Article
Mathematics, Interdisciplinary Applications
Junting Gou, Xiaofang Zhang, Yibo Xia, Qinsheng Bi
Summary: This paper investigates the different types of bursting attractors that may appear in a vector field with Hopf bifurcation when periodic excitation is introduced. By treating the excitation term as a slow-varying bifurcation parameter, all possible equilibrium branches of the generalized autonomous system are derived. The trajectory of the system can visit four qualitatively different regions in the parameter space, leading to periodic symmetric oscillations, periodic symmetric mixed-mode oscillations, fold/Hopf/Hopf/fold and fold-Hopf/fold-Hopf bursting attractors.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2022)
Article
Automation & Control Systems
Hongbo Cao, Faqiang Wang
Summary: This article investigates the slow-scale instability occurring in the three-level T-type inverter with a passive memristive load. The average model of the inverter is constructed and harmonic balance method and Floquet theory are applied to explore the mechanism of the instability. Theoretical results show that the instability is caused by Hopf bifurcation in a frequency range higher than the line frequency but much lower than the switching frequency. The parameters for accurate analysis and the impact of different parameters on the stability boundary are discussed.
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
(2022)
Article
Computer Science, Information Systems
Ke Wang, Yizi Cheng, Zunbo Zhang, Fuhong Min
Summary: The paper investigates the asymmetric memristive diode bridge-based Sallen-Key Filter (AMSKF) by connecting an asymmetry diode bridge with a capacitor and an inductor to the Sallen-Key Filter. The stability of the circuit is discussed through equilibrium point analysis, and the dynamics of the circuit is found to be greatly affected by the negative feedback gain of the Sallen-Key Filter, as shown by the bifurcation diagram. Various oscillating behaviors are discovered using phase portraits and Lyapunov exponents, including six types of typical oscillating behaviors. The bifurcation mechanisms of the bursting oscillating behaviors are further researched using the fast-slow analysis method. Multisim experiments are conducted to validate the numerical simulation results, and it is found that the bursting oscillation with larger amplitude and wider periodic bursting range can be detected by adjusting the negative feedback gain compared to the Sallen-Key Filter cascaded with the symmetric memristive diode bridge.
Article
Mechanics
Miaorong Zhang, Qinsheng Bi
Summary: This paper investigates the normal form of a four-dimensional cubic order system with parametric excitation, revealing the presence of higher co-dimensional bifurcations in high dimensional slow-fast dynamical systems, leading to more complicated mechanisms for bursting oscillations. The study shows that the codimension-2 double Hopf bifurcation may result in the occurrence of bursting oscillations in four dimensions, with the trajectory switching between equilibrium branches of single-mode and mixed-mode solutions as the excitation amplitude increases.
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS
(2021)
Article
Acoustics
Juanjuan Huang, Qinsheng Bi
Summary: This study investigates bursting oscillations in a vector field with triple Hopf bifurcation, and observes the evolution of stable limit cycles and the synchronization behavior of state variables by introducing slow-varying external excitation. An interesting finding is the quasi-periodic behavior in the three-mode bursting oscillations.
JOURNAL OF SOUND AND VIBRATION
(2023)
Article
Engineering, Mechanical
Runxia Wang, Huaguang Gu, Hongtao Hua, Kaihua Ma
Summary: This paper successfully analyzes the mixed-mode oscillation (MMO) bursting modulated by two slow variables, and establishes the relationship between the pseudo-plateau burst and depolarization block/subcritical Hopf bifurcation of the fast subsystem, as well as the spike and coexisting firing/limit point bifurcation of cycles. It is also found that there is no quiescent state related to resting state or saddle-node bifurcation on an invariant cycle (SNIC), and the bursting trajectory exhibits a narrow shape around an oblique line in the (c, h) plane, with bifurcations along the line presenting a simple and effective candidate to characterize the bursting.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Youhua Qian, Danjin Zhang, Bingwen Lin
Summary: This study investigates the bursting oscillation mechanisms in systems with periodic excitation, analyzing different types of symmetric bursting oscillations and their bifurcation mechanisms through numerical simulations. The results show that these bursting oscillations exhibit symmetry in their patterns.
Article
Mathematics, Interdisciplinary Applications
Miaorong Zhang, Xiaofang Zhang, Qinsheng Bi
Summary: This paper focuses on the influence of two scales in the frequency domain on the behaviors of a typical dynamical system with a double Hopf bifurcation. An external periodic excitation is introduced to establish a theoretical model, and it is found that with the increase of the exciting amplitude, different types of bifurcations may be involved in the system, leading to several qualitatively different forms of bursting attractors.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2021)
Article
Engineering, Mechanical
Chunyan Gao, Fangqi Chen
Summary: The study demonstrates that transcription and translation delays act as bifurcation parameters driving oscillation behavior in a gene expression model, with their length determining the amplitude and period of the oscillations. Optimal parameter rates are also crucial for inducing limit-cycle oscillations. Additionally, transcription factor concentration serves as a signal inducing bifurcations and affecting delay effects on the system, with subcritical Hopf bifurcation occurring under small signal strength.
NONLINEAR DYNAMICS
(2021)
Article
Engineering, Mechanical
Feng Zhao, Xindong Ma, Shuqian Cao
Summary: This paper focuses on the periodic complex bursting dynamics in a hybrid Rayleigh-Van der Pol-Duffing oscillator driven by external and parametric slow-changing excitations. Different bursting modes are proposed and analyzed, and the theoretical analysis results are validated through numerical simulations. The study reveals the dependence of bursting patterns on system parameters and the influence of different stable attractors on the manifolds of the excited state oscillations.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics
Ivan Kipelkin, Svetlana Gerasimova, Davud Guseinov, Dmitry Pavlov, Vladislav Vorontsov, Alexey Mikhaylov, Victor Kazantsev
Summary: This article introduces a mathematical and experimental model of a neuronal oscillator with memristor-based nonlinearity. The mathematical model describes the dynamics of an electronic circuit implementing the FitzHugh-Nagumo neuron model. The nonlinear component of the circuit is the Au/Zr/ZrO2(Y)/TiN/Ti memristive device. This device is fabricated on an oxidized silicon substrate using magnetron sputtering. The circuit with this nonlinearity is described by a three-dimensional ordinary differential equation system. The article explores the effect of spontaneous self-oscillations, identifies a bifurcation scenario based on supercritical Andronov-Hopf bifurcation, and analyzes the dependence of the critical point on system parameters, particularly the size of the electrode area. Experimental demonstrations of self-oscillating and excitable modes are provided.
Article
Mathematics, Interdisciplinary Applications
Hao Dai, Zikun Han, Qiubao Wang
Summary: In this paper, a stochastic time-delay mathematical model of the feedback system of glucose-insulin endocrine regulation with noise effects is proposed. The hopf bifurcation of the system is obtained with the delay as the parameter. Considering the influence of time delay and noise, the random bifurcation of the system is obtained, and the occurrence of bursting phenomenon is found more likely in a noise environment.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Computer Science, Interdisciplinary Applications
Fei Yu, Yuanshi Wang
Summary: This paper investigates an extended predator-prey model with the consideration that predators' fear reduces prey reproduction and the search speed of predators is influenced by prey density. The results show that high levels of fear can stabilize the coexistence steady state, while low levels lead to periodic oscillation. The analysis also reveals that a relatively small search speed of predators promotes the stability of the coexistence steady state, while a large speed results in periodic oscillation. Enhancing prey's sensitivity to predation risk or slowing the predator search speed can stabilize the coexistence steady state.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2022)
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, Interdisciplinary Applications
Qinsheng Bi, Junting Gou
Summary: Hopf bifurcation is a common phenomenon that leads to transitions between quiescence and spiking states in bursting attractors. The number of bursting attractor types near a Hopf bifurcation point remains an open problem. In this study, by introducing a low-frequency external excitation to a normal form, we obtained four types of quasi-periodic bursting oscillations based on the equilibrium branches and bifurcations of the fast subsystem as the excitation varied. The mechanisms of these bursting oscillations were obtained through overlap of equilibrium branches and bifurcations in the autonomous system.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Neurosciences
Quan Xu, Tong Liu, Shoukui Ding, Han Bao, Ze Li, Bei Chen
Summary: This paper investigates the memristive electromagnetic induction effect in a bi-neuron network with heterogeneous neurons. Theoretical analysis reveals the stability of the network depends on memristor coupling strength and initial conditions. Numerical simulations demonstrate various dynamic behaviors and phase synchronization. Hardware experiments are conducted to confirm the results.
COGNITIVE NEURODYNAMICS
(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
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, 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
Quan Xu, Yiteng Wang, Bei Chen, Ze Li, Ning Wang
Summary: This study proposes a memristive Hodgkin-Huxley circuit based on second-order and first-order local active memristors (LAMs) to simulate the complex nonlinearities of sodium and potassium ion channels, thus generating abundant spiking firing patterns. Numerical simulations and hardware experiments demonstrate the effectiveness of the circuit in generating periodic and chaotic spiking firing patterns.
CHAOS SOLITONS & FRACTALS
(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, Mechanical
Quan Xu, Liping Huang, Ning Wang, Han Bao, Huagan Wu, Mo Chen
Summary: This paper introduces a two-dimensional memristive Chialvo neuron map with hyperchaotic dynamics by incorporating a memristor with sinusoidal mem-conductance function and hyper-tangent function modulated input into the one-dimensional Chialvo neuron map. The stability and dynamical behaviors of the map are analyzed theoretically and through numerical simulation. The results show that the 2D memristive Chialvo neuron map can generate initial-offset boosting behavior. Furthermore, a new encryption algorithm using hyperchaotic sequences is designed and tested, demonstrating good performance in image encryption.
NONLINEAR DYNAMICS
(2023)
Article
Engineering, Mechanical
Han Bao, Zhuguan Chen, Mo Chen, Quan Xu, Bocheng Bao
Summary: This article investigates the dynamical behavior of neural networks with changeable synaptic weights, and discovers through experiments and numerical simulations that under certain conditions, the tri-neuron memristive-cyclic Hopfield neural network can generate spatial multi-scroll chaotic attractors and spatial initial-offset coexisting attractors.
NONLINEAR DYNAMICS
(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)
Article
Mathematics, Interdisciplinary Applications
Han Bao, Xihong Yu, Yunzhen Zhang, Xiaofeng Liu, Mo Chen
Summary: This paper synthesizes a neural network without equilibrium point by connecting two Hindmarsh-Rose neurons with memristor coupling. The synchronization dynamics and energy diversity are regulated by the coupling strength and initial condition of the memristor. Experimental results validate the numerical ones.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Automation & Control Systems
Mo Chen, Ankai Wang, Huagan Wu, Bei Chen, Quan Xu
Summary: This article proposes a dc-offset strategy for flexible control of hidden and multistable dynamics. It demonstrates the feasibility of this strategy through a modified Chua's circuit with multiple dc control signals. The kinetic effects of these control signals are systematically demonstrated. The article also shows how to induce hidden and coexisting behaviors by configuring the initial voltages of capacitors using dc voltage signals.
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
(2023)
