Article
Mathematics, Interdisciplinary Applications
Qiang Lai, Liang Yang
Summary: This paper proposes a simple ring memristive neural network (MNN) with unique features of generating heterogeneous coexisting attractors and enabling large-scale amplitude control. Various types of attractors are numerically found in the MNN, including chaos with a stable point, chaos with a limit cycle, and a limit cycle with a stable point. The MNN's chaotic variables can be increased by adjusting parameter values, allowing for parameter-dependent large-scale amplitude control. A circuit implementation platform is established and experimental results demonstrate the validity and reliability of the proposed MNN.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2023)
Article
Physics, Multidisciplinary
Sixiao Kong, Chunbiao Li, Shaobo He, Serdar Cicek, Qiang Lai
Summary: By introducing a discrete memristor and periodic sinusoidal functions, a two-dimensional map with coexisting chaos and hyperchaos is constructed in this study. Various coexisting chaotic and hyperchaotic attractors under different Lyapunov exponents are discovered, along with capturing other regimes of coexistence such as coexisting chaos, quasi-periodic oscillation, and discrete periodic points. Additionally, the hyperchaotic attractors can be flexibly controlled to be unipolar or bipolar by newly embedded constants, providing potential applications in artificial intelligence.
Article
Physics, Multidisciplinary
Ramesh Ramamoorthy, Zahra Shahriari, Hayder Natiq, Karthikeyan Rajagopal, Chunbiao Li
Summary: The collective behavior of oscillators in a ring network of non-locally coupled VB5 chaotic systems with multistability is studied in this paper. The patterns of the oscillators are investigated by adjusting various internal parameters, and the state of the network is characterized by computing the strength of incoherence. The effects of coupling strength and number of neighbors in connections are considered, and synchronous, chimera, and asynchronous states are observed under different parameters.
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
Multidisciplinary Sciences
Xuejiao Zhou, Chunbiao Li, Xu Lu, Tengfei Lei, Yibo Zhao
Summary: An absolute value function was introduced for chaos construction, where hyperchaotic oscillation was found with amplitude rescaling. The study discusses two regimes of amplitude control and captures symmetrical pairs of coexisting attractors. Circuit implementation by the platform STM32 is consistent with numerical exploration and theoretical observation.
Article
Physics, Multidisciplinary
Wang-Peng Huang, Qiang Lai
Summary: This article proposes a non-ideal flux-controlled memristor and a new multi-wing memristive chaotic system based on it. Diverse coexisting attractors are numerically found in the system, demonstrating its validity and reliability.
Article
Physics, Multidisciplinary
Xinying Li, Shaoze Sun, Zongkai Yang, Jinping Li
Summary: This paper combines a memristor with a chaotic system to construct a four-dimensional memristive chaotic system with infinite coexisting attractors. The system's dynamical behavior is thoroughly studied, revealing complex dynamics and the potential for practical engineering applications.
Article
Physics, Multidisciplinary
Li-Li Jia, Bang-Cheng Lai
Summary: This article introduces a new memristive chaotic system and highlights its ability to generate multiple stable states and control the amplitude.
EUROPEAN PHYSICAL JOURNAL PLUS
(2022)
Article
Mathematics, Interdisciplinary Applications
Qiang Lai, Zhijie Chen
Summary: In this paper, a novel five-dimensional chaotic system devoid of equilibria is constructed, and its existence is experimentally verified. Through analyzing the evolution of the system and manipulating the parameters, partial amplitude modulation of the system can be achieved.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Physics, Applied
Qiang Lai, Zhiqiang Wan, Paul Didier Kamdem Kuate, Hilaire Fotsin
Summary: This paper introduces a novel memristive hyperchaotic system with two equilibria and two symmetric hyperchaotic attractors. The dynamic behaviors of the system are studied through bifurcation analysis, and analog circuit design and experimental implementation are presented. Synchronization of the system is achieved using adaptive control technique, with sufficient conditions established through theoretical and numerical analysis.
MODERN PHYSICS LETTERS B
(2021)
Article
Engineering, Multidisciplinary
Bao Han, Chen ZhuGuan, Cai JianMing, Xu Quan, Bao BoCheng
Summary: This paper presents a neural network that uses memristive synaptic weights, which can exhibit chaos and coexisting attractors composed of stable points and orbits.
SCIENCE CHINA-TECHNOLOGICAL SCIENCES
(2022)
Article
Multidisciplinary Sciences
A. O. Adelakun, Y. A. Odusote
Summary: This work provides an in-depth analysis of a novel multiple scroll memristive-based hyperchaotic system with no equilibrium. It identifies a family of more complicated nth-order multiple scroll hidden attractors for a unique, enhanced 4-dimensional Sprott-A system. The system is particularly sensitive to initial conditions and exhibits coexistence and multistability of attractors when changing the associated parameters and the finite transient simulation time. The complexity (CO), spectral entropy (SE) algorithms, and 0-1 complexity characteristics are thoroughly discussed. On the other hand, the outcomes of the electronic simulation are validated by theoretical calculations and numerical simulations.
SCIENTIFIC REPORTS
(2023)
Article
Mathematics, Interdisciplinary Applications
Qiang Lai, Cong Lai, Hui Zhang, Chunbiao Li
Summary: This paper presents a novel neuron model by coupling a memristor to obtain a memristive neuron model. The study shows that memristor can enhance the chaos complexity of the discrete neuron, resulting in hyperchaos. Additionally, a new encryption scheme for image encryption is proposed, which exhibits excellent security characteristics.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Interdisciplinary Applications
Ran Wang, Chunbiao Li, Sixiao Kong, Yicheng Jiang, Tengfei Lei
Summary: Based on the special structure of variable-boostable chaotic system VB24, a 3D memristive chaotic system with conditional symmetry is constructed by embedding a quadratic flux-controlled memristor, and the coexisting oscillations with conditional symmetry are systematically confirmed through bifurcation analysis and circuit verification.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Physics, Multidisciplinary
Qin Ming-Hong, Lai Qiang, Wu Yong-Hong
Summary: This paper proposes a simple four-dimensional memristive chaotic system with an infinite number of coexisting attractors, which exhibits complex dynamical behavior. The system is further investigated through digital simulations and the results are consistent with the experimental findings, demonstrating the feasibility and existence of this memristive chaotic system.
ACTA PHYSICA SINICA
(2022)
Article
Mathematics, Interdisciplinary Applications
Chunbiao Li, Zhenyu Gu, Zuohua Liu, Sajad Jafari, Tomasz Kapitaniak
Summary: The introduction of surfaces of equilibria in a dynamical system is a useful tool for constructing a chaotic repellor. There are infinitely many available functions for transforming an attractor to a repellor. Chaotic repellors can be constructed from various types of chaotic attractors, and offset boosting of a variable driven by embedded functions provides flexible control over system attractors and coexisting repellors.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Interdisciplinary Applications
Jesus M. Munoz-Pacheco, Luis Carlos Lujano-Hernandez, Carlos Muniz-Montero, Akif Akgul, Luis A. Sanchez-Gaspariano, Chun-Biao Li, Mustafa Cagri Kutlu
Summary: This paper presents the design, simulation, and experimental verification of the fractional-order multiscroll Lu chaotic system based on op-amp-based approximations of fractional-order integrators and saturated series of nonlinear functions. The results include simulations in SPICE and experimental measurements confirming the effectiveness and robustness of the system. Compared to passive counterparts, the suggested realizations significantly reduce design and implementation efforts.
Article
Engineering, Multidisciplinary
Balamurali Ramakrishnan, Ramesh Ramamoorthy, Chunbiao Li, Akif Akgul, Karthikeyan Rajagopal
Summary: Josephson junction-memristor (JJM) devices play a crucial role in physical nonlinear systems due to their complex characteristics. This study investigated the network behavior of JJM devices, considering both AC- and DC-type external excitation currents. The system exhibited megastability under AC excitation and formed spiral waves when excited by DC bias current, showcasing the impact of external bias currents on the collective performance of Josephson junction devices.
MATHEMATICAL PROBLEMS IN ENGINEERING
(2021)
Article
Mathematics, Applied
Karthikeyan Rajagopal, Iqtadar Hussain, Zahra Rostami, Chunbiao Li, Viet-Thanh Pham, Sajad Jafari
Summary: The combination of chemical, physical, electrical, and structural properties of neurons creates highly complex dynamical units. Studying neural spatiotemporal patterns, specifically the spiral pattern, is crucial in understanding cortical activities and potential neurological disorders. External forces like amplitude and frequency play a significant role in controlling the dynamics of spiral waves in neural networks.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Mathematics, Interdisciplinary Applications
Ran Wang, Chunbiao Li, Serdar Cicek, Karthikeyan Rajagopal, Xin Zhang
Summary: A controllable hyperjerk system was constructed using a memristor's nonlinear factor to induce chaos, with amplitude control achieved through a single coefficient. The system exhibited equilibria and extreme multistability, as shown in the initial value-associated bifurcation diagram. The physical verification was conducted with a FPGA-based circuit realization, and the system's performance was successfully predicted using artificial neural networks for AI-based engineering applications.
Article
Engineering, Electrical & Electronic
Chunbiao Li, Julien Clinton Sprott, Wesley Joo-Chen Thio, Zhenyu Gu
Summary: The study introduces a simple memristive chaotic jerk system with one variable representing the internal state, which exhibits hidden chaotic oscillation in a narrow parameter space. A circuit modeling the jerk system is constructed and validates the predicted oscillation. This new memristive jerk system appears to be one of the algebraically simplest memristive chaotic systems.
IET CIRCUITS DEVICES & SYSTEMS
(2021)
Article
Mathematics, Applied
Chunbiao Li, Guanrong Chen, Juergen Kurths, Tengfei Lei, Zuohua Liu
Summary: Complex dynamic evolution may stem from parameter-controlled bifurcation or initial-condition-oriented multistability. Enhancing the offset of any attractor in a system can be achieved by introducing a constant or nudging an initial condition, and designing a piecewise-linear function is crucial for transporting desired attractors.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2021)
Article
Multidisciplinary Sciences
Xuejiao Zhou, Chunbiao Li, Xu Lu, Tengfei Lei, Yibo Zhao
Summary: An absolute value function was introduced for chaos construction, where hyperchaotic oscillation was found with amplitude rescaling. The study discusses two regimes of amplitude control and captures symmetrical pairs of coexisting attractors. Circuit implementation by the platform STM32 is consistent with numerical exploration and theoretical observation.
Article
Multidisciplinary Sciences
Sixiao Kong, Chunbiao Li, Haibo Jiang, Yibo Zhao, Yanling Wang
Summary: Trigonometric functions were used to construct a 2-D symmetrical hyperchaotic map with infinitely many attractors. The multistability of the system depends on the periodicity of the trigonometric function and the initial condition, which can be triggered by an offset controller. The study explores the evolution of specific multistability triggered by initial conditions, resulting in countless symmetric and asymmetric attractors.
Review
Mathematics, Interdisciplinary Applications
Chunbiao Li, Xin Zhang, Lin Chai, Zuohua Liu, Julien Clinton Sprott
Summary: Based on polarity balance and exhaustive computer searching, a series of symmetric chaotic flows with conditional symmetry were found. These flows have elegant symmetric phase trajectories and coexisting symmetric attractors.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Interdisciplinary Applications
Xin Zhang, Chunbiao Li, Enzeng Dong, Yibo Zhao, Zuohua Liu
Summary: This study proposes a conservative chaotic system based on a variable-boostable chaotic system, which exhibits rich symmetrical dynamics. The system variable can be partially controlled by a parameter of a memristor. Experimental circuit and simulation demonstrate the properties of the system, including amplitude control and offset boosting.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2022)
Article
Multidisciplinary Sciences
Lili Huang, Xin Zhang, Hongyan Zang, Tengfei Lei, Haiyan Fu
Summary: A new 3D offset-boostable symmetric system is proposed by introducing an absolute value function. The system is more fragile and prone to a state of broken symmetry. Coexisting attractor pairs get closer and finally merge together. The basins of attraction demonstrate the arrangement of these coexisting attractors in phase space.
Article
Mathematics
Zhoubin Sheng, Chunbiao Li, Yikai Gao, Zhinan Li, Lin Chai
Summary: Due to the wide frequency spectrum of chaotic signals, it is challenging to condition chaotic signals. Researchers have thus explored chaotic systems with independent non-bifurcation control for easier modification. This paper modifies a system with only one non-quadratic term to provide multiscale amplitude/frequency control. The efficiency and convenience of chaotic signal control is demonstrated through a Multisim-based circuit simulation.
Article
Physics, Multidisciplinary
K. Rajagopal, Y. Shekofteh, F. Nazarimehr, C. Li, S. Jafari
Summary: This paper introduces a multi-stable chaotic hyperjerk system with both self-excited and hidden attractors, which is rare among dynamical systems. State-space, bifurcation, and Lyapunov exponent plots demonstrate the existence of chaotic dynamics, and the fractional-order model and dynamical properties of the system are studied in this paper.
INDIAN JOURNAL OF PHYSICS
(2022)
Article
Mathematics, Interdisciplinary Applications
Bo Li, Tian Huang
Summary: This paper proposes an approximate optimal strategy based on a piecewise parameterization and optimization (PPAO) method for solving optimization problems in stochastic control systems. The method obtains a piecewise parameter control by solving first-order differential equations, which simplifies the control form and ensures a small model error.
CHAOS SOLITONS & FRACTALS
(2024)
Article
Mathematics, Interdisciplinary Applications
Guram Mikaberidze, Sayantan Nag Chowdhury, Alan Hastings, Raissa M. D'Souza
Summary: This study explores the collective behavior of interacting entities, focusing on the co-evolution of diverse mobile agents in a heterogeneous environment network. Increasing agent density, introducing heterogeneity, and designing the network structure intelligently can promote agent cohesion.
CHAOS SOLITONS & FRACTALS
(2024)
Article
Mathematics, Interdisciplinary Applications
Gengxiang Wang, Yang Liu, Caishan Liu
Summary: This investigation studies the impact behavior of a contact body in a fluidic environment. A dissipated coefficient is introduced to describe the energy dissipation caused by hydrodynamic forces. A new fluid damping factor is derived to depict the coupling between liquid and solid, as well as the coupling between solid and solid. A new coefficient of restitution (CoR) is proposed to determine the actual physical impact. A new contact force model with a fluid damping factor tailored for immersed collision events is proposed.
CHAOS SOLITONS & FRACTALS
(2024)
