Article
Mathematics, Interdisciplinary Applications
Mo Chen, Ankai Wang, Chao Wang, Huagan Wu, Bocheng Bao
Summary: This paper proposes a DC-offset method for obtaining hidden dynamics in preexisting nonlinear circuits. An improved memristive Chua's circuit with hidden behaviors is constructed, and the hidden and asymmetric dynamical behaviors induced by the DC-offset are revealed and verified. The measurements of hidden and coexisting attractors with relatively small attraction basins are facilitated by a reconstituted model.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Engineering, Electrical & Electronic
Mengjie Hua, Huagan Wu, Quan Xu, Mo Chen, Bocheng Bao
Summary: This study introduces an asymmetric memristor emulator to simulate the asymmetric property of the pinched hysteresis loop in real memristors. By coupling the emulator with classical Chua's circuit, two asymmetric memristive Chua's circuits are proposed and analyzed for their stability and attractor characteristics through numerical simulations and hardware experiments.
INTERNATIONAL JOURNAL OF ELECTRONICS
(2021)
Article
Mathematics, Interdisciplinary Applications
Chunbo Xiu, Jingyao Fang, Yuxia Liu
Summary: A novel five-dimension memristive cellular neural network hyperchaotic system is designed to enrich the dynamic characteristics of CNN and reveal the influence of memristor nonlinearity. The effects of system parameters, initial values, and noise on the dynamic behavior are studied, providing criteria for parameter selection and verifying the physical realizability of chaotic characteristics. Additionally, a secure communication application example based on the hyperchaotic system is presented.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Engineering, Electrical & Electronic
Yi-Fei Pu, Bo Yu, Qiu-Yan He, Xiao Yuan
Summary: This paper proposes a chaotic circuit FMCC using fractional-order memristors. By replacing the diode in Chua's chaotic circuit with a fractional-order memristor and a negative resistor in parallel, the FMCC provides two extra degrees of freedom. Numerical simulations and hardware experiments demonstrate that the FMCC exhibits multistability, transient chaos, state transition phenomena, and has a fractional-order-sensitivity characteristic.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS
(2022)
Article
Neurosciences
Xiaoyan Fang, Yao Tan, Fengqing Zhang, Shukai Duan, Lidan Wang
Summary: The Resistors-Capacitor (RC) circuit and the Memristor-Capacitor (MC) circuit serve as circuit models of neuron cell membranes. The MC neuron circuit shows faster charging and discharging speed. Both circuits can generate action potentials and reproduce the nonlinear dynamic behavior of biological neurons.
FRONTIERS IN NEUROSCIENCE
(2022)
Article
Physics, Multidisciplinary
G. Sivaganesh, K. Srinivasan, A. Arulgnanam
Summary: This study develops explicit analytical solutions for higher-dimensional chaotic and hyperchaotic systems and investigates the dynamical behaviors of third-order and fourth-order nonlinear dissipative systems as well as their coupled dynamics. The analytical results are validated through experimental results.
PRAMANA-JOURNAL OF PHYSICS
(2022)
Article
Mathematics, Interdisciplinary Applications
Iacyel Gomes, Wojciech Korneta, Stavros G. Stavrinides, Rodrigo Picos, Leon O. Chua
Summary: This paper reports the observation of chaotic hysteresis in a Chua's electronic circuit driven by both a dc and a slow triangular voltage source. One and two hysteresis loops were observed in single and double scroll chaotic regimes, respectively. The results contribute to expanding our knowledge on unexplored dynamics of Chua's circuit and chaos control theory.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Multidisciplinary Sciences
Serhii Haliuk, Oleh Krulikovskyi, Dmytro Vovchuk, Fernando Corinto
Summary: This paper proposes an approach to generate pseudo-random sequences based on the discrete-time model of the simple memristive chaotic system. The method can obtain chaotic sequences that maintain the general properties of the original chaotic system. A criterion based on the binary sequence balance estimation is used to separate random and non-random parts of the chaotic time sequences. The method successfully passes statistical tests and has potential applications in encryption.
Article
Mathematics, Applied
Nadjet Boudjerida, Mohammed Salah Abdelouahab, Rene Lozi
Summary: A modified hyperchaotic memristor-based Chua's circuit and its generalized discrete model are presented in this paper. The dynamics of the continuous system are analyzed using various tools, including stability theory, phase portraits, Lyapunov exponents, and bifurcation diagrams. The study reveals that the proposed circuit model exhibits a line of equilibrium and demonstrates rich dynamics, such as the coexistence of regular and chaotic attractors, and mixed-mode oscillations. The dynamics of the generalized discrete version of the system are also explored, and a useful stability test is constructed to identify stable regions in three parameter planes using the Jury criterion. The presence of an exact periodic solution is numerically emphasized, and chaotic behavior is confirmed through the largest Lyapunov exponent and the 0-1 test.
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS
(2023)
Article
Mathematics, Interdisciplinary Applications
Qiang Lai, Zhijie Chen
Summary: The paper establishes a four-dimensional multi-scroll chaotic system by adding a flux-controlled non-volatile memristor to a simple three-dimensional chaotic system. The system is extended to generate grid-scroll chaotic attractors by replacing the linear term with a triangular wave function. The evolution of chaos is studied and the existence of coexisting attractors is observed. In addition, the proposed system can be controlled by adjusting the parameters and the circuit implementation results are consistent with numerical simulations.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Applied
Xiangxin Leng, Bowen Tian, Limeng Zhang, Baoxiang Du
Summary: A novel five-dimensional conservative chaotic system is proposed and solved in a fractional-order form using the Adomian decomposition method. Special dynamical behaviors are analyzed in detail and compared with an integer-order system, revealing rare dynamical behaviors and influencing factors.
Article
Nanoscience & Nanotechnology
Pingying Liu, Hui Chu, Bo-Chao Zheng
Summary: This paper proposes a design method based on robust sliding mode control for the memristive Chua's circuit system. By applying delta operator discretization technology and the working principle of signal encoding and decoding, the dynamical model is established, and the sliding surface is designed to ensure robust quadratic stability. A sliding mode reaching control law is then designed to achieve robust and stable operation, which is validated on the Matlab/Simulink simulation platform.
Article
Engineering, Electrical & Electronic
Mauro Di Marco, Mauro Forti, Luca Pancioni, Alberto Tesi
Summary: The article demonstrates the presence of transient chaos in a generalized memristor Chua's circuit, where a nonlinear resistor is introduced to better model the behavior of the real memristor. The flux-charge analysis method is utilized to explain the origin of the transient chaos, which is attributed to the drift of the index of the memristor circuit invariant manifolds caused by the charge flowing into the nonlinear resistor.
ELECTRONICS LETTERS
(2023)
Article
Engineering, Electrical & Electronic
Mauro Di Marco, Mauro Forti, Luca Pancioni, Alberto Tesi
Summary: The article demonstrates the presence of transient chaos in a generalized memristor Chua's circuit by introducing a nonlinear resistor to better replicate the behavior of a real memristor. The origin of transient chaos is explained using the flux-charge analysis method, which attributes it to the drift of the index of the memristor circuit's invariant manifolds caused by the charge flowing into the nonlinear resistor.
ELECTRONICS LETTERS
(2023)
Article
Mathematics, Interdisciplinary Applications
Zhixiang Wang, Chun Zhang, Zuqin Ding, Qinsheng Bi
Summary: The aim of this paper is to reveal the dynamical mechanism of bursting oscillations in non-smooth dynamical systems, with a focus on the effects of period-doubling bifurcation and chaotic attractor. A modified fourth-order Chua's circuit is used to establish a dynamical system with non-smooth switching manifold and multiple scale variables. Subcritical non-smooth Hopf bifurcation, C-bifurcation, and period-doubling bifurcation are observed in the fast subsystem, along with chaotic attractors generated from period-doubling bifurcations. Eight typical bursting patterns are obtained through numerical simulations and bifurcation analysis, revealing their dynamical mechanism.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Neurosciences
Han Bao, Xihong Yu, Quan Xu, Huagan Wu, Bocheng Bao
Summary: A three-dimensional memristive Morris-Lecar neuron model is proposed to characterize the magnetic induction flow induced by neuron membrane potential. The effects of magnetic induction on firing activities and the bifurcation mechanisms of bursting patterns are explained using spiking/bursting firings and fast-slow analysis method. The model also demonstrates the ability to exhibit homogeneous coexisting bursting patterns when switching the memristor initial states.
COGNITIVE NEURODYNAMICS
(2023)
Article
Engineering, Mechanical
Bocheng Bao, Jingting Hu, Jianming Cai, Xi Zhang, Han Bao
Summary: This paper constructs a memristor-based neuron model and investigates the memristor effect in a discrete map as well as its impact on neuronal behavior. Numerical methods reveal complex mode transition behaviors, which are strongly dependent on the initial state of the memristor. Furthermore, a hardware platform is developed to demonstrate the effectiveness of the memristive neuron model in imitating firing activities of biological neurons.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Shoukui Ding, Ning Wang, Han Bao, Bei Chen, Huagan Wu, Quan Xu
Summary: This paper proposes a new neural network model based on memristors to simulate the electromagnetic induction effect between neurons. The theoretical analysis and numerical simulations investigate the multistability and various dynamic behaviors of the model, and a simple analog circuit is designed for verification.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Interdisciplinary Applications
Haotian Wang, Xin Li, Qin Zhou, Wenjun Liu
Summary: This study investigates the dynamics of optical rogue waves in the coupled nonlinear Schrodinger equation using various effective calculation methods. Exact rogue wave solutions are obtained based on the Lax integrable nature of the equation and a new matrix form Darboux transformation. These rogue waves exhibit dark or ultrahigh peak patterns with observable peaks and depressions in their structures. Numerical simulations show that they are more stable than the standard eye-shaped rogue waves. Modulation instability can generate a large number of rogue wave structures from perturbed continuous waves. Spectral analysis allows for the mathematical characterization and prediction of rogue waves in mode-locked fiber lasers. These results contribute to the understanding of ultrashort wave phenomena in optics, plasma, alkali-atom Bose-Einstein condensates, and other physics and engineering domains.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Engineering, Electrical & Electronic
Xi Zhang, Tianshi Wang, Han Bao, Yihua Hu, Bocheng Bao
Summary: This study investigates the stability effect of the feedforward current ripple of a load converter on a source converter in a cascaded power converter. By establishing a map model, the instability mechanism of the source converter under variations of circuit parameters is expounded and the stability boundaries are obtained.
IEEE TRANSACTIONS ON POWER ELECTRONICS
(2023)
Article
Engineering, Mechanical
Mo Chen, Xuefeng Luo, Yunhe Suo, Quan Xu, Huagan Wu
Summary: This work presents a memristor-coupled homogeneous network consisting of two identical non-autonomous memristive Fitzhugh-Nagumo models and investigates its coexisting and synchronous behaviors. The numerical results reveal coexisting hidden chaotic, periodic, and quasi-periodic attractors, and their synchronicities are controlled by the initial condition and coupling strength of the coupling memristor. In addition, phase synchronization is easily achieved due to the existence of external stimuli, and these synchronous states are flexibly controlled by the initial conditions.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Han Bao, Ruoyu Ding, Bei Chen, Quan Xu, Bocheng Bao
Summary: This work proposes a 2-D non-autonomous tabu learning single neuron (TLSN) model based on sinusoidal activation function (SAF), which can generate a class of multi-scroll chaotic attractors with parameters controlling the number of scrolls. The equilibrium trajectories of the SAF-TLSN model with different stability types can be distributed in the phase plane, resulting in the generation of multi-scroll chaotic attractors. The numerical and experimental results confirm the relationship between the equilibrium trajectories and the scrolls of multi-scroll chaotic attractors.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Interdisciplinary Applications
Xihong Yu, Han Bao, Mo Chen, Bocheng Bao
Summary: This study reveals that synapses can regulate the energy balance in neural networks. A two-neuron network was established by coupling two Morris-Lecar neurons using a memristor synapse. The periodic/hyperchaotic spiking-bursting patterns in the network were analyzed using bifurcation plot, phase portrait, and time-domain waveform. The asynchronous behaviors observed in the numerical results demonstrate the difference in the inner field energy of individual neurons.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Physics, Multidisciplinary
Zhuowu Wang, Han Bao, Huagan Wu, Mo Chen, Bocheng Bao
Summary: In this article, a two-dimensional discrete adaptive synapse-based neuron (DASN) model without external excitation is proposed using Euler's discretization method. The proposed model has a complicated nonlinear activation function with upper and lower bounds, and its fixed points are not only variable in number, but also have different types of stability, resulting in the emergence of complex dynamics and multi-stability. The dynamical effects of control parameters and initial values on the DASN model are explored, revealing complicated dynamical behaviors such as hyperchaos, chaos, quasi-period, period, etc.
EUROPEAN PHYSICAL JOURNAL PLUS
(2023)
Article
Mathematics, Interdisciplinary Applications
Han Bao, Kang Rong, Mo Chen, Xi Zhang, Bocheng Bao
Summary: This article proposes a simple memristor-coupled Logistic map (MCLM) model, which couples two identical Logistic maps through a memristive coupler. Numerical methods reveal chaotic/hyperchaotic attractors with outstanding performance indicators, and demonstrate initial-related heterogeneous multistability and memristor initial-boosting homogeneous multistability based on the basins of attraction that have complex and fractal evolutions. The synchronous behaviors of the two Logistic maps in the MCLM model are examined, disclosing lag and complete synchronization behaviors dependent on the coupling strength and memristor initial condition, especially the homogeneous synchronization behavior boosted by the memristor initial condition. An MCU-based hardware platform is fabricated to experimentally validate the numerical results. Particularly, the initial-boosting synchronization has not been reported in the literature to the authors' knowledge.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Interdisciplinary Applications
Bocheng Bao, Qianhan Zhao, Xihong Yu, Huagan Wu, Quan Xu
Summary: Recently, discrete memristor maps can be directly constructed using discrete memristors. However, some discrete memristors with reciprocal polynomial memristances cannot be directly used to generate mapping models. To achieve an available memristive map, a simple and effective implementation scheme is proposed to construct a two-dimensional (2-D) sine-bounded memristive map (SBMM).
CHAOS SOLITONS & FRACTALS
(2023)
Article
Engineering, Electrical & Electronic
Yang Gu, Han Bao, Quan Xu, Xi Zhang, Bocheng Bao
Summary: This study presents a cascaded bi-memristor (CBM) hyperchaotic map by cascading two memristors with identical memristance to explore the dynamical effects of cascaded memristors. The CBM map exhibits complex dynamics depending on the control parameters and initial states, revealing quasi-periodic bifurcation and hyperchaos. An FPGA implementation is made to experimentally verify the numerical results.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS
(2023)
Article
Automation & Control Systems
Han Bao, Mengjie Hua, Jun Ma, Mo Chen, Bocheng Bao
Summary: In this article, a Memristor synapse with activated synaptic plasticity is introduced as an adaptive connection synaptic weight. An improved Hopfield neural network with two memristive self-connection synaptic weights is presented to demonstrate its kinetic effects. The stability distributions of the network are analyzed by analyzing the two nonzero roots of the eigenvalue polynomial. Bifurcation behaviors and phase portraits are used to investigate the parameter-related behaviors. Furthermore, the kinetic effects of memristor synapses are demonstrated by taking the memristor initial conditions as two invariant measures.
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
(2023)
Article
Engineering, Electrical & Electronic
Xi Zhang, Dahui Lu, Han Bao, Xiaohui Qu, Yihua Hu, Bocheng Bao
Summary: In this paper, the stability effects of the feedforward current ripple from the load converter on the source converter in a cascaded converter are investigated. An equivalent modeling method of the feedforward current ripple is proposed and bifurcation analysis of the source converter is carried out. The results indicate that the stability prediction accuracy using the equivalent representation is related to the duty-cycle of the source converter.
IEEE TRANSACTIONS ON POWER ELECTRONICS
(2023)
Article
Engineering, Multidisciplinary
Han Bao, KeXin Li, Jun Ma, ZhongYun Hua, Quan Xu, BoCheng Bao
Summary: This paper presents an improved ID-Rulkov neuron model by coupling a memristor with a discrete Rulkov neuron model, and investigates the dynamic effects of the memristor on the neuron model. The experimental results demonstrate that the memristor enhances the diversity of the neuron model and generates hyperchaotic attractors.
SCIENCE CHINA-TECHNOLOGICAL SCIENCES
(2023)
