Antimonotonicity and multistability in a fractional order memristive chaotic oscillator

Chen, Chaoyang; Rajagopal, Karthikeyan; Hamarash, Ibrahim Ismael; Nazarimehr, Fahimeh; Alsaadi, Fawaz E.; Hayat, Tasawar

doi:10.1140/epjst/e2019-800222-7

Cited by 14 publications

(4 citation statements)

References 61 publications

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“…Multistability signifies the coexistence of attractors in a dynamical system for the same parameter values [33]. In recent years, there is great research on chaotic and hyperchaotic systems with multistability in the literature [34][35][36]. In this work, we show that the new hyperchaotic system exhibits multistability with three coexisting attractors for three different initial conditions.…”

Section: Introductionmentioning

confidence: 71%

Archives of Control Sciences

Vaidyanathan¹,

Irene²,

Aceng³

2020

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A new 4-D dynamical system with hyperchaos is reported in this work. It is shown that the proposed nonlinear dynamical system with hyperchaos has no equilibrium point. Hence, the new dynamical system exhibits hidden hyperchaotic attractor. An in-depth dynamic analysis of the new hyperchaotic system is carried out with bifurcation transition diagrams, multistability analysis, period-doubling bubbles and offset boosting analysis. Using Integral Sliding Mode Control (ISMC), global hyperchaos synchronization results of the new hyperchaotic system are described in detail. Furthermore, an electronic circuit realization of the new hyperchaotic system has been simulated in MultiSim software version 13.0 and the results of which are in good agreement with the numerical simulations using MATLAB.

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Section: Introductionmentioning

confidence: 71%

Archives of Control Sciences

Vaidyanathan¹,

Irene²,

Aceng³

2020

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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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“…Memristors, describing the missing relationship between charge and magnetic flux, are consider as the fourth type of electronic components in addition to resistors, capacitors and inductors [10]. Due to their strong nonlinearity, nanometer size, low power consumption and unique memory characteristics, memristors have been employed to construct chaotic systems [11,12], which can exhibit rich nonlinear dynamical behaviors, such as multi-scroll attractors [13,14], antimonotonicity [15], hidden extreme multistability [16,17] and hyperchaotic phenomena [18]. In addition, memristors play an important role in studying neuron dynamics.…”

Section: Introductionmentioning

confidence: 99%

Switchable memristor-based Hindmarsh-Rose neuron under electromagnetic radiation

Zhang,

2024

Nonlinear Dyn

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Memristors are prevalently used to simulate biological neuronal synapses due to their unique memductance plasticity and memory effects. A new switchable memristor, which can be configured as a nonvolatile discrete memristor, a nonvolatile continuum memristor or a volatile memristor by adjusting its internal parameter, is proposed to mimic the autapse of the Hindmarsh-Rose (HR) neuron. In the meantime, a flux-controlled memristor is introduced to simulate the effect of external electromagnetic radiation on the HR neuron, thus, an improved 4D HR neuron model without equilibrium points is developed in this study. The hidden firing activities related to the strength of autapse and the electromagnetic radiation intensity are revealed through phase diagrams, time series, bifurcation diagrams, Lyapunov exponent spectrums, and two-parameter dynamical maps. More interestingly, it is found that the memory attributes of memristive autapse play an important role in the firing activities of the neuron, which can induce the mutual transition among periodic spiking with different frequencies and chaotic firing. Additionally, the transition between periodic and chaotic firing induced by the initial value of the switchable memristor is also discovered when it is configured as three different types of memristors. Finally, a neuron circuit is designed with the current-mode devices to improve accuracy and reduce power consumption. The Multisim simulation results are provided to validate the correctness of the neuron model and the effectiveness of numerical analysis.

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Antimonotonicity and multistability in a fractional order memristive chaotic oscillator

Cited by 14 publications

References 61 publications

Archives of Control Sciences

Archives of Control Sciences

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

Switchable memristor-based Hindmarsh-Rose neuron under electromagnetic radiation

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