Article
Biology
Dianavinnarasi Joseph, Raja Ramachandran, Anitha Karthikeyan, Karthikeyan Rajagopal
Summary: This study focuses on the synchronization analysis of Hindmarsh-Rose neurons coupled through a common memristor. The stability of the model, eigenvalues, bifurcation analysis, and maximum Lyapunov exponents are used to determine chaotic and hyperchaotic behavior, as well as the influence of coupling strength. Exponential stability of the synchronous model is derived analytically and verified through numerical simulations. Furthermore, the impact of initial conditions, memristor synapses, and coupling coefficient on synchronization is explored.
Article
Mathematics, Interdisciplinary Applications
Sajedeh Aghababaei, Sundarambal Balaraman, Karthikeyan Rajagopal, Fatemeh Parastesh, Shirin Panahi, Sajad Jafari
Summary: This paper investigates the influence of autaptic connections on chimera states, showing that the occurrence domain of chimeras is affected differently by coupling strength and autapse parameters. By adjusting the coupling strength and autapse parameters, an ideal dynamical state can be achieved.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Computer Science, Information Systems
Alexander L. Fradkov, Aleksandr Kovalchukov, Boris Andrievsky
Summary: In this paper, a new adaptive model for neurons based on the Hindmarsh-Rose third-order model is proposed. The learning algorithm for adaptive identification of neuron parameters is analyzed theoretically and through computer simulation. The algorithm is based on the Lyapunov functions approach and a reduced adaptive observer, allowing for parameter estimation of synchronized neuron populations. Rigorous stability conditions for synchronization and identification are presented.
Article
Engineering, Mechanical
L. Messee Goulefack, A. Cheage Chamgoue, C. Anteneodo, R. Yamapi
Summary: In this study, we modified the Hindmarsh-Rose neuron model to account for the effect of electromagnetic induction on membrane potential. We found that increasing magnetic flux reduces the number of equilibrium points and enhances their stability. As a result, electromagnetic induction tends to regularize chaotic regimes and affect regular and quasi-regular states by reducing the number of spikes or even destroying oscillations.
NONLINEAR DYNAMICS
(2022)
Article
Mathematics, Applied
L. Messee Goulefack, Marlon F. Ramos, R. Yamapi, C. Anteneodo
Summary: In this study, the dynamics of nonlocally coupled Hindmarsh-Rose neurons modified by coupling the induced magnetic flux to the membrane potential with a quadratic memristor of strength k were investigated. The nonlocal coupling involved the interaction of each neuron with its neighbors within a fixed radius, influencing the membrane potential with coupling intensity sigma. The study examined how variations of k and sigma affect the collective dynamics, finding that coherence typically increased when k and sigma were increased, except for small parameter ranges where the opposite behavior could occur. Moreover, varying k also affected the pattern of bursts and spikes, resulting in an increase in burst frequency, a decrease in the number and amplitude of spikes, and longer quiescent periods.
Article
Mathematics, Interdisciplinary Applications
Zhanqing Wang, Yong Xu, Yongge Li, Tomasz Kapitaniak, Jurgen Kurths
Summary: This paper investigates alpha-stable noise-induced chimera states in a small-world Hindmarsh-Rose neuronal network, showing that changes in network and noise parameters can affect the occurrence and disappearance of chimera states. The concept of coherence strength based on the local order parameter is proposed for identifying both the occurrence of chimera states and the proportion of coherent neurons in the entire network.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Engineering, Multidisciplinary
Lin Xu, Guoyuan Qi, Jun Ma
Summary: This paper introduces a novel 4D HR model with a threshold flux-controlled memristor, which describes the electromagnetic induction effect. Compared to existing models, this model can more simply describe the dynamics of neuronal electrical activities and uncovers hidden dynamics.
APPLIED MATHEMATICAL MODELLING
(2022)
Article
Mathematics
Branislav Rehak, Volodymyr Lynnyk
Summary: An algorithm for synchronization of interconnected Hindmarsh-Rose neurons network is presented, incorporating delays and noise in the network. The synchronization algorithm utilizes convex optimization and linear matrix inequalities formulation, showing synchronized recovery and adaptation variables through the minimum-phase property of the Hindmarsh-Rose neuron. The results are demonstrated with an example.
Article
Mathematics, Interdisciplinary Applications
A. Moujahid, F. Vadillo
Summary: Mathematical modeling is crucial for studying the impact of delay in neural systems and evaluating its effects on the signaling activity of coupled neurons. This study focuses on the energy perspective of delayed coupling in Hindmarsh-Rose burst neurons, examining the average energy consumption required to maintain cooperative behavior and quantifying the contribution of synapses to total energy consumption.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Engineering, Multidisciplinary
Yuan YuanYuan, Yang Hao, Han Fang, Wang ZhiJie
Summary: This study investigates the traveling chimera states in memristive neuronal networks of locally coupled Hindmarsh-Rose neurons. Various traveling chimera patterns and firing modes are observed, including two kinds of traveling chimera states in opposite directions and a new type of chimera state called semi-traveling chimera state. Multi-head traveling chimera states and a firing pattern called mixed-amplitude bursting state are also observed. The study demonstrates the generation of traveling chimera states in real circuits and provides insights into the dynamics of neuronal networks.
SCIENCE CHINA-TECHNOLOGICAL SCIENCES
(2022)
Article
Physics, Multidisciplinary
Zeric Tabekoueng Njitacke, Sishu Shankar Muni, Soumyajit Seth, Jan Awrejcewicz, Jacques Kengne
Summary: This study focuses on the collective behavior of two HR neurons and a network of HR neurons. By connecting a traditional 3D HR neuron and a memristive 2D HR neuron through a gap junction, the collective behavior of the coupled neurons is obtained. Numerical simulations reveal that the coupled neurons exhibit various behaviors, including periodic, quasi-periodic, and chaotic bursting or spiking, by adjusting the control parameter. The network topology affects the spatiotemporal patterns, with cluster states observed in non-homogenous ring and star structures.
Article
Physics, Multidisciplinary
Weiwei Fan, Xiongjian Chen, Yiteng Wang, Bei Chen, Huagan Wu, Quan Xu
Summary: Electromagnetic induction can induce abundant firing patterns in neurons. This paper proposes a 3D memristive Hindmarsh-Rose neuron model with an ideal flux-controlled memristor to capture the electromagnetic induction effect. The model exhibits rich hidden dynamics, including periodic spiking, chaotic spiking, bifurcation, and chaos crisis, which are influenced by the memristor coupling strength and external stimulus.
FRONTIERS IN PHYSICS
(2023)
Article
Engineering, Mechanical
S. Dinesh Vijay, K. Thamilmaran, A. Ishaq Ahamed
Summary: This paper investigates the occurrence of superextreme spiking (SES) oscillations and multistability behavior in a memristor-based Hindmarsh-Rose neuron model. The study finds that the presence of SES oscillations is due to an interior crisis. Numerical simulations and statistical tools are used to characterize the SES oscillations and bounded chaotic spiking oscillations, while bifurcation analysis and Lyapunov exponents are employed to confirm the multistability behavior.
NONLINEAR DYNAMICS
(2023)
Article
Engineering, Mechanical
Jianming Cai, Han Bao, Quan Xu, Zhongyun Hua, Bocheng Bao
Summary: This paper introduces a novel smooth nonlinear fitting scheme to implement the HR neuron model in analog without using multipliers. By constructing nonlinear fitting functions and implementing analog multiplierless circuits, the nonlinear fitting effects of the adapted HR neuron model are successfully demonstrated.
NONLINEAR DYNAMICS
(2021)
Article
Physics, Multidisciplinary
Yanzhang Wang
Summary: Neurophysiological studies have shown that there are complex dynamical characteristics in electrical activities between neurons. Electromagnetic stimulation can change the dynamics of the nervous system and affect the effectiveness of neurological diseases. By connecting a memristor to a 2-dimensional HindMarsh-Rose neuron model, a new memristive HindMarsh-Rose neuron model is developed to explore the complex dynamic effect of magnetic field on neuron activities. The model exhibits rich nonlinear dynamics and generates hidden attractors when the electromagnetic induction changes. This model can be considered as a chaotic system and applied in image encryption algorithm. A security analysis confirms the reliability of the proposed encryption algorithm.
Article
Neurosciences
Karthikeyan Rajagopal, Janarthanan Ramadoss, Shaobo He, Prakash Duraisamy, Anitha Karthikeyan
Summary: This article discusses various dynamical properties of a four-dimensional mammalian cold receptor model, focusing on the effects of noise and temperature on collective behavior. By introducing obstacles in the network, the study shows how they affect wave reentry and proposes a new technique to identify it using individual node periods.
COGNITIVE NEURODYNAMICS
(2023)
Article
Neurosciences
Shaobo He, Karthikeyan Rajagopal, Anitha Karthikeyan, Ashokkumar Srinivasan
Summary: This study proposes a new discrete neuron model derived from the Huber-Braun neuron, which introduces additional slow and subthreshold currents and temperature dependent ion channels to study the firing pattern of neurons. Bifurcation, Lyapunov exponents, and sample entropy algorithm are used to analyze the dynamical behaviors of the model. The spatiotemporal behavior of the discrete neuron model is investigated in both single- and two-layer networks, and the induction of spiral waves in the network is studied.
COGNITIVE NEURODYNAMICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Najmeh Pakniyat, Gayathri Vivekanandhan, Karthikeyan Rajagopal, Ondrej Krejcar, Kamil Kuca, Hamidreza Namazi
Summary: One important research area in neuroscience is investigating how brain activity changes during aging. In this study, complexity techniques were used to analyze the age-related changes in brain activity during sleep. By analyzing the EEG signals of 22 subjects induced by sleep medication using fractal theory and sample entropy, it was found that the fractal dimension and sample entropy of EEG signals decrease with aging. Therefore, it was concluded that aging leads to lower complexity in EEG signals during sleep. The employed method of analysis can be applied to study the effects of aging on the activity variations of other organs, such as the heart and muscles, by analyzing their related physiological signals, such as ECG and EMG.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2023)
Article
Physics, Multidisciplinary
Janarthanan Ramadoss, Hayder Natiq, Fahimeh Nazarimehr, Shaobo He, Karthikeyan Rajagopal, Sajad Jafari
Summary: This paper proposes the behavior of a 1D chaotic map that includes two sine terms and shows unique dynamics. By varying the bifurcation parameter, the map generates a shift and the system's dynamics are generated around the cross points of the map and the identity line. The irrational frequency of the sine term results in stable fixed points in some parameter intervals by increasing the bifurcation parameter. The proposed system, known as multistable, achieves multiple steady states in some intervals of the parameter, and the multistability dynamics are investigated using cobweb diagrams that reveal an interesting asymmetry in repeating parts of the bifurcation diagram.
Article
Physics, Multidisciplinary
Balamurali Ramakrishnan, Victor Kamdoum Tamba, Justin Roger Mboupda Pone, Serge Gervais Mbouna Ngueuteu, Karthikeyan Rajagopal
Summary: This paper presents a report on the microcontroller implementation of an autonomous three-dimensional oscillator with five terms (ATDOFT) and performance analysis based on partial and total amplitude controls. The ATDOFT displays periodic spiking behaviors, chaotic states, coexisting attractors, and bistable attractors. The study reveals that the spiking oscillations in the ATDOFT arise from the system switching between the unstable state and the stable state of the lone equilibrium point of the fast subsystem. Total and partial amplitude controls are achieved by inserting two controller parameters into the rate equations of the ATDOFT. The dynamical behaviors found in ATDOFT are validated by the microcontroller implementation.
Editorial Material
Multidisciplinary Sciences
Shaobo He
Article
Engineering, Electrical & Electronic
Yan Zhao, Jiafeng Ding, Shaobo He, Huihai Wang, Kehui Sun
Summary: In this paper, fully fixed-point digital integrated circuits for discrete memristive systems are designed to have very low circuit area cost, using a two-stage pipeline and multi-cycle architecture. Mathematical models for the discrete memristor and a memristor chaotic map are presented and their dynamics are analyzed. Data flow design is carried out and the feasibility of the fixed-point model is discussed, providing a foundation for further circuit design. Different architectures are designed to obtain optimal results. Gate area and gate counts are provided for the discrete memristor and the discrete memristor map. Additionally, a chaotic pseudo random sequence generator is designed and passes the NIST test, laying the foundation for further applications of the discrete memristor and discrete memristor chaotic systems.
AEU-INTERNATIONAL JOURNAL OF ELECTRONICS AND COMMUNICATIONS
(2023)
Article
Mathematics, Applied
D. Vignesh, Shaobo He, Santo Banerjee
Summary: This article introduces a discrete time fractional order three-dimensional Rucklidge system with complex state variables and compares its dynamical properties and chaotic behavior with the Rucklidge system with real state variables and higher dimensional system derived from complex state variables. The stability of the proposed system is analyzed at equilibrium states by obtaining eigenvalues numerically. Chaotic dynamics exhibited by the system with real and complex variables are studied using bifurcation analysis, maximum Lyapunov exponents, and the Jacobian matrix method. Nonlinear controllers are implemented for chaos synchronization of the subsystems of the proposed system. The article also discusses the coexisting behavior of the attractors in the Rucklidge system with real state variables and coexisting bifurcation diagrams.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Mathematics, Applied
Mengjiao Wang, Mingyu An, Shaobo He, Xinan Zhang, Herbert Ho-Ching Lu, Zhijun Li
Summary: This paper first proposes a discrete memristor model and analyzes the voltage-current characteristics of the memristor. Then, the discrete memristor is coupled with a one-dimensional sine chaotic map through different coupling frameworks, and two different two-dimensional chaotic map models are generated. The dynamic behavior of the chaotic map under different coupled map frameworks is investigated by using various analytical methods, and the results show that different coupling frameworks can produce different complex dynamical behaviors for memristor chaotic maps.
Article
Mathematics, Interdisciplinary Applications
Xinkang Liu, Kehui Sun, Huihai Wang, Shaobo He
Summary: In this paper, a new type of chaotic map based on discrete memristor and original boundary function is introduced, and its improved dynamic performance and chaos complexity are demonstrated through several examples. The influences of introducing memristor on chaotic map and the generality for designing discrete chaotic maps of the proposed memristive model are analyzed. Moreover, the ability to robustly control the output sequence by setting initial states is highlighted, which is applicable to various applications of chaotic systems.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Computer Science, Artificial Intelligence
Shaobo He, D. Vignesh, Lamberto Rondoni, Santo Banerjee
Summary: This article introduces a novel model of asymmetric neural networks combined with fractional difference memristors, and explores the complex dynamical characteristics of neural network systems with sine memristors. The authenticity of the constructed memristor is confirmed through fingerprint verification, and the model demonstrates coexisting state variables depending on the initial conditions when incorporating sine memristors, revealing the emergence of multi-layer attractors.
Article
Multidisciplinary Sciences
Worke Adugna Yihyis, Shaobo He, Zhouqing Tang, Huihai Wang
Summary: This study investigates the influence of discrete memristors on chaotic system behavior and proposes a class of chaotic maps with discrete memristors based on the Sine map. Numerical simulations demonstrate that internal perturbations of discrete memristors enhance the Sine map's chaotic characteristics, expand the chaos range, and improve ergodicity and the Lyapunov exponent. The type of discrete memristors significantly impacts the dynamic characteristics of the system, while the number of discrete memristors has little influence. Therefore, this study provides a direction for the design of discrete memristor chaotic systems.
Article
Materials Science, Multidisciplinary
Xianming Wu, Longxiang Fu, Shaobo He, Zhao Yao, Huihai Wang, Jiayu Han
Summary: This paper presents a new fractional-order Chua's system with arctan function and an algorithm for determining the initial value of fractional-order hidden attractors. The dynamics of the system are investigated using stability analysis, phase diagrams, and other methods, showing rich dynamics. Hidden attractors are found and verified through numerical simulation and experimental results, confirming the effectiveness of the proposed methods.
RESULTS IN PHYSICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Mengjiao Wang, Jiwei Peng, Shaobo He, Xinan Zhang, Herbert Ho-Ching Iu, Antonio Lopes
Summary: This study investigates the firing dynamics and phase synchronization behavior of a heterogeneous coupled network and reveals its complex dynamic behavior, as well as an abnormal synchronization behavior that differs from existing findings. The findings contribute to the understanding of brain activity mechanisms and the development of bionic systems.
FRACTAL AND FRACTIONAL
(2023)
Article
Automation & Control Systems
Longxiang Fu, Xianming Wu, Shaobo He, Huihai Wang, Kehui Sun
Summary: This article proposes an improved memristive Henon map by using the state variable difference as the input of a discrete memristor. The system exhibits rich dynamical behaviors as shown by bifurcation diagrams, Lyapunov exponent spectrums, and sample entropy complexity analysis results. In addition, analog circuits of the discrete memristor and memristive chaotic map are designed and validated through simulations and experiments, demonstrating the physical realizability of the discrete memristor and laying the foundation for its applications.
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
(2023)
