Simple Chaotic Circuit Research Articles

Strange Fractal Attractors and Optimal Chaos of Memristor–Memcapacitor via Non-local Differentials

The multi-dimensional electronic devices are so called memory circuit elements (memristor or memcapacitor); such memory circuit elements usually rely on previous applied voltage, current, flux or charge based on memory capability with their resistance, capacitance or inductance. In view of above fact, this manuscript investigates the non-integer modeling of memristor–memcapacitor in discrete-time domain through non-singular kernels of fractal fractional differentials and integrals operators. The governing equations of memristor–memcapacitor have been developed for the sake of the dynamical characteristics of simple chaotic circuit. The fractal fractional differentials and integrals operators have been invoked for non-integer modeling of memristor–memcapacitor that can exhibit a combination of dynamical chaotic phenomena. The numerical schemes, numerical simulations, stability analysis and equilibrium points have been highlighted in detail. The comparative chaotic graphs have been discussed in three ways (i) by keeping fractal component fixed and varying fractional component distinctly, (ii) by keeping fractional component fixed and varying fractal component distinctly and (iii) by varying both fractal component and fractional component distinctly. Our results suggest that fractal-fractional model of memristor–memcapacitor retains the memory characteristics.

Implementation of the Simple Hyperchaotic Memristor Circuit with Attractor Evolution and Large-Scale Parameter Permission

A novel, simple, four-dimensional hyperchaotic memristor circuit consisting of two capacitors, an inductor and a magnetically controlled memristor is designed. Three parameters (a, b, c) are especially set as the research objects of the model through numerical simulation. It is found that the circuit not only exhibits a rich attractor evolution phenomenon, but also has large-scale parameter permission. At the same time, the spectral entropy complexity of the circuit is analyzed, and it is confirmed that the circuit contains a significant amount of dynamical behavior. By setting the internal parameters of the circuit to remain constant, a number of coexisting attractors are found under symmetric initial conditions. Then, the results of the attractor basin further confirm the coexisting attractor behavior and multiple stability. Finally, the simple memristor chaotic circuit is designed by the time-domain method with FPGA technology and the experimental results have the same phase trajectory as the numerical calculation results. Hyperchaos and broad parameter selection mean that the simple memristor model has more complex dynamic behavior, which can be widely used in the future, in areas such as secure communication, intelligent control and memory storage.

A new 4D Memristor chaotic system: Analysis and implementation

In this paper, a new chaotic memristor system is developed based on a well-known nonlinear circuit. By replacing the nonlinear positive conductance of Shinriki's circuit with a memristor emulator, the new simple chaotic circuit can reduce the number of active elements and reduce power consumption. An analysis of equilibria and stability, dissipative properties, Lyapunov exponents, Kaplan-Yorke dimensions, and bifurcation diagrams is presented as well as numerical simulation of the new memristor chaotic system. As a final step, the electronic circuit is designed using Multisim software, which is complemented by a physical realization to demonstrate the feasibility of the chaotic system.

A unity‐gain approach to a simple FDNR‐based chaotic jerk oscillator

A unity-gain approach is proposed for a simple chaotic jerk oscillator based on frequency-dependent negative resistance. Both unity-gain and frequency-dependent negative resistance techniques are demonstrated together, for the first time, for a simple chaotic jerk circuit. The oscillator is attractive due to the use of a grounded diode and circuit simplicity of only seven electronic components, only one of which is an active device. The simplicity results in fewer components of both active and passive devices compared to existing frequency-dependent negative resistance-based chaotic circuits. The maximised value of the largest Lyapunov exponent is relatively high at 14.62.

A simple chaotic circuit based on memristor and its analyzation of bifurcation

A simple chaotic circuit based on memristor and its analyzation of bifurcation

Coexistence of Multiple Attractors in a Novel Simple Jerk Chaotic Circuit With CFOAs Implementation

A novel, simple Jerk chaotic circuit with three current feedback operational amplifiers included (CFOA-JCC) is proposed, which has a simpler circuit structure, fewer components, but higher frequency characteristics. The dynamic behaviors of CFOA-JCC are analyzed, including equilibrium, stability, Lyapunov exponent, bifurcation diagram, offset boosting, and phase diagram. Furthermore, the frequency spectrum characteristic of the ordinary op-amps Jerk chaotic circuit was compared with CFOA-JCC under the same circuit parameters, and the chaotic attractor frequency of CFOA-JCC can reach about 650 kHz, much better than that of ordinary op-amps (12 kHz). Numerical simulation shows that CFOA-JCC has coexisting attractors, verified by hardware circuit experiments.

A new simple chaotic circuit based on memristor and meminductor

A new simple chaotic circuit based on memristor and meminductor

A memristive RLC oscillator dynamics applied to image encryption

One of the major challenges in chaos dynamics is the design of simple and realisable electronic circuits capable of complex dynamic behaviours. Our contribution studies the dynamics and implementation of a simple chaotic memristive RLC oscillator circuit of jerky type as well as its application in designing image cryptosystem. The proposed circuit consists of an operational amplifier and an RLC network, comprising a resistor, an inductor, and two capacitors. Considering the crucial role of symmetry in physical, chemical, biological, and mechanical systems, a voltage control memristor emulator is employed to induce symmetry in the proposed circuit. For the dynamic analysis, fourth-order differential equation with exponential nonlinearities is used. Furthermore, standard analysis tools such as Lyapunov spectrum, bifurcation analysis, and phase space trajectories are employed. The phase space is magnetized using four symmetric attractors coexisting for the same set of parameters and different initial conditions indicate the symmetricity of the proposed system. Meanwhile, asymmetric attractor is capable of merging into one symmetric attractor through an attractor-merging bifurcation. Extensive experimental validations of these properties via PSPICE simulations and by using real electronic components are reported. Finally, the chaotic sequences emanating from the proposed oscillator are exploited to design an encryption algorithm that is subsequently validated via simulations and standard image security analysis with prominent outcomes in terms of very low encryption time (0.0746s for 128 × 128 colour image), mean entropy of 7.999 and mean NPCR of 99.62% just to name a few.

Design of a simple and low cost chaotic signal generation circuit for UWB applications

Design of a simple and low cost chaotic signal generation circuit for UWB applications

A simple chaotic circuit with magnetic flux-controlled memristor

A simple chaotic circuit with magnetic flux-controlled memristor

FPGA Implementation of a Novel Two-internal-State Memristor and its Two Component Chaotic Circuit

Objectives: To propose a second-order locally- active memristor, a twocomponent chaotic circuit resulting from this current-controlled generic memristor and an application in steganography. Methods/statistical analysis: Using a one-state-variable first-order memristor, a model is proposed which is obtained by modifying a locally-active memristor based on a current-controlled generic memristor. The model has two internal state variables: a voltage stored up in a capacitor and a current stored up in an inductor. With an external inductor, 3D-two-component chaotic circuit is developed. Numerical studies are made using MATLAB and confirmed by a field programmable gate array (FPGA) based hardware implementation. Findings: A two-state-variable based second-order memristor model is presented. The novel memristor configuration leads to the design of a simple two-component chaotic circuit. By investigating the characteristics of the memristor, it is shown that the memristor can be switched from a predominantly passive region to an active region with a wide locally-active region. An application in steganography helps to hide a secrete message inside an image. Application/improvements: The results obtained in this investigation will enrich the literature of memristive circuits, enhance the simplification of chaotic circuits and can be used to improve the memristive circuit based applications in many research domains such as secure information in telecommunications, Random Number Generation (RNG) and image encryption. Keywords: Memristor; Two component circuit; Chaos; Local activity; FPGA; Steganography

A Simple Parallel Chaotic Circuit Based on Memristor.

This paper reports a simple parallel chaotic circuit with only four circuit elements: a capacitor, an inductor, a thermistor, and a linear negative resistor. The proposed system was analyzed with MATLAB R2018 through some numerical methods, such as largest Lyapunov exponent spectrum (LLE), phase diagram, Poincaré map, dynamic map, and time-domain waveform. The results revealed 11 kinds of chaotic attractors, 4 kinds of periodic attractors, and some attractive characteristics (such as coexistence attractors and transient transition behaviors). In addition, spectral entropy and sample entropy are adopted to analyze the phenomenon of coexisting attractors. The theoretical analysis and numerical simulation demonstrate that the system has rich dynamic characteristics.

A tristable locally-active memristor and its complex dynamics

It has been well recognized that local activity is the origin of complex dynamics. Many important commercial applications would benefit from the locally-active memristors. To explore the locally active characteristics of memristors, a new tristable voltage-controlled locally-active memristor model is proposed based on Chua's unfolding theorem, which has three asymptotically equilibrium points and three locally-active regions. Non-volatility and the local activity of the memristor are demonstrated by POP (Power-Off Plot) and DC V - I plot. A small-signal equivalent circuit is established on a locally active operating point of the memristor to describe the characteristic of the memristor at the locally active region. Based on the admittance function Y ( i ω , V ) of the small-signal equivalent circuit, the parasitic capacitor and the oscillation frequency of the are determined. The parasitic oscillation circuit consisting of the memristor, a parasitic resistor and a parasitic capacitor is analyzed in detail by Hopf bifurcation theory and the pole diagram of the composite admittance function Y P ( s, Q ) of the parasitic oscillation circuit. Furthermore, by adding an inductor to the periodic parasitic circuit, we derive a simple chaotic circuit whose basic properties and coexisting dynamics are analyzed in detail. We concluded that the locally-active memristor provides the energy for the circuit to excite and maintain the periodic and chaotic oscillations.

Symmetrical Hopf-induced bursting and hyperchaos control in memristor-based circuit.

In this paper, a simple chaotic memristor-based circuit with an external stimulation is proposed, and its basic dynamic properties are demonstrated. When the external perturbation becomes time varying and its frequency is low enough, the system has two-time scales, which can be employed to explore the mechanisms of symmetrical Hopf-induced bursting oscillations and delay effects. Furthermore, delay-times on Hopf-induced bursting at different frequencies of the external stimulation are measured. The results show that the relationship between the delay-time and external frequency is subject to a power law. In order to enhance the existing chaos of the system, a 4D system is developed by adding a nonlinear state feedback controller, which shows hyperchaos under some suitable parameters. These two systems are implemented on Multisim and hardware platforms, and the corresponding experimental results verify the correctness of the numerical simulations.

Nonparametric Bifurcation and Anti-Control of Hyperchaos in a Memristor–Memcapacitor-Based Circuit

In this paper, a new memristor model and a new memcapacitor model are proposed. Based on the two models, a simple chaotic circuit is constructed. Due to the special characteristics of the memristor and memcapacitor, the proposed circuit has two-dimensional normally hyperbolic manifolds of equilibria, and nonparametric bifurcation can occur when the conditions supporting the normal hyperbolicity of such manifolds are not satisfied. By adding a nonlinear controller to the proposed circuit, an anti-controlled system is realized, which has hyperchaotic dynamic behaviors under some suitable control parameters. The stability of equilibrium points and dynamic properties of the original system and the anti-controlled system are explored by Lyapunov exponents, bifurcation diagrams and so on. Furthermore, the anti-controlled system is applied to design a random sequence generator on digital signal processor platform.

Experimental Validation of Multiple Attractors in a Simple Chaotic Circuit

In this paper, a simple jerk circuit that allows studying the dynamical behavior of a three-dimensional autonomous chaotic system with only one nonlinear term is further investigated by numerical simulations and experimental validation. Depending on a single tuning parameter, the chaotic system is theoretically studied using standard techniques such as equilibrium analysis, bifurcation diagram, and Lyapunov exponents. Subsequently, the circuit that models the chaotic system is implemented to validate theoretical prediction experimentally. Despite the simple structure of the jerk circuit, experimental study of Fourier spectra has shown that the jerk circuit displays complex dynamics characterized by periodic limit cycles and aperiodic strange attractors. In addition, the jerk circuit has exhibited a wide tuning range and experimental results have shown good agreement with theoretical prediction except for few cases where numerical simulation has failed to accurately match experimental results due to sensitivity to initial conditions which is a signature of chaotic nonlinear systems.

A Simple Autonomous Chaotic Circuit With Dead-Zone Nonlinearity

This brief proposes a simple autonomous chaotic circuit based on minimum discrete component implementation. First, the circuit employs only five discrete components, including one op-amp, one resistor, one inductor, and two capacitors. Second, the circuit equations have six linear terms and one invariant dead-zone nonlinearity. Third, the circuit is robust stand-alone and has the most common implementation. The comprehensive dynamical behaviors are analyzed by using two-parameter bifurcation diagrams, Lyapunov exponents, and phase plots. The experimental demonstrations validated the analyses.

A modified simple chaotic hyperjerk circuit: coexisting bubbles of bifurcation and mixed-mode bursting oscillations

Abstract A relatively simple chaotic hyperjerk circuit, which is the modified chaotic hyperjerk system [Dalkiran and Sprott, IJBC 2016] is proposed and investigated in this paper. Only one semiconductor diode modelled the nonlinear function capable of rich and complex dynamical behaviours of the system. We investigate a new kind of behaviours name “bubbles of bifurcation’’ (referred as BsB hereafter) observed here for the first time in the hyperjerk system. An interesting phenomenon of mixed-mode bursting oscillations (MMBOs) is also investigated. The complex dynamics of the novel oscillator (such as MMBOs, BsB, offset boosting and multistability) with respect to its parameters and initial conditions are uncovered using bifurcation diagrams, Lyapunov exponents (LE) and phase portraits. As another interesting property of this circuit, some parameter regions are determined for the existence of coexisting BsB and the coexistence of asymmetric mixed-mode bursting oscillations. Let us emphasized that the complex phenomena observed in this work is very rare in the literature and henceforth merit dissemination. Finally, a physical circuit is constructed to demonstrate some experimental observation of MMBOs.

A novel simple chaotic circuit based on memristor–memcapacitor

In this paper, we focus on a novel simple chaotic circuit with a memristor, a memcapacitor and a linear inductor in parallel. Then we establish the circuit’s dimensionless mathematical model. Nineteen types of different chaotic attractors are found in the circuit. The chaotic system’s equilibrium point and stability are analyzed by using the traditional dynamic analysis methods, and the dynamical behaviors with three varying parameters of this circuit are analyzed in detail. Furthermore, some special phenomena such as state transition, chaos degradation and the multiple coexisting attractors are discovered. Finally, we implement this circuit through the DSP platform and the results illustrate the validity of the theoretical analysis. Theoretical analysis and simulation results indicate that the simple chaotic circuit has very rich dynamical characteristics.

Complex dynamic behaviors in a new Colpitts oscillator topology based on a voltage comparator

Designing simple chaotic circuits with complex dynamic behaviors that can generate coexisting and hidden attractors has attracted much interest recently. In this paper, a new voltage-tunable Colpitts oscillator based on a two op-amps voltage comparator that can exhibit self-excited and hidden behaviors is proposed. Only the intrinsic nonlinearity of the voltage comparators is responsible for the complex dynamic behaviors of the proposed model and no additionally nonlinear devices are required. In this circuit, a reference voltage source acts as a reversible control parameter, since it can be varied indifferently in a positive or negative direction. Basic dynamic properties of the proposed Colpitts oscillator are investigated and the entire dynamics is analyzed numerically based on standard nonlinear analytical tools. Very rich dynamic behaviors and phenomena are reported, including; hidden attractors, period-doubling bifurcations, antimonotonicity, bursting oscillations, offset-boosting, and coexistence of multiple attractors for a set parameter values of the system. PSpice simulations are also carried out to validate theoretical and numerical results. Furthermore, the feasibility of the proposed Colpitts oscillator is confirmed through a practical realization which is in good agreement with the theoretical results.