Dynamical analysis and FPGA implementation of a chaotic oscillator with fractional-order memristor components

Rajagopal, Karthikeyan; Srinivasan, Ashokkumar

doi:10.1007/s11071-017-3960-9

Cited by 53 publications

(16 citation statements)

References 82 publications

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“…Most recently, eight layers of monolithically integrated Ta/HafO 2 memristive arrays were reported for a 3D convolutional neural network in applications of edge detection in video processing (Lin et al, 2020). These memristive devices attract wide attention and offer promising opportunities for emerging applications (Du et al, 2021) in highly efficient reconfigurable logic implementations (Tan et al, 2017;Xu N. et al, 2018;Luo et al, 2021), low-cost hardware security primitives (Mazady et al, 2015;Gao et al, 2018;Du et al, 2019) and chaotic oscillators (Li et al, 2018;Rajagopal et al, 2018;Singh et al, 2019). Especially, a memristive device intrinsically provides electrically tunable conductance, i.e., it enables updating of its conductance (artificial synaptic weight), upon electrical stimuli (neuronal activity), and demonstrates stable resistive states within its dynamic range (analog behavior) (Zhang et al, 2019;Huang et al, 2021).…”

Section: Introductionmentioning

confidence: 99%

Synaptic Plasticity in Memristive Artificial Synapses and Their Robustness Against Noisy Inputs

Zhao

Chen

et al. 2021

Front. Neurosci.

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Emerging brain-inspired neuromorphic computing paradigms require devices that can emulate the complete functionality of biological synapses upon different neuronal activities in order to process big data flows in an efficient and cognitive manner while being robust against any noisy input. The memristive device has been proposed as a promising candidate for emulating artificial synapses due to their complex multilevel and dynamical plastic behaviors. In this work, we exploit ultrastable analog BiFeO3 (BFO)-based memristive devices for experimentally demonstrating that BFO artificial synapses support various long-term plastic functions, i.e., spike timing-dependent plasticity (STDP), cycle number-dependent plasticity (CNDP), and spiking rate-dependent plasticity (SRDP). The study on the impact of electrical stimuli in terms of pulse width and amplitude on STDP behaviors shows that their learning windows possess a wide range of timescale configurability, which can be a function of applied waveform. Moreover, beyond SRDP, the systematical and comparative study on generalized frequency-dependent plasticity (FDP) is carried out, which reveals for the first time that the ratio modulation between pulse width and pulse interval time within one spike cycle can result in both synaptic potentiation and depression effect within the same firing frequency. The impact of intrinsic neuronal noise on the STDP function of a single BFO artificial synapse can be neglected because thermal noise is two orders of magnitude smaller than the writing voltage and because the cycle-to-cycle variation of the current–voltage characteristics of a single BFO artificial synapses is small. However, extrinsic voltage fluctuations, e.g., in neural networks, cause a noisy input into the artificial synapses of the neural network. Here, the impact of extrinsic neuronal noise on the STDP function of a single BFO artificial synapse is analyzed in order to understand the robustness of plastic behavior in memristive artificial synapses against extrinsic noisy input.

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Section: Introductionmentioning

confidence: 99%

Synaptic Plasticity in Memristive Artificial Synapses and Their Robustness Against Noisy Inputs

Zhao

Chen

et al. 2021

Front. Neurosci.

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“…Numerical methods to simulate fractional-order nonlinear system have been proposed in [41], and Matlab solutions for fractional-order chaotic systems have been discussed in [42]. Field Programmable Gate Array (FPGA) implementation of chaotic systems has been a hot topic recently [43][44][45].…”

Section: Introductionmentioning

confidence: 99%

“…Here we investigate a fractional order memristor (called Fracmemristor) which is derived by replacing the integer order differentiator to a fractional order differentiator. The fractional order memristor [44] is defined as,…”

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confidence: 99%

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Chaotic Dynamics of Modified Wien Bridge Oscillator with Fractional Order Memristor

Karthikeyan¹,

Duraisamy²,

Nazarimehr³

et al. 2019

RADIOENGINEERING

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In this paper a modified third order Wien bridge oscillator with fractional order memristor is proposed. Various dynamical properties of the proposed oscillator are investigated such as equilibrium points, Eigenvalues, Lyapunov exponents and bifurcation diagrams. The Lyapunov spectrum of the system for various values of fractional order is derived. Using forward and backward continuation methods of plotting bifurcation diagram, the multistability of the oscillator is investigated. The proposed oscillator is realized using Field Programmable Gate Arrays and the experiment is conducted using hardwaresoftware co-simulation.

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“…It has essentially the same mathematical principles as the memory characteristics of memory circuit elements. It is feasible to introduce fractional calculus theory into the dynamic behavior analysis and application of memory circuit elements [25,26]. The relationship between fractional calculus and the behavior of memory system is proposed in [17], and it is pointed out that the memristor can be extended to fractional-order one.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Behaviors Analysis of a Chaotic Circuit Based on a Novel Fractional‐Order Generalized Memristor

Yang

Cheng

et al. 2019

Complexity

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In this paper, a fractional-order chaotic circuit based on a novel fractional-order generalized memristor is proposed. It is proved that the circuit based on the diode bridge cascaded with fractional-order inductor has volt-ampere characteristics of pinched hysteresis loop. Then the mathematical model of the fractional-order memristor chaotic circuit is obtained. The impact of the order and system parameters on the dynamic behaviors of the chaotic circuit is studied by phase trajectory, Poincaré Section, and bifurcation diagram method. The order, as an important parameter, can increase the degree of freedom of the system. With the change of the order and parameters, the circuit will exhibit abundant dynamic behaviors such as coexisting upper and lower limit cycle, single scroll chaotic attractors, and double scroll chaotic attractors under different initial conditions. And the system exhibits antimonotonic behavior of antiperiodic bifurcation with the change of system parameters. The equivalent circuit simulations are designed to verify the results of the theoretical analysis and numerical simulation.

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Dynamical analysis and FPGA implementation of a chaotic oscillator with fractional-order memristor components

Cited by 53 publications

References 82 publications

Synaptic Plasticity in Memristive Artificial Synapses and Their Robustness Against Noisy Inputs

Synaptic Plasticity in Memristive Artificial Synapses and Their Robustness Against Noisy Inputs

Chaotic Dynamics of Modified Wien Bridge Oscillator with Fractional Order Memristor

Dynamic Behaviors Analysis of a Chaotic Circuit Based on a Novel Fractional‐Order Generalized Memristor

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