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
Engineering, Mechanical
Miaomiao Xing, Zhuoqin Yang, Yong Chen
Summary: This study investigates the effect of temperature on the bursting discharge behavior of temperature-sensitive ion channels in neurons. The results show that an increase in temperature can promote the generation of bursting discharge, but eventually the bursting discharge phenomenon disappears. It is also found that even if the dynamic paths are consistent, the bursting discharge types and waveforms may be different, and vice versa.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Yi Lin, Wenbo Liu, Cheng Hang
Summary: It is important to construct physical hardware circuits that can reproduce abundant electrical activities of neurons for neuron-based engineering applications. In this study, a novel third-order nonautonomous memristive FitzHugh-Nagumo (FHN) neuron circuit is designed, which can generate abundant electrical activities with the use of a memristive-diode-bridge (MDB) emulator. The characteristics and dynamical behaviors of the circuit are analyzed through theoretical analysis, numerical simulation, and hardware experiments, revealing various non-chaotic firing activities.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Engineering, Mechanical
Linan Guan, Huaguang Gu, Zhiguo Zhao
Summary: The study demonstrates the modulation of resonance by I-h current in a bursting neuron model, which closely matches experimental observations. It reveals the modulation patterns of I-h current on the frequency and amplitude of resonance, as well as the mechanisms underlying subthreshold and suprathreshold resonance.
NONLINEAR DYNAMICS
(2021)
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
Engineering, Mechanical
Huijun Xu, Zhengdi Zhang, Miao Peng
Summary: The paper investigates the influence of the coupling of two scales on the dynamics of a piecewise smooth dynamical system. A relatively simple model with two switching boundaries is taken as an example to demonstrate four different types of bursting oscillations. The equilibrium branches and bifurcations of the fast subsystem under periodic excitation are explored using theoretical and numerical methods, and the mechanism of the bursting oscillations is analyzed in detail.
NONLINEAR DYNAMICS
(2022)
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
Mathematics, Interdisciplinary Applications
Yibo Xia, Shi Hua, Qinsheng Bi
Summary: The main purpose of this paper is to demonstrate that parts of the trajectory for chaotic bursting oscillations may oscillate according to different limit cycles, indicating the existence of orderly movement within chaos. By introducing a slow-varying controlling term, bursting oscillations can be observed, along with the presence of multiple periodic windows in the chaotic region.
CHAOS SOLITONS & FRACTALS
(2023)
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
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, Applied
Fang Wu, Lihong Huang, Jiafu Wang
Summary: This work focuses on the bifurcation of periodic orbits in a perturbed piecewise smooth system with a generalized heteroclinic loop connecting a hyperbolic critical point and a quadratic tangential singularity. By constructing displacement functions dependent on the perturbation parameter epsilon and time t, the conditions for the existence of a homoclinic loop and a sliding generalized heteroclinic loop are obtained. A concrete example is provided to demonstrate the occurrence of corresponding phenomena under suitable perturbations of the generalized heteroclinic loop.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
(2022)
Article
Mathematics
Danqi Feng, Yu Chen, Quanbao Ji
Summary: This study explores the numerical computation of Hopf bifurcation in the Chay model to illustrate the emergence of neuronal bursting induced by variations in the conductance of the Ca2+-sensitive IC+ channel. The results show that the formation and removal of various firing activities in this model are due to two subcritical Hopf bifurcations of equilibrium based on theoretical computation.
ELECTRONIC RESEARCH ARCHIVE
(2023)
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, Applied
Xindong Ma, Qinsheng Bi, Lifeng Wang
Summary: This paper theoretically presents complex bursting patterns caused by the coupling effect of different frequency scales in the RVDPDO driven by the external excitation term. Seven different kinds of bursting are studied using various analytical techniques, and the sensitivity of dynamical characteristics of RVDPDO to parameter variation is shown. The research validity is tested and verified through numerical simulations.
JOURNAL OF NONLINEAR SCIENCE
(2022)
Article
Physics, Multidisciplinary
Qianqian Han, Song-Mei Huan
Summary: This paper studies the inner dynamics of special sliding points in piecewise linear differential systems, including their definitions, existence, and stability. The explicit relationship between the system parameters and the existence, stability, and number of these special sliding points is obtained through the study of cases where the two zones are separated by straight lines. Concrete examples are provided to illustrate the main results and their application in studying DIBs.
