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Chinese Physics B 2012年第2期21卷 153-162页

作者：王发强张浩马西奎 State Key Laboratory of Electrical Insulation and Power Equipment School of Electrical EngineeringXi'an Jiaotong UniversityXi'an 710049China

In this paper, period-doubling bifurcation in a two-stage power factor correction converter is analyzed by using the method of incremental harmonic balance （IHB） and Floquet theory. A two-stage power factor correction converter typically employs a cascade configuration of a pre-regulator boost power factor correction converter with average current mode control to achieve a near unity power factor and a tightly regulated post-regulator DC-DC Buck converter with voltage feedback control to regulate the output voltage. Based on the assumption that the tightly regulated postregulator DC-DC Buck converter is represented as a constant power sink and some other assumptions, the simplified model of the two-stage power factor correction converter is derived and its approximate periodic solution is calculated by the method of IHB. And then, the stability of the system is investigated by using Floquet theory and the stable boundaries are presented on the selected parameter spaces. Finally, some experimental results are given to confirm the effectiveness of the theoretical analysis.

关键词： two-stage power factor correction converter incremental harmonic balance Floquet theory period-doubling bifurcation

Two-Dimensional Simulation of Spatial-Temporal Behaviors About period doubling bifurcation in an Atmospheric-Pressure Dielectric Barrier Discharge

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Plasma Science and Technology 2014年第2期16卷 110-117页

作者：张佼王艳辉王德真庄娟 School of Physics and Optoelectronic Technology Dalian University of Technology

As a spatially extended dissipated system, atmospheric-pressure dielectric barrier discharges （DBDs） could in principle possess complex nonlinear behaviors. In order to improve the stability and uniformity of atmospheric-pressure dielectric barrier discharges, studies on tem- poral behaviors and radial structure of discharges with strong nonlinear behaviors under different controlling parameters are much desirable. In this paper, a two-dimensional fluid model is devel- oped to simulate the radial discharge structure of period-doubling bifurcation, chaos, and inverse period-doubling bifurcation in an atmospheric-pressure DBD. The results show that the period-2n （n = 1, 2... ） and chaotic discharges exhibit nonuniform discharge structure. In period-2n or chaos, not only the shape of current pulses doesn＇t remains exactly the same from one cycle to an- other, but also the radial structures, such as discharge spatial evolution process and the strongest breakdown region, are different in each neighboring discharge event. Current-voltage characteris- tics of the discharge system are studied for further understanding of the radial structure.

关键词： atmospheric-pressure dielectric barrier discharge period-doubling bifurcation radial nonuniform structures

Cavity optomechanical chaos

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Fundamental Research 2023年第1期3卷 63-74页

作者： Gui-Lei Zhu Chang-Sheng Hu Ying Wu Xin-You Lü School of Physics Huazhong University of Science and TechnologyWuhan 430074China

Cavity optomechanics provides a powerful platform for observing many interesting classical and quantum nonlinear phenomena due to the radiation-pressure coupling between its optical and mechanical modes.In particular,the chaos induced by optomechanical nonlinearity has been of great concern because of its importance both in fundamental physics and potential applications ranging from secret information processing to optical communications.This review focuses on the chaotic dynamics in optomechanical systems.The basic theory of general nonlinear dynamics and the fundamental properties of chaos are introduced.Several nonlinear dynamical effects in optomechanical systems are demonstrated.Moreover,recent remarkable theoretical and experimental efforts in manipulating optomechanical chaotic motions are addressed.Future perspectives of chaos in hybrid systems are also discussed.

关键词： Cavity optomechanics Chaos Nonlinear dynamics Bistability period-doubling bifurcation

Determination of the exact range of the value of the parameter corresponding to chaos based on the Silnikov criterion

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Chinese Physics B 2010年第6期19卷 139-147页

作者：李伟义张琪昌王炜 Department of Mechanics School of Mechanical EngineeringTianjin University State Key Laboratory of Engines Tianjin University

Based on the Silnikov criterion, this paper studies a chaotic system of cubic polynomial ordinary differential equations in three dimensions. Using the Cardano formula, it obtains the exact range of the value of the parameter corresponding to chaos by means of the centre manifold theory and the method of multiple scales combined with Floque theory. By calculating the manifold near the equilibrium point, the series expression of the homoclinic orbit is also obtained. The space trajectory and Lyapunov exponent are investigated via numerical simulation, which shows that there is a route to chaos through period-doubling bifurcation and that chaotic attractors exist in the system. The results obtained here mean that chaos occurred in the exact range given in this paper. Numerical simulations also verify the analytical results.

关键词： Silnikov criterion chaos homoclinic orbit period-doubling bifurcation

Transitional function of DG to CA3 in the hippocampus

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Progress in Natural Science:Materials International 2007年第12期17卷 1436-1444页

作者： Yan Chuankui1 and Liu Shenquan2(1. Department of Mathematics, Hangzhou Normal University, Hangzhou 310036, China 2. Department of Applied Mathematics, School of Mathematical Sciences, South China University of Technology, Guangzhou 510640, China) Department of Mathematics Hangzhou Normal University Hangzhou 310036 China Department of Applied Mathematics School of Mathematical Sciences South China University of Technology Guangzhou 510640 China

Using single cell channel model, the transmission features of CA3-DG network in the hippocampus are investigated. The influence of the stimulation on discharge pattern of pyramidal neurons is analyzed, which shows that it starts with period spiking discharges, followed by period-doubling bifurcation to chaos, and period 3 discharge evolving into chaos, and ultimately a period of bursting discharges. By the synaptic model, the CA3-DG network model is constructed, which analyzes the summation of postsynaptic currents in the network, the influence of postsynaptic current on discharge rhythm as well as the mechanism of bursting discharges. The strong capacity of spatiotemporal encoding in the network indicates the features of CA3 network during the information transmission process in the hippocampus. The modeling result with time delay of the synaptic transmission is in accordance with the experimental phenomena of action potential in the hippocampus.

关键词： hippocampus CA3-DG period-doubling bifurcation chaos.

periodical bifurcation Analysis of a Type of Hematopoietic Stem Cell Model with Feedback Control

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International Journal of Modern Nonlinear Theory and Application 2023年第1期12卷 18-29页

作者： Suqi Ma Department of Mathematics China Agricultural University Beijing China

The delay feedback control brings forth interesting periodical oscillation bifurcation phenomena which reflect in Mackey-Glass white blood cell model. Hopf bifurcation is analyzed and the transversal condition of Hopf bifurcation is given. Both the period-doubling bifurcation and saddle-node bifurcation of periodical solutions are computed since the observed floquet multiplier overpass the unit circle by DDE-Biftool software in Matlab. The continuation of saddle-node bifurcation line or period-doubling curve is carried out as varying free parameters and time delays. Two different transition modes of saddle-node bifurcation are discovered which is verified by numerical simulation work with aids of DDE-Biftool.

关键词： bifurcation Saddle-Node bifurcation period-doubling bifurcation Hopf bifurcation Time Delay

Qualitative properties and bifurcations of discrete-time Bazykin–Berezovskaya predator–prey model

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International Journal of Biomathematics 2020年第6期13卷 23-51页

作者： A.A.Elsadany Qamar Din S.M.Salman Department of Mathematics College of Science and Humanities in Al-Kharj Prince Sattam bin Abdulaziz University Al-Kharj 11942Saudi Arabia Department of Basic Science Faculty of Computers and Informatics IsmailiaSuez Canal UniversityEgypt Department of Mathematics The University of Poonch Rawalakot Hawalakot 12350Pakistan Department of Mathematics Faculty of EducationAlexandria University AlexandriaEgypt

The positive connection between the total individual fitness and population density is called the demographic Allee effect.A demographic Allee effect with a critical population size or density is strong Allee effect.In this paper,discrete counterpart of Bazykin–Berezovskaya predator–prey model is introduced with strong Allee effects.The steady states of the model,the existence and local stability are examined.Moreover,proposed discrete-time Bazykin–Berezovskaya predator–prey is obtained via implementation of piecewise constant method for differential equations.This model is compared with its continuous counterpart by applying higher-order implicit Runge–Kutta method(IRK)with very small step size.The comparison yields that discrete-time model has sensitive dependence on initial conditions.By implementing center manifold theorem and bifurcation theory,we derive the conditions under which the discrete-time model exhibits flip and Niemark–Sacker bifurcations.Moreover,numerical simulations are provided to validate the theoretical results.

关键词： Bazykin-Berezovskaya model period-doubling bifurcation Niemark-Sacker bifurcation transcritical bifurcation Chaotic dynamics

bifurcation Analysis of a Neutrophil periodic Oscillation Model with State Feedback Control

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International Journal of Modern Nonlinear Theory and Application 2023年第1期12卷 1-17页

作者： Suqi Ma Department of Mathematics China Agricultural University Beijing China

The mathematical model of stem cells is discussed with its motivation to describe the tissue relationship by technically introducing a two compartments model. The clear link between the proliferation phase of stem cells and the circulating neutrophil phase is set forth after delay feedback control of the state variable of stem cells. Hopf bifurcation is discussed with varying free parameters and time delays. Based on the center manifold theory, the normal form near the critical point is computed and the stability of bifurcating periodical solution is rigorously discussed. With the aids of the artificial tool on-hand which implies how much tedious work doing by DDE-Biftool software, the bifurcating periodic solution after Hopf point is continued by varying time delay.

关键词： Neutrophil Phase Time Delay Hopf bifurcation DDE-Biftool Fold periodical bifurcation period-doubling bifurcation

period Multiplication in a Continuous Time Series of Radio-Frequency DBDs at Atmospheric Pressure

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Communications in Computational Physics 2012年第4期11卷 1226-1235页

作者： Jiao Zhang Yanhui Wang Dezhen Wang State Key Laboratory of Materials Modification by Laser Electronand Ion BeamsSchool of Physics and Optoelectronic TechnologyDalian University of TechnologyDalian 116024China

As a spatially extended dissipative system with strong nonlinearity,the radio-frequency(rf)dielectric-barrier discharges(DBDs)at atmospheric pressure possess complex spatiotemporal nonlinear behaviors.In this paper,the time-domain nonlinear behaviors of rf DBD in atmospheric argon are studied numerically by a onedimensional fluid model.Simulation results show that,under appropriate controlling parameters,the rf DBD can undergo a transition from single-period state to chaos through period doubling bifurcation with increasing discharge time,i.e.,the regular periodic oscillation and chaos can coexist in a long time series of the atmosphericpressure rf DBD.With increasing applied voltage amplitude,the duration of the periodic oscillation reduces gradually and chaotic zone increases,and finally the whole discharge series becomes completely chaotic state.This is different from conventional period doubling route to chaos.Moreover,the spatial characteristics of rf perioddoubling discharge and chaos,as well as the parameter range of various discharge behaviors occurring are also investigated in this paper.

关键词： Atmospheric radio-frequency discharge period-doubling bifurcation chaos

EXISTENCE OF periodIC SOLUTIONS TO A PERTURBED FOUR-DIMENSIONAL SYSTEM

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Annals of Differential Equations 2009年第1期25卷 46-53页

作者： Liu Xuanliang, Liu Yongqi, Meng Xiaoying (Dept. of Math., South China University of Technology, Guangzhou 510640) Dept. of Math. South China University of Technology Guangzhou 510640

Consider a k multiple closed orbit on an invariant surface of a four dimensional system, after a suitable perturbation, the closed orbit can generate periodic orbits and double-period orbits. Using bifurcation methods and techniques, sufficient conditions for the existence of periodic solutions to the perturbed four dimensional system are obtained, and the period-doubling bifurcations is discussed.

关键词： bifurcation periodic orbit period-doubling bifurcation