Fracmemristor chaotic oscillator with multistable and antimonotonicity properties

Lu, Hongqian; Petržela, Jiří; Götthans, Tomáš; Rajagopal, Karthikeyan; Jafari, Sajad; Hussain, Iqtadar

doi:10.1016/j.jare.2020.05.025

Cited by 13 publications

(5 citation statements)

References 29 publications

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“…It was well established in the literature that fractional-order analysis can very well match real-time systems [16][17][18][19]. It was shown that models with memory can be effectively modelled using fractional calculus and we could explore some complex dynamical properties when using fractional-order analysis [20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 94%

Network Dynamics of a Fractional-Order Phase-Locked Loop with Infinite Coexisting Attractors

Karthikeyan

2020

Complexity

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We have investigated a fractional-order phase-locked loop characterised by a third-order differential equation. The integer-order mathematical model of the phase-locked loop (PLL) is first converted to fractional order using the Caputo-Fabrizio method. The stability of the equilibrium points is discussed in detail in both parameter and fractional-order domain. The proposed fractional-order phase-locked loop (FOPLL) model shows multiple coexisting attractors which was not discussed in the earlier literature of PLL. The significance of these infinite coexisting attractors is that they exist in the operation region of the PLL between [−π,π] which increases the complexity of operation of the PLLs. Mainly when such FOPLLs are used in large-scale networks, the synchronisation of the FOPLLs becomes complicated and will result in unstable control conditions. Hence, studying the network dynamics of such FOPLLs is significant which motivates us to investigate the synchronisation phenomenon of the FOPLLs constructed in a square network. We could show that, because of the multiple coexisting attractors, the FOPLLs show various synchronisation phenomena, and more importantly in the chaotic region for lower fractional-order values, we could show that the FOPLLs are synchronised and this finding is very useful to completely analyse the FOPLL networks in high-frequency operations.

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Section: Introductionmentioning

confidence: 94%

Network Dynamics of a Fractional-Order Phase-Locked Loop with Infinite Coexisting Attractors

Karthikeyan

2020

Complexity

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“…When the same set of parameters takes diverse introductory values, two or more attractors show up, which are called coexisting attractors or different attractors, which could be an exceptional one-of-a-kind nonlinear phenomenon and is multistable (Lu et al , 2020). Fixing the memristor synaptic coupling strength k = 1.65, the initial values ( x 1 (0), x 2 (0), x 3 (0), x 4 (0)) = (1, 1, 1, 1) are kept constant.…”

Section: Dynamics Analysis Of Memristive Hopfield Neural Networkmentioning

confidence: 99%

Five-dimensional memristive Hopfield neural network dynamics analysis and its application in secure communication

Yin

Chen²,

Yu³

et al. 2022

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Purpose This study aims to improve the complexity of chaotic systems and the security accuracy of information encrypted transmission. Applying five-dimensional memristive Hopfield neural network (5D-HNN) to secure communication will greatly improve the confidentiality of signal transmission and greatly enhance the anticracking ability of the system. Design/methodology/approach Chaos masking: Chaos masking is the process of superimposing a message signal directly into a chaotic signal and masking the signal using the randomness of the chaotic output. Synchronous coupling: The coupled synchronization method first replicates the drive system to get the response system, and then adds the appropriate coupling term between the drive The synchronization error and the coupling term of the system will eventually converge to zero with time. The synchronization error and coupling term of the system will eventually converge to zero over time. Findings A 5D memristive neural network is obtained based on the original four-dimensional memristive neural network through the feedback control method. The system has five equations and contains infinite balance points. Compared with other systems, the 5D-HNN has rich dynamic behaviors, and the most unique feature is that it has multistable characteristics. First, its dissipation property, equilibrium point stability, bifurcation graph and Lyapunov exponent spectrum are analyzed to verify its chaotic state, and the system characteristics are more complex. Different dynamic characteristics can be obtained by adjusting the parameter k. Originality/value A new 5D memristive HNN is proposed and used in the secure communication

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“…In addition to the discovery of a new 4D system, many studies have been carried out to obtain 4D chaotic or hyperchaotic system from 3D chaotic system with various methods (Chen et al, 2006;Jia, 2007). Hence, they have been used for many applications of chaos theory in different fields of engineering and science like ecology (Stone and He, 2007), biology (Itik and Banks, 2010), oscillators (Lu et al, 2020), electrical circuits (Chen et al, 2008;Faradja and Qi, 2020) and so on.…”

Section: Introductionmentioning

confidence: 99%

“…So, chaos control has paid attention with the goal of the stabilization on chaotic systems. In addition to chaos control, chaos synchronization has become one of the important topics in science and engineering for several researchers owing to potential applications of it in many areas such as secure communications (Hu and Chan, 2018), oscillators (Lu et al, 2020) and so on.…”

Section: Introductionmentioning

confidence: 99%

A new hyperchaotic system from T chaotic system: dynamical analysis, circuit implementation, control and synchronization

Emiroğlu

Akgül

Adıyaman

et al. 2021

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Purpose The purpose of this paper is to develop new four-dimensional (4D) hyperchaotic system by adding another state variable and linear controller to three-dimensional T chaotic dynamical systems. Its dynamical analyses, circuit experiment, control and synchronization applications are presented. Design/methodology/approach A new 4D hyperchaotic attractor is achieved through a simulation, circuit experiment and mathematical analysis by obtaining the Lyapunov exponent spectrum, equilibrium, bifurcation, Poincaré maps and power spectrum. Moreover, hardware experimental measurements are performed and obtained results well validate the numerical simulations. Also, the passive control method is presented to make the new 4D hyperchaotic system stable at the zero equilibrium and synchronize the two identical new 4D hyperchaotic system with different initial conditions. Findings The passive controllers can stabilize the new 4D chaotic system around equilibrium point and provide the synchronization of new 4D chaotic systems with different initial conditions. The findings from Matlab simulations, circuit design simulations in computer and physical circuit experiment are consistent with each other in terms of comparison. Originality/value The 4D hyperchaotic system is presented, and dynamical analysis and numerical simulation of the new hyperchaotic system were firstly carried out. The circuit of new 4D hyperchaotic system is realized, and control and synchronization applications are performed.

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Fracmemristor chaotic oscillator with multistable and antimonotonicity properties

Abstract: Graphical abstract

Cited by 13 publications

References 29 publications

Network Dynamics of a Fractional-Order Phase-Locked Loop with Infinite Coexisting Attractors

Network Dynamics of a Fractional-Order Phase-Locked Loop with Infinite Coexisting Attractors

Five-dimensional memristive Hopfield neural network dynamics analysis and its application in secure communication

A new hyperchaotic system from T chaotic system: dynamical analysis, circuit implementation, control and synchronization

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