Article
Mathematics, Interdisciplinary Applications
Wen Lu, Yuhao Zhang, Yu Qian, Vikas Pandey, Zhilin Qu, Zhaoyang Zhang
Summary: The study found that bursting behavior can occur in gene regulatory network systems without the need for distinct fast and slow time scales. Bifurcation analyses revealed that bursting behavior originates from a secondary Hopf bifurcation of a limit cycle and terminates at a saddle-node bifurcation on an invariant circle. During the bursting cycle, the system evolves from a ghost point to an unstable focus, then to an unstable limit cycle, and finally back to the vicinity of the ghost point, providing a new mechanism for bursting dynamics in complex systems.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Engineering, Mechanical
Arturo Buscarino, Carlo Famoso, Luigi Fortuna
Summary: This paper presents a new nonlinear discrete-time map that is able to produce rich dynamical behavior, including the onset of spiking trends. The map is based on a second-order dynamics and can be considered as a novel discrete-time model for spiking neurons. The study uses numerical bifurcation approach and also shows the possibility of obtaining spiking behavior using noise. The implementation of the map using advanced microcontroller units and the obtained experimental results are discussed.
NONLINEAR DYNAMICS
(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
Mathematics
Weipeng Lyu, Shaolong Li, Zhenyang Chen, Qinsheng Bi
Summary: This paper discusses two types of codimension-2 bifurcation that may lead to complex bursting oscillations by considering the normal form of the vector field with triple zero bifurcation. By using the fast-slow analysis method and introducing the slow variable W=Asin(?t), the evolution process of the system's motion trajectory changing with W was investigated, and the dynamical mechanism of several types of bursting oscillations was revealed. Furthermore, a class of chaotic bursting phenomena caused by the period-doubling cascade is deduced by varying the frequency of the slow variable. These studies have played a positive role in deepening the understanding of the nature of various complex bursting phenomena and strengthening the application of basic disciplines such as mechanics and mathematics in engineering practice.
Article
Mathematics, Applied
Zhixiang Wang, Chun Zhang, Qinsheng Bi
Summary: This paper investigates bursting oscillations and the dynamical mechanism in the Filippov system using a modified Chua's circuit with an external excitation current and a piecewise nonlinear resistor. The effects of sliding bifurcations on the bursting dynamics are focused on, and five typical representative bursting oscillations are observed. The bifurcations of the fast subsystem are discussed, and the conditions for conventional bifurcations and bifurcations of boundary equilibria are obtained. Numerical methods are used to observe various bifurcations, and the dynamical mechanism is discovered using slow-fast analysis method.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Mathematics
Sergey V. V. Stasenko, Victor B. B. Kazantsev
Summary: We propose a mathematical model of a spiking neural network that interacts with the brain extracellular matrix (ECM). The model shows that ECM-mediated regulation of neuronal activity promotes the formation of population bursts. We investigate how varying the strength of ECM influence on synaptic transmission affects spiking dynamics and neuronal population synchrony.
Article
Mathematics, Interdisciplinary Applications
Shaohui Yan, Zhenlong Song, Wanlin Shi, Weilong Zhao, Yu Ren, Xi Sun
Summary: An autonomous memristive circuit based on an active third-order generalized memristor is implemented, and the stability and complex dynamical behaviors of the system are analyzed using mathematical models. The feasibility of the theoretical analysis is verified through circuit experiments and numerical simulations.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2022)
Article
Physics, Multidisciplinary
Sergey V. Stasenko, Victor B. Kazantsev
Summary: We investigated how a mathematical model composed of a spiking neural network (SNN) interacting with astrocytes can represent information content in the form of two-dimensional images. The SNN includes excitatory and inhibitory neurons, while the astrocytes provide slow modulation of synaptic transmission strength. We found that astrocytic modulation prevents hyperexcitation and non-periodic bursting activity, allowing the restoration of the image supplied during stimulation.
Article
Physics, Multidisciplinary
E. Zhang, Liao Yu, Zhuoqin Yang
Summary: This study investigates the topological types of bursting discharges in dynamical models with multiple time scales using multi-layered fast-slow analysis. Two parameters are identified in the Chay-Cook model that control the timescales of the system. By combining two different fast-slow analyses, the researchers define the topological types of bursting discharges more accurately. This new definition extends the existing classification and provides a dynamic basis for studying the complexity of information encoding in neuronal systems.
EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS
(2022)
Review
Biochemical Research Methods
Mathieu Desroches, John Rinzel, Serafim Rodrigues
Summary: Bursting is a fundamental rhythm in excitable cells that has been extensively studied in computational biology. The classification of bursting oscillations has been actively researched since the early 1980s and provides a foundation for understanding complex temporal behaviors in cellular activity models. This review presents the seminal works in classifying bursting patterns and introduces an extended classification that considers both fast and slow subsystems of an underlying model. The proposed framework allows for the analysis of a larger class of bursters and introduces a new class of bursters called folded-node bursters. The importance of developing modeling frameworks to capture and understand bursting patterns is emphasized. The review also highlights the potential applications of the proposed classification system in studying complex cellular activity.
PLOS COMPUTATIONAL BIOLOGY
(2022)
Article
Computer Science, Information Systems
Liangyu Huang, Yimin Lu
Summary: This study proposes a discrete model that addresses the challenges of discrete modeling for power electronic nonlinear switched systems. Experimental results confirm the effectiveness of the model and the accuracy of the bifurcation characteristics. The research lays a foundation for theory and further studies in this field.
Article
Mathematics, Applied
Yue Deng, Yuxia Li
Summary: This paper introduces a novel chaotic memristor-based circuit with external excitation, investigates the impact of external perturbation on system dynamics, and explores delay effects at different frequencies. Experimental results demonstrate a power-law relationship between delay-time and external frequency.
Article
Mathematics, Interdisciplinary Applications
Diogo Ricardo da Costa, Julia G. S. Rocha, Luam S. de Paiva, Rene O. Medrano-T
Summary: This paper studies a logistic-like and Gauss coupled maps model to investigate the period-adding phenomenon, revealing the complete process of forming complex sets of period-adding periodicity by changing control parameters in a closed domain of isoperiodicity.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Interdisciplinary Applications
Xin Yang, GuangJun Zhang, XueRen Li, Dong Wang
Summary: The study investigated the firing activities of neurons using fractional-order neuronal models, leading to the discovery of novel phenomena like Hopf bifurcation and firing pattern transitions induced by external current stimulus. The fractional-order model exhibited more diverse dynamic behaviors compared to integer-order models under different external current stimuli.
Article
Engineering, Mechanical
Halgurd Taher, Daniele Avitabile, Mathieu Desroches
Summary: We report a detailed analysis on the emergence of bursting in a recently developed neural mass model that includes short-term synaptic plasticity. The study reveals the importance of synaptic dynamics in bursting activity and the complex process of bursting initiation.
NONLINEAR DYNAMICS
(2022)
Article
Automation & Control Systems
Xiaoling Wang, Housheng Su, Fan Zhang, Guanrong Chen
Summary: This article investigates the state estimation problem of a continuous-time linear time-invariant system in the presence of unknown external disturbance and measurement noise. A robust distributed interval observer is designed, which consists of a group of sensors communicating through a directed graph. The communication, heterogeneity, and undetectability of the sensors impose stringent requirements on the observer construction. To address these restrictions, an internally positive representation from a single agent system is introduced. Numerical simulations are conducted to validate the theoretical results.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2023)
Article
Automation & Control Systems
Xu Zhang, Guanrong Chen
Summary: A new geometric criterion is developed to determine the existence of chaos in continuous-time autonomous systems in three-dimensional Euclidean spaces. This criterion differs from traditional methods as it does not rely on equilibrium points or the condition of transversal homoclinic or heteroclinic orbit of a Poincare map.
JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS
(2023)
Article
Mathematics, Interdisciplinary Applications
Xianjun Wang, Huaguang Gu, Yanbing Jia
Summary: Recent studies on neurodynamics have focused on paradoxical phenomena where inhibitory modulations enhance neuronal firing activity or excitatory modulations reduce firing activity. In this paper, the authors identify that fast and slow excitatory autapses induce opposite responses in a neuronal model. The fast decay of the excitatory autapse is found to be the essential factor for reducing bursting activity, while the slow decay of the autapse leads to increased bursting activity.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Computer Science, Artificial Intelligence
Yang Lou, Ruizi Wu, Junli Li, Lin Wang, Chang-Bing Tang, Guanrong Chen
Summary: This study proposes an efficient robustness predictor based on multiple convolutional neural networks (mCNN-RP) for predicting the network connectivity robustness. By classifying and estimating networks, it can accurately predict the connectivity robustness of different complex networks and outperforms existing prediction measures.
Article
Engineering, Mechanical
Yongxia Yang, Yuye Li, Huaguang Gu, Changsheng Qi
Summary: This paper investigates the opposite roles of inhibitory autapses with fast and slow time scales on modulating bursting activities in theoretical models, providing a novel viewpoint on inhibitory autapse and bursting in brain neurons. The results show that fast and slow inhibitory autapses induce enhancement and reduction of bursting activities respectively, and the underlying bifurcation mechanisms and dynamics of autaptic current are acquired.
NONLINEAR DYNAMICS
(2023)
Article
Automation & Control Systems
Yong Wang, Zhuo Liu, Leo Yu Zhang, Fabio Pareschi, Gianluca Setti, Guanrong Chen
Summary: This article performs a theoretical study on pseudorandom number generation using the well-studied 2-D coupled map lattice (2D CML). It proposes a method to extract uniformly distributed independent bits from the system orbits and demonstrates its effectiveness through simulation experiments.
IEEE TRANSACTIONS ON CYBERNETICS
(2023)
Article
Physics, Multidisciplinary
Xianjun Wang, Huaguang Gu, Yanbing Jia
Summary: This study found that the inhibition-induced enhancement or paradoxical response of firing is related to Hopf bifurcation instead of the saddle-node bifurcation on an invariant cycle (SNIC), due to the negative threshold and rotated vector fields. By adjusting the vector fields through changing multiple parameters, the condition for the paradoxical response and negative threshold is extended to SNIC near a co dimension-2 bifurcation appearing prior to the Hopf bifurcation, which establishes a comprehensive relationship between bifurcations and threshold. The results, especially for a specific current, can effectively explain the enhanced firing and seizure induced by inhibitory interneuron, suggesting that SNIC far from the co dimension-2 bifurcation of pyramidal neuron can potentially prevent seizure.
Article
Automation & Control Systems
Bing Mao, Xiaoqun Wu, Jinhu Lu, Guanrong Chen
Summary: This article investigates the uniformly predefined-time bounded consensus of leader-following multiagent systems with unknown system nonlinearity and external disturbance. Distributed adaptive fuzzy control is used to analyze and design the system, achieving global consensus within a predefined time.
IEEE TRANSACTIONS ON CYBERNETICS
(2023)
Article
Automation & Control Systems
Jie-Ning Wu, Xiang Li, Guanrong Chen
Summary: This article examines the controllability of multi-input/multi-output linear time-invariant systems in a snapback interlayer coupling framework. It establishes necessary and sufficient conditions for the controllability of three-layer snapback networks and obtains controllability conditions for the superposition of these networks. These conditions are related to smaller scale factor networks and illustrate the impact of interlayer coupling frameworks, intralayer network topologies, node dynamics, inner interactions, and external control inputs on the controllability of snapback networks. The controllability conditions of three-layer snapback networks are also extended to the M-layer setting. Several examples are provided to illustrate the effectiveness of these controllability conditions.
IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS
(2023)
Article
Mathematics
Jiali Wang, Changbing Tang, Jianquan Lu, Guanrong Chen
Summary: In this paper, a decision optimization method based on zero-determinant (ZD) strategies is proposed to help workers in a crowdsourcing system make optimal decisions under incomplete information. The problem is formulated as an iterated game with incomplete information, and the optimal decision of workers in terms of ZD strategies is analyzed. Numerical simulations are conducted to demonstrate the performances of different strategies and the impact of parameters on the payoffs of workers.
Article
Automation & Control Systems
Wenbo Hu, Fei Chen, Linying Xiang, Guanrong Chen
Summary: This article studies coordinated tracking of underactuated and uncertain autonomous surface vehicles (ASVs) via model-reference reinforcement learning control. It is demonstrated that the proposed algorithm has a better performance over baseline control and effectively improves the training efficiency over reinforcement learning.
IEEE TRANSACTIONS ON CYBERNETICS
(2023)
Article
Automation & Control Systems
Zhen Liu, Liangguang Pan, Guanrong Chen
Summary: In this article, a computational model called link-information augmented twin autoencoders is proposed to remove noisy links from observed network and recover the real network. Extensive experiments show that the proposed model outperforms other methods in network denoising and provides interpretable evidence to support its superiority.
IEEE TRANSACTIONS ON CYBERNETICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Yuqian Zhou, Guanrong Chen, Jibin Li
Summary: By applying the techniques from dynamical systems and singular traveling wave theory developed by Li and Chen [2007] to analyze the traveling wave system of the cubic Camassa-Holm type equation, it has been discovered that the bifurcation portraits of this equation exhibit all possible exact explicit bounded solutions (solitary wave solutions, periodic wave solutions, peakon as well as periodic peakons) under different parameter conditions. A total of 19 explicit exact parametric representations of the traveling wave system of the Camassa-Holm type equation are provided.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2023)
Article
Computer Science, Artificial Intelligence
Jiajun Zhou, Zhi Chen, Min Du, Lihong Chen, Shanqing Yu, Guanrong Chen, Qi Xuan
Summary: In this paper, robust community detection methods are proposed to improve the performance and robustness of community detection for real-world networks. By enhancing network structure through two generic algorithms, significant performance improvement is achieved for representative community detection algorithms. Additionally, the new methods also optimize the network structure and enhance robustness against adversarial attack.
IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING
(2023)
Article
Mathematics, Applied
Zhensu Wen, Guanrong Chen
Summary: This paper uses the methodology of dynamical systems and singular traveling wave theory to prove the existence of all possible bounded solutions of the traveling wave system in the Hertz chain model under different parameter conditions. Furthermore, it obtains 23 exact explicit parametric representations for various types of traveling wave systems.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S
(2023)
