A general configuration for nonlinear circuit employing current-controlled nonlinearity: Application in Chua’s circuit

Wang, Ning; Xu, Dan; Li, Ze; Xu, Quan

doi:10.1016/j.chaos.2023.114233

Cited by 11 publications

(4 citation statements)

References 35 publications

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“…Multistability [31][32][33][34][35][36][37][38][39][40][41][42] that is, two or more attractors coexist in a chaotic system with fixed parameters. In particular, when the coexisting attractors have the same topology but different locations in phase space, it is called homogeneous multistability.…”

Section: Spatially Distributed Multi-scroll Attractorsmentioning

confidence: 99%

A novel memristor Hopfield neural network with homogeneous coexisting multi-scroll attractors

Huang,

Chen,

Yang

et al. 2024

Phys. Scr.

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Compared to conventional single-scroll or double-scroll attractors, multi-scroll chaotic attractors possess wide potential for application due to their adjustability and complex topology. However, neural network models for generating multiple scrolls are often implemented using memristors with piecewise nonlinear functions. To further explore multi-scroll attractors with different working mechanisms,a unique memristor containing a group of hyperbolic tangent functions is designed and then applied in a three-dimensional Hopfield neural network (HNN). The proposed memristive Hopfield neural network (MHNN) has multi-scroll chaotic attractors, where the number and parity of the scrolls be changed by adjusting the control parameters of the memristor. The complex dynamical behaviors of MHNN are studied by utilizing diverse numerical modeling approaches like bifurcation diagrams, Lyapunov exponents and phase plot. In addition, the proposed MHNN also has a complicated offset boosting coexisting behavior. By selecting suitable parameters, multiple coexisting chaotic attractors could be obtained. Homogeneous coexisting multi-scroll attractors can be shifted in multiple directions including unidirectional, planar and spatial ones. Moreover, theoretically speaking, there could be an infinite number of coexisting attractors. Finally, experimental results are validated through numerical simulations and circuit experiments to confirm the feasibility of the proposed MHNN model.

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Section: Spatially Distributed Multi-scroll Attractorsmentioning

confidence: 99%

A novel memristor Hopfield neural network with homogeneous coexisting multi-scroll attractors

Huang,

Chen,

Yang

et al. 2024

Phys. Scr.

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“…As we know, study of mathematical models is the tool to understand characteristics of interesting problems [1][2][3][4][5][6]. One of the problems is to research by differential equations a mathematical model of hysteresis games [7,8].…”

Section: Mathematical Model Of Hysteresis Gamesmentioning

confidence: 99%

Mathematical model written by ordinary differential equations for hysteresis games

Hien,

Rahman

2024

IJITS

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In game theory, the hysteresis effect manifests itself in the fact that small differences in one or more parameters lead two systems to opposite stable equilibrium. The mathematical model (called smooth model) of hysteresis game writing by ordinary differential equations with the great parameter K is studied. Estimations of closeness of output functions for smooth and classical models through the continuity module of continuous input function are received. This error can be controlled by increasing the parameter K to a sufficiently large value. The result was conducted by studying of mathematical model and using programs Mathematica, Matlab or Maple. Experiments were carried out, and the obtained results were summarized and presented through evaluations and graphical interpretation.

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“…In the same year, a numerical calculation method was used to study the hidden Cai’s attractor, and detailed system construction and equilibrium calculation were carried out, resulting in the visualization of the local attraction domain of a new multi-fold hidden Cai’s attractor [ 24 ]. The following year, a memristor was proposed to replace the Zea diode in the Zea circuit, enriching the circuit structure of the Zea circuit family [ 25 ]. Wu et al [ 26 ] reported a new fractional-order Chua’s system with arctan function and an algorithm for determining the initial value of fractional-order hidden attractors.…”

Section: Introductionmentioning

confidence: 99%

Integrated Circuit of a Chua’s System Based on the Integral-Differential Nonlinear Resistance with Multi-Path Voltage-Controlled Oscillator

Duan,

Li,

et al. 2024

Micromachines

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In this paper, we present a fully integrated circuit without inductance implementing Chua’s chaotic system. The circuit described in this study utilizes the SMIC 180 nm CMOS process and incorporates a multi-path voltage-controlled oscillator (VCO). The integral-differential nonlinear resistance is utilized as a variable impedance component in the circuit, constructed using discrete devices from a microelectronics standpoint. Meanwhile, the utilization of a multi-path voltage-controlled oscillator ensures the provision of an adequate oscillation frequency and a stable waveform for the chaotic circuit. The analysis focuses on the intricate and dynamic behaviors exhibited by the chaotic microelectronic circuit. The experimental findings indicate that the oscillation frequency of the VCO can be adjusted within a range of 198 MHz to 320 MHz by manipulating the applied voltage from 0 V to 1.8 V. The circuit operates within a 1.8 V environment, and exhibits power consumption, gain–bandwidth product (GBW), area, and Lyapunov exponent values of 1.0782 mW, 4.43 GHz, 0.0165 mm2, and 0.6435∼1.0012, respectively. The aforementioned circuit design demonstrates the ability to generate chaotic behavior while also possessing the benefits of low power consumption, high frequency, and a compact size.

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A general configuration for nonlinear circuit employing current-controlled nonlinearity: Application in Chua’s circuit

Cited by 11 publications

References 35 publications

A novel memristor Hopfield neural network with homogeneous coexisting multi-scroll attractors

A novel memristor Hopfield neural network with homogeneous coexisting multi-scroll attractors

Mathematical model written by ordinary differential equations for hysteresis games

Integrated Circuit of a Chua’s System Based on the Integral-Differential Nonlinear Resistance with Multi-Path Voltage-Controlled Oscillator

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