Coexisting Attractors and Multistability in a Simple Memristive Wien-Bridge Chaotic Circuit

An evergreen scientific feature is the ability for scientific works to be reproduced. Since chaotic systems are so hard to understand analytically, numerical simulations assume a key role in their investigation. Such simulations have been considered as reproducible in many works. However, few studies have focused on the effects of the finite precision of computers on the simulation reproducibility of chaotic systems; moreover, code sharing and details on how to reproduce simulation results are not present in many investigations. In this work, a case study of reproducibility is presented in the simulation of a chaotic jerk circuit, using the software LTspice. We also employ the OSF platform to share the project associated with this paper. Tests performed with LTspice XVII on four different computers show the difficulties of simulation reproducibility by this software. We compare these results with experimental data using a normalised root mean square error in order to identify the computer with the highest prediction horizon. We also calculate the entropy of the signals to check differences among computer simulations and the practical experiment. The methodology developed is efficient in identifying the computer with better performance, which allows applying it to other cases in the literature. This investigation is fully described and available on the OSF platform.

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

A Note on the Reproducibility of Chaos Simulation

Nazare

Nepomuceno

Martins

et al. 2020

“…Some scholars have proposed a memristor that possesses a cubic nonlinear [37], a quadratic nonlinear characteristic, and some other improved models [16]. If these models are introduced into a specific circuit, the behavior of the circuit exhibits extremely complex nonlinear behavior, and even chaotic oscillations may occur [37][38][39][40]. The concept of memristors greatly enriches the circuit theory, causing the circuit to have more nonlinear dynamical behavior [32].…”

Section: Introductionmentioning

confidence: 99%

A High Spectral Entropy (SE) Memristive Hidden Chaotic System with Multi-Type Quasi-Periodic and its Circuit

Liu

Liang

et al. 2019

As a new type of nonlinear electronic component, a memristor can be used in a chaotic system to increase the complexity of the system. In this paper, a flux-controlled memristor is applied to an existing chaotic system, and a novel five-dimensional chaotic system with high complexity and hidden attractors is proposed. Analyzing the nonlinear characteristics of the system, we can find that the system has new chaotic attractors and many novel quasi-periodic limit cycles; the unique attractor structure of the Poincaré map also reflects the complexity and novelty of the hidden attractor for the system; the system has a very high complexity when measured through spectral entropy. In addition, under different initial conditions, the system exhibits the coexistence of chaotic attractors with different topologies, quasi-periodic limit cycles, and chaotic attractors. At the same time, an interesting transient chaos phenomenon, one kind of novel quasi-periodic, and weak chaotic hidden attractors are found. Finally, we realize the memristor model circuit and the proposed chaotic system use off-the-shelf electronic components. The experimental results of the circuit are consistent with the numerical simulation, which shows that the system is physically achievable and provides a new option for the application of memristive chaotic systems.

“…Reference [24] analyzed the complex dynamics in a memcapacitor-based circuit. Reference [25] proposed a memristive wien-bridge chaotic circuit, and the coexisting attractors and multi-stability of chaotic systems were analyzed in these two references. A new three-dimensional fractional order chaotic system without equilibrium was proposed in Reference [26], and a circuit implementation of the fractional order system was presented.…”

Section: Introductionmentioning

confidence: 99%

A Nonvolatile Fractional Order Memristor Model and Its Complex Dynamics

Wang

et al. 2019

It is found that the fractional order memristor model can better simulate the characteristics of memristors and that chaotic circuits based on fractional order memristors also exhibit abundant dynamic behavior. This paper proposes an active fractional order memristor model and analyzes the electrical characteristics of the memristor via Power-Off Plot and Dynamic Road Map. We find that the fractional order memristor has continually stable states and is therefore nonvolatile. We also show that the memristor can be switched from one stable state to another under the excitation of appropriate voltage pulse. The volt–ampere hysteretic curves, frequency characteristics, and active characteristics of integral order and fractional order memristors are compared and analyzed. Based on the fractional order memristor and fractional order capacitor and inductor, we construct a chaotic circuit, of which the dynamic characteristics with respect to memristor’s parameters, fractional order α, and initial values are analyzed. The chaotic circuit has an infinite number of equilibrium points with multi-stability and exhibits coexisting bifurcations and coexisting attractors. Finally, the fractional order memristor-based chaotic circuit is verified by circuit simulations and DSP experiments.