received increasing interests in recent years. In this paper, numerical solution of a conformable fractional nonlinear system is obtained based on the conformable differential transform method. Dynamics of a conformable fractional memcapacitor (CFM) system is analyzed by means of bifurcation diagram and Lyapunov characteristic exponents (LCEs). Rich dynamics is found, and coexisting attractors and transient state are observed. Symbol complexity of the CFM system is estimated by employing the symbolic entropy (SybEn) algorithm, symbolic spectral entropy (SybSEn) algorithm, and symbolic C 0 (SybC 0 ) algorithm. It shows that pseudorandom sequences generated by the system have high complexity and pass the rigorous NIST test. Results demonstrate that the conformable memcapacitor nonlinear system can also be a good model for real applications.

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Section: Introductionmentioning

confidence: 99%

Chaos and Symbol Complexity in a Conformable Fractional‐Order Memcapacitor System

Banerjee

2018

Complexity

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“…Boltzmann and Shannon were pioneers in defining entropy [33]. The famous definition of entropy can be evaluated using the mathematical expression given in (4), where ρ i is the probability of the i − th state.…”

Section: Entropy Analysis As An Early Warning Signalmentioning

confidence: 99%

“…Investigating chaotic flows is an important topic in nonlinear dynamics [1,2]. Many researches have been worked on the design of special chaotic systems [3][4][5]. This work helps researchers to reveal the mystery of chaotic dynamics [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Investigation of Early Warning Indexes in a Three-Dimensional Chaotic System with Zero Eigenvalues

Chen

Nazarimehr

Jafari

et al. 2020

Entropy

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A rare three-dimensional chaotic system with all eigenvalues equal to zero is proposed, and its dynamical properties are investigated. The chaotic system has one equilibrium point at the origin. Numerical analysis shows that the equilibrium point is unstable. Bifurcation analysis of the system shows various dynamics in a period-doubling route to chaos. We highlight that from the evaluation of the entropy, bifurcation points can be predicted by identifying early warning signals. In this manner, bifurcation points of the system are analyzed using Shannon and Kolmogorov-Sinai entropy. The results are compared with Lyapunov exponents.

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“…Wang et al [44] presented a novel memristive chaotic system with a line of equilibrium, and used the ADM algorithm for analysis and solution. Combining CFD with the ADM decomposition (CADM) algorithm has become a novel research direction [50]- [52] . At present, the references about CADM algorithm used to solve fractional chaotic systems is rarely reported.…”

Section: Introductionmentioning

confidence: 99%

A Fractional-Order Chaotic System With Infinite Attractor Coexistence and its DSP Implementation

Liu

Yan

et al. 2020

IEEE Access

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In this paper, the fractional calculus is introduced into a simplest memristive circuit to construct a new four-dimensional fractional-order chaotic system. Combining conformable differential definition and Adomian decomposition method (ADM) algorithm is used to solve the numerical solution of the system. The attractor coexistence of the fractional-order system is investigated from the attractor phase diagram, coexistence bifurcation model, coexistence Lyapunov exponent spectrum and attractor basin. In addition, the hardware circuit of the system is implemented on the DSP platform. The simulation results show that the fractional-order chaotic system exhibits rich dynamic characteristics. In particular, the initial value of the system could control the offset, amplitude and frequency of the attractor better, and increase the complexity and randomness of the chaotic sequences. The research provides theoretical basis and guidance for the applications of fractional-order chaotic system.

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Fractional-order simplest memristor-based chaotic circuit with new derivative

Cited by 104 publications

References 22 publications

Chaos and Symbol Complexity in a Conformable Fractional‐Order Memcapacitor System

Chaos and Symbol Complexity in a Conformable Fractional‐Order Memcapacitor System

Investigation of Early Warning Indexes in a Three-Dimensional Chaotic System with Zero Eigenvalues

A Fractional-Order Chaotic System With Infinite Attractor Coexistence and its DSP Implementation

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