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Kopel系统中Neimark-Sacker分岔的不变曲线
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作者 袁利国 魏周超 郭军 《动力学与控制学报》 2023年第1期81-88,共8页
首先阐述了Kopel系统的复杂动力学的研究进展.再基于分岔与规范型理论,给出了Kopel系统的Neimark-Sacker(N-S)分岔的一类新证明,并得到N-S分岔所产生不变曲线的近似表达式.最后,对N-S分岔及不变曲线进行了数值模拟分析,验证了理论推导... 首先阐述了Kopel系统的复杂动力学的研究进展.再基于分岔与规范型理论,给出了Kopel系统的Neimark-Sacker(N-S)分岔的一类新证明,并得到N-S分岔所产生不变曲线的近似表达式.最后,对N-S分岔及不变曲线进行了数值模拟分析,验证了理论推导所得结果,并对N-S分岔中的扰动参数与不变曲线的近似表达式中参数之间的相互影响进行了分析.所有这些分析对Kopel系统的已有动力学研究是一个补充,对其经济现象的内在规律提供了理论支撑. 展开更多
关键词 Kopel系统 neimark-sacker分岔 不变曲线 不动点
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Left bundle branch pacing vs biventricular pacing in heart failure patients with left bundle branch block:A systematic review and meta-analysis 被引量:1
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作者 Farah Yasmin Abdul Moeed +7 位作者 Rohan Kumar Ochani Hamna Raheel Malik Ali Ehtsham Awan Ayesha Liaquat Arisha Saleem Muhammad Aamir Nael Hawwa Salim Surani 《World Journal of Cardiology》 2024年第1期40-48,共9页
BACKGROUND Left bundle branch pacing(LBBP)is a novel pacing modality of cardiac resynchronization therapy(CRT)that achieves more physiologic native ventricular activation than biventricular pacing(BiVP).AIM To explore... BACKGROUND Left bundle branch pacing(LBBP)is a novel pacing modality of cardiac resynchronization therapy(CRT)that achieves more physiologic native ventricular activation than biventricular pacing(BiVP).AIM To explore the validity of electromechanical resynchronization,clinical and echocardiographic response of LBBP-CRT.METHODS Systematic review and Meta-analysis were conducted in accordance with the standard guidelines as mentioned in detail in the methodology section.RESULTS In our analysis,the success rate of LBBP-CRT was determined to be 91.1%.LBBP CRT significantly shortened QRS duration,with significant improvement in echocardiographic parameters,including left ventricular ejection fraction,left ventricular end-diastolic diameter and left ventricular end-systolic diameter in comparison with BiVP-CRT.CONCLUSION A significant reduction in New York Heart Association class and B-type natriuretic peptide levels was also observed in the LBBP-CRT group vs BiVP-CRT group.Lastly,the LBBP-CRT cohort had a reduced pacing threshold at follow-up as compared to BiVP-CRT. 展开更多
关键词 Left bundle branch pacing Biventricular pacing QRS duration Left ventricular ejection fraction Heart failure
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Left bundle branch area pacing combined with implantable cardioverter-defibrillator treatment for heart failure after myocardial infarction
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作者 Bing-Chen GUO Jian XU +4 位作者 Yan-Zong LIU Guo-Qing DU Bo YU Shu-Feng LI Wen-Juan DU 《Journal of Geriatric Cardiology》 SCIE CAS CSCD 2024年第5期577-582,共6页
Left bundle branch area pacing(LBBAP)has emerged as a new physiological pacing mode.Previous studies have confirmed the feasibility and efficacy of LBBAP for cardiac resynchronization therapy(CRT)in heart failure(HF)p... Left bundle branch area pacing(LBBAP)has emerged as a new physiological pacing mode.Previous studies have confirmed the feasibility and efficacy of LBBAP for cardiac resynchronization therapy(CRT)in heart failure(HF)patients with left bundle branch block(LBBB)and a narrower QRS duration(QRSd)to have a higher percentage of super responders,and lower pacing thresholds than biventricular pacing(BiVP). 展开更多
关键词 PACING branch BUNDLE
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Unilateral branch retinal artery occlusion in association with COVID-19:a case report
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作者 Kunihiko Hirosawa Takenori Inomata +7 位作者 Jaemyoung Sung Yuki Morooka Tianxiang Huang Yasutsugu Akasaki Yuichi Okumura Ken Nagino Kaho Omori Shintaro Nakao 《International Journal of Ophthalmology(English edition)》 SCIE CAS 2024年第4期777-782,共6页
Dear Editor,I am Kunihiko Hirosawa of the Department of Ophthalmology at Juntendo University Hospital.I am writing to present a case of concomitant Coronavirus Disease 2019(COVID-19)with branch retinal artery occlusio... Dear Editor,I am Kunihiko Hirosawa of the Department of Ophthalmology at Juntendo University Hospital.I am writing to present a case of concomitant Coronavirus Disease 2019(COVID-19)with branch retinal artery occlusion(BRAO).BRAO presents as a sudden,painless loss of vision on the afflicted side and is most often focal in nature[1]. 展开更多
关键词 branch COV OCCLUSION
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Thermal pretreatment of willow branches impacts yield and pore development of activated carbon in subsequent activation with ZnCl_(2) via modifying cellulose structure
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作者 Linghui Kong Chao Li +7 位作者 Runxing Sun Shu Zhang Yi Wang Jun Xiang Song Hu Dong Wang Chuanjun Leng Xun Hu 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 2024年第5期227-237,共11页
Development of pore structures of activated carbon(AC)from activation of biomass with ZnCl_(2) relies on content and structure of cellulose/hemicellulose in the feedstock.Thermal pretreatment of biomass could induce d... Development of pore structures of activated carbon(AC)from activation of biomass with ZnCl_(2) relies on content and structure of cellulose/hemicellulose in the feedstock.Thermal pretreatment of biomass could induce dehydration and/or aromatization to change the structure of cellulose/hemicellulose.This might interfere with evolution of structures of AC,which was investigated herein via thermal pretreatment of willow branch(WB)from 200 to 360℃and the subsequent activation with ZnCl_(2) at 550℃.The results showed that thermal pretreatment at 360℃(WB-360)could lead to substantial pyrolysis to form biochar,with a yield of 31.9%,accompanying with nearly complete destruction of cellulose crystals and remarkably enhanced aromatic degree.However,cellulose residual in WB-360 could still be activated to form AC-360 with specific surface area of 1837.9 m~2·g^(-1),which was lower than that in AC from activation of untreated WB(AC-blank,2077.8 m~2·g^(-1)).Nonetheless,the AC-200 from activation of WB-200 had more developed pores(2113.9 m~2·g^(-1))and superior capability for adsorption of phenol,due to increased permeability of ZnCl_(2) to the largely intact cellulose structure in WB-200.The thermal pretreatment did increase diameters of micropores of AC but reduced the overall yield of AC(26.8%for AC-blank versus 18.0%for AC-360),resulting from accelerated cracking but reduced intensity of condensation.In-situ infrared characterization of the activation showed that ZnCl_(2) mainly catalyzed dehydration,dehydrogenation,condensation,and aromatization but not cracking,suppressing the formation of derivatives of cellulose and lignin in bio-oil.The thermal pretreatment formed phenolic-OH and C=O with higher chemical innerness,which changed the reaction network in activation,shifting morphology of fibrous structures in AC-blank to“melting surface”in AC-200 or AC-280. 展开更多
关键词 Thermal pretreatment Activation with ZnCl_(2) Willow branch Activated carbon Biochar
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DCFNet:An Effective Dual-Branch Cross-Attention Fusion Network for Medical Image Segmentation
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作者 Chengzhang Zhu Renmao Zhang +5 位作者 Yalong Xiao Beiji Zou Xian Chai Zhangzheng Yang Rong Hu Xuanchu Duan 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第7期1103-1128,共26页
Automatic segmentation of medical images provides a reliable scientific basis for disease diagnosis and analysis.Notably,most existing methods that combine the strengths of convolutional neural networks(CNNs)and Trans... Automatic segmentation of medical images provides a reliable scientific basis for disease diagnosis and analysis.Notably,most existing methods that combine the strengths of convolutional neural networks(CNNs)and Transformers have made significant progress.However,there are some limitations in the current integration of CNN and Transformer technology in two key aspects.Firstly,most methods either overlook or fail to fully incorporate the complementary nature between local and global features.Secondly,the significance of integrating the multiscale encoder features from the dual-branch network to enhance the decoding features is often disregarded in methods that combine CNN and Transformer.To address this issue,we present a groundbreaking dual-branch cross-attention fusion network(DCFNet),which efficiently combines the power of Swin Transformer and CNN to generate complementary global and local features.We then designed the Feature Cross-Fusion(FCF)module to efficiently fuse local and global features.In the FCF,the utilization of the Channel-wise Cross-fusion Transformer(CCT)serves the purpose of aggregatingmulti-scale features,and the Feature FusionModule(FFM)is employed to effectively aggregate dual-branch prominent feature regions from the spatial perspective.Furthermore,within the decoding phase of the dual-branch network,our proposed Channel Attention Block(CAB)aims to emphasize the significance of the channel features between the up-sampled features and the features generated by the FCFmodule to enhance the details of the decoding.Experimental results demonstrate that DCFNet exhibits enhanced accuracy in segmentation performance.Compared to other state-of-the-art(SOTA)methods,our segmentation framework exhibits a superior level of competitiveness.DCFNet’s accurate segmentation of medical images can greatly assist medical professionals in making crucial diagnoses of lesion areas in advance. 展开更多
关键词 Convolutional neural networks Swin Transformer dual branch medical image segmentation feature cross fusion
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A Light and Simplified Branch Bending Method for Young Pear Trees
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作者 Jintao XU Longfei LI +3 位作者 Minghui JI Huan LIU Lijuan GAO Baofeng HAO 《Plant Diseases and Pests》 2024年第2期19-21,共3页
Aiming at high cost and low efficiency of conventional branch bending method in the modern intensive planting and labor-saving cultivation mode of young pear trees,this paper provides a new branch bending method with ... Aiming at high cost and low efficiency of conventional branch bending method in the modern intensive planting and labor-saving cultivation mode of young pear trees,this paper provides a new branch bending method with wide source of raw materials,cheap price and simple operation,which is also suitable for the management of low-age branches in the process of high grafting and upgrading of traditional big trees. 展开更多
关键词 Pear tree Light and simplified branch bending METHOD
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Adsorption Effect of Phosphate Modified Grape Branch Biochar on Cd2
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作者 Yu Han Yuming Yin +4 位作者 Hao Zhang Sijing Sun Zuzhi Huang Yishu Deng Li Bao 《Journal of Geoscience and Environment Protection》 2024年第4期59-77,共19页
Two major problems facing agriculture at present are soil pollution and the disposal of solid wastes generated during plant growth. The method of preparing biochar from solid wastes produced by plants is a means of ma... Two major problems facing agriculture at present are soil pollution and the disposal of solid wastes generated during plant growth. The method of preparing biochar from solid wastes produced by plants is a means of maximizing the use of resources to combat the problem of soil pollution. In this study, we did not choose straw in the traditional sense but the waste branches from grape pruning, which has higher lignin cellulose, as the raw material. The biochar derived from grape branches pyrolyzed at 300˚C for two hours was utilized as a raw material to prepare modified biochar with varying concentrations of phosphoric acid. The adsorption performance and mechanism of Cd<sup>2 </sup> were explored through experiments involving different concentrations, addition amounts, reaction times, kinetic analyses, and isothermal adsorption tests. The findings indicated that the optimal adsorption of Cd<sup>2 </sup> occurred with a 20% phosphoric acid concentration, achieving the highest adsorption rate of 84.62%. At a dosage of 10 g/L, the maximum adsorption capacity reached 7.02 mg/g. The adsorption kinetics and isothermal adsorption of Cd<sup>2 </sup> on biochar modified with 0.2% phosphoric acid (0.2 PB) closely followed the pseudo-first-order kinetics model (R<sup>2</sup> > 0.98) and the Freundlich model (R<sup>2</sup> > 0.97), respectively. This suggests that the adsorption process involves both physical and chemical mechanisms. SEM and FTIR analyses revealed that phosphoric acid modification primarily increased the biochar’s specific surface area and enhanced certain original functional groups. The adsorption process predominantly involved rapid ion diffusion and chemical adsorption, as confirmed by kinetic analysis and isothermal adsorption model analysis. In summary, the adsorption efficiency of 0.2 PB significantly improved, showing potential and feasibility for heavy metal remediation in soil. This supports the environmentally friendly concept of “treating waste with waste”. 展开更多
关键词 Phosphate Modified Grape branch Biochar Adsorbs CD
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Left bundle branch pacing set to outshine biventricular pacing for cardiac resynchronization therapy?
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作者 Akash Batta Juniali Hatwal 《World Journal of Cardiology》 2024年第4期186-190,共5页
The deleterious effects of long-term right ventricular pacing necessitated the search for alternative pacing sites which could prevent or alleviate pacinginduced cardiomyopathy.Until recently,biventricular pacing(BiVP... The deleterious effects of long-term right ventricular pacing necessitated the search for alternative pacing sites which could prevent or alleviate pacinginduced cardiomyopathy.Until recently,biventricular pacing(BiVP)was the only modality which could mitigate or prevent pacing induced dysfunction.Further,BiVP could resynchronize the baseline electromechanical dssynchrony in heart failure and improve outcomes.However,the high non-response rate of around 20%-30%remains a major limitation.This non-response has been largely attributable to the direct non-physiological stimulation of the left ventricular myocardium bypassing the conduction system.To overcome this limitation,the concept of conduction system pacing(CSP)came up.Despite initial success of the first CSP via His bundle pacing(HBP),certain drawbacks including lead instability and dislodgements,steep learning curve and rapid battery depletion on many occasions prevented its widespread use for cardiac resynchronization therapy(CRT).Subsequently,CSP via left bundle branch-area pacing(LBBP)was developed in 2018,which over the last few years has shown efficacy comparable to BiVP-CRT in small observational studies.Further,its safety has also been well established and is largely free of the pitfalls of the HBP-CRT.In the recent metanalysis by Yasmin et al,comprising of 6 studies with 389 participants,LBBPCRT was superior to BiVP-CRT in terms of QRS duration,left ventricular ejection fraction,cardiac chamber dimensions,lead thresholds,and functional status amongst heart failure patients with left bundle branch block.However,there are important limitations of the study including the small overall numbers,inclusion of only a single small randomized controlled trial(RCT)and a small follow-up duration.Further,the entire study population analyzed was from China which makes generalizability a concern.Despite the concerns,the meta-analysis adds to the growing body of evidence demonstrating the efficacy of LBBP-CRT.At this stage,one must acknowledge that the fact that still our opinions on this technique are largely based on observational data and there is a dire need for larger RCTs to ascertain the position of LBBPCRT in management of heart failure patients with left bundle branch block. 展开更多
关键词 Biventricular pacing Cardiac resynchronization therapy Conduction system pacing Left bundle branch-area pacing Left bundle branch block Electromechanical dssynchrony
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Synthesis of Branched Polyethylene via Bulky α-Diimine Nickel(II)-Catalyzed Ethylene Chain-Walking Polymerization
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作者 Zhengquan Dong Pei Li +1 位作者 Guoyong Xu Fuzhou Wang 《Open Journal of Organic Polymer Materials》 2024年第1期1-12,共12页
The catalysis of olefin polymerization through the chain-walking process is a subject of great interest. In this contribution, the successful synthesis of a Brookhart-type unsymmetrical α-diimine nickel catalyst Ni, ... The catalysis of olefin polymerization through the chain-walking process is a subject of great interest. In this contribution, the successful synthesis of a Brookhart-type unsymmetrical α-diimine nickel catalyst Ni, which contains both dibenzhydryl and phenyl groups, was determined by X-ray crystallography. The compound has a pseudo-tetrahedral geometry at the Ni center, showing pseudo-C2-symmetry. Upon activation with modified methylaluminoxane (MMAO), Ni1 exhibits high catalytic activity up to 1.02 × 107 g PE (mol Ni h)−1 toward ethylene polymerization, enabling the synthesis of high molecular weight branched polyethylene. The molecular weights and branching densities could be tuned over a very wide range. The polymerization results indicated the possibility of precise microstructure control, depending on the polymerization temperature. The branching densities were decreased with increasing the polymerization temperature. 展开更多
关键词 Ethylene Polymerization α-Diimine Ni(II) Complex Chain-Walking Polymerization branched Polyethylene
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Attribute Reduction Method Based on Sequential Three-Branch Decision Model
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作者 Peiyu Su Fu Li 《Applied Mathematics》 2024年第4期257-266,共10页
Attribute reduction is a research hotspot in rough set theory. Traditional heuristic attribute reduction methods add the most important attribute to the decision attribute set each time, resulting in multiple redundan... Attribute reduction is a research hotspot in rough set theory. Traditional heuristic attribute reduction methods add the most important attribute to the decision attribute set each time, resulting in multiple redundant attribute calculations, high time consumption, and low reduction efficiency. In this paper, based on the idea of sequential three-branch decision classification domain, attributes are treated as objects of three-branch division, and attributes are divided into core attributes, relatively necessary attributes, and unnecessary attributes using attribute importance and thresholds. Core attributes are added to the decision attribute set, unnecessary attributes are rejected from being added, and relatively necessary attributes are repeatedly divided until the reduction result is obtained. Experiments were conducted on 8 groups of UCI datasets, and the results show that, compared to traditional reduction methods, the method proposed in this paper can effectively reduce time consumption while ensuring classification performance. 展开更多
关键词 Attribute Reduction Three-branch Decision Sequential Three-branch Decision
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三自由度含间隙碰撞振动系统Neimark-Sacker分岔的反控制 被引量:9
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作者 伍新 文桂林 +1 位作者 徐慧东 何莉萍 《物理学报》 SCIE EI CAS CSCD 北大核心 2015年第20期89-96,共8页
分岔反控制作为传统分岔控制的逆问题,其目的是在预先指定的系统参数点通过控制主动设计出具有所期望特性的分岔解.以一类三自由度含间隙双面碰撞振动系统为研究对象,在不改变原系统平衡解结构的前提下,考虑到在碰撞振动系统反控制过程... 分岔反控制作为传统分岔控制的逆问题,其目的是在预先指定的系统参数点通过控制主动设计出具有所期望特性的分岔解.以一类三自由度含间隙双面碰撞振动系统为研究对象,在不改变原系统平衡解结构的前提下,考虑到在碰撞振动系统反控制过程中由Poincaré映射的隐式特点和传统的映射Neimark-Sacker分岔临界准则带来的困难,通过对原系统施加线性反馈控制器并利用不直接依赖于特征值计算的Neimark-Sacker分岔显式临界准则研究了此系统的分岔反控制问题.首先对原系统施加线性反馈控制,建立闭环控制系统的六维Poincaré映射.由于六维映射的雅克比矩阵的特征值没有解析的表达式,利用高维映射Neimark-Sacker分岔的显式临界准则,获得了系统出现拟周期碰撞振动运动的控制参数区域.然后采用中心流形-正则形方法分析了拟周期分岔解的稳定性.数值仿真结果表明本文方法可以在指定的系统参数点通过控制设计出稳定的拟周期碰撞运动. 展开更多
关键词 neimark-sacker分岔 分岔反控制 稳定性 碰撞振动系统
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一类具分段常数变量的捕食-食饵系统的Neimark-Sacker分支 被引量:3
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作者 陈斯养 靳宝 《生态学报》 CAS CSCD 北大核心 2015年第7期2339-2348,共10页
讨论了具时滞与分段常数变量的捕食-食饵生态模型的稳定性及Neimark-Sacker分支;通过计算得到连续模型对应的差分模型,基于特征值理论和Schur-Cohn判据得到正平衡态局部渐进稳定的充分条件;以食饵的内禀增长率为分支参数,运用分支理论... 讨论了具时滞与分段常数变量的捕食-食饵生态模型的稳定性及Neimark-Sacker分支;通过计算得到连续模型对应的差分模型,基于特征值理论和Schur-Cohn判据得到正平衡态局部渐进稳定的充分条件;以食饵的内禀增长率为分支参数,运用分支理论和中心流形定理分析了Neimark-Sacker分支的存在性与稳定性条件;通过举例和数值模拟验证了理论的正确性。 展开更多
关键词 分段常数变量 时滞 稳定性 neimark-sacker分支
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一类潜伏期有传染力的离散SEIR传染病模型的Neimark-Sacker分岔 被引量:1
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作者 杜文举 秦爽 +1 位作者 张建刚 俞建宁 《暨南大学学报(自然科学与医学版)》 CAS CSCD 北大核心 2016年第6期518-524,共7页
目的:传染病模型的研究能更好地显示疾病发展过程,揭示其流行规律,寻求对其预防及控制的最优策略.方法:欧拉向前差分法、Neimark-Sacker分岔准则、Kuznetsov's理论和中心流形定理.结果:构造了1个新的离散的潜伏期具有传染力的SEIR... 目的:传染病模型的研究能更好地显示疾病发展过程,揭示其流行规律,寻求对其预防及控制的最优策略.方法:欧拉向前差分法、Neimark-Sacker分岔准则、Kuznetsov's理论和中心流形定理.结果:构造了1个新的离散的潜伏期具有传染力的SEIR传染病模型.主要研究离散SEIR传染病模型的动力学性质、讨论系统平衡点的存在性,并进一步分析系统无病平衡点的稳定性.结论:对g EIR传染模型在无病平衡点处Neimark-Sacker分岔的存在性、稳定性和方向进行详细的理论分析后,通过数值模拟验证了结论的正确性. 展开更多
关键词 离散SEIR模型 稳定性 中心流形定理 neimark-sacker分岔
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带有分段常数变量的捕食者-食饵模型的稳定性和Neimark-Sacker分支 被引量:1
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作者 豆中丽 王锐 《四川师范大学学报(自然科学版)》 CAS 北大核心 2018年第2期169-175,共7页
讨论一类带有分段常数变量的捕食者-食饵模型的稳定性和Neimark-Sacker分支行为.首先通过转化得到该模型所对应的差分方程,然后利用线性方程稳定性理论讨论正平衡点局部渐近稳定的充分条件;其次运用正规形理论和中心流形定理阐释系统随... 讨论一类带有分段常数变量的捕食者-食饵模型的稳定性和Neimark-Sacker分支行为.首先通过转化得到该模型所对应的差分方程,然后利用线性方程稳定性理论讨论正平衡点局部渐近稳定的充分条件;其次运用正规形理论和中心流形定理阐释系统随参数变化而发生的Neimark-Sacker分支,从而发生混沌现象. 展开更多
关键词 分段常数变量 稳定性 neimark-sacker分支
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双时滞物价瑞利方程的Neimark-Sacker分支 被引量:2
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作者 吕堂红 《中北大学学报(自然科学版)》 CAS 北大核心 2012年第5期490-494,共5页
研究了以滞量为参数的双时滞物价瑞利方程的数值Hopf分支问题.首先利用欧拉方法将得到的时滞差分方程表示为映射,然后利用离散动力系统的分支理论,在物价瑞利方程具有Hopf分支的条件下,讨论了差分方程Hopf分支存在的条件及连续系统与其... 研究了以滞量为参数的双时滞物价瑞利方程的数值Hopf分支问题.首先利用欧拉方法将得到的时滞差分方程表示为映射,然后利用离散动力系统的分支理论,在物价瑞利方程具有Hopf分支的条件下,讨论了差分方程Hopf分支存在的条件及连续系统与其数值逼近间的关系,最后证明了当连续系统产生Hopf分支时,其Euler离散将产生Neimark-Sacker分支,进而得到Euler离散使得方程的Hopf分支性质得以保持的结论. 展开更多
关键词 物价瑞利方程 双时滞 EULER方法 HOPF分支 neimark-sacker分支 数值逼近
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带有分段常数变量的Logistic模型的稳定性和Neimark-Sacker分支
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作者 豆中丽 王瑞 《东北师大学报(自然科学版)》 CAS CSCD 北大核心 2018年第1期25-31,共7页
讨论了一类带有分段常数变量的Logistic模型的稳定性和Neimark-Sacker分支行为.首先,通过计算转化得到该类模型对应的差分方程,利用线性稳定性理论讨论了正平衡点局部渐近稳定的充分条件;其次,运用正规形理论和中心流形投影法阐释了系... 讨论了一类带有分段常数变量的Logistic模型的稳定性和Neimark-Sacker分支行为.首先,通过计算转化得到该类模型对应的差分方程,利用线性稳定性理论讨论了正平衡点局部渐近稳定的充分条件;其次,运用正规形理论和中心流形投影法阐释了系统随参数变化而发生翻转分支和Neimark-Sacker分支进入混沌的情形;最后,通过数值模拟验证了理论结果的正确性. 展开更多
关键词 分段常数变量 稳定性 neimark-sacker分支
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具时滞物价瑞利方程的Neimark-Sacker分支
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作者 吕堂红 《长春理工大学学报(自然科学版)》 2014年第1期120-123,共4页
研究了以滞量为参数的具时滞物价瑞利方程的数值Hopf分支问题。首先利用欧拉方法将得到的时滞差分方程表示为映射,然后利用离散动力系统的分支理论,在瑞利方程具有Hopf分支的条件下,讨论了差分方程Hopf分支存在的条件及连续系统与其数... 研究了以滞量为参数的具时滞物价瑞利方程的数值Hopf分支问题。首先利用欧拉方法将得到的时滞差分方程表示为映射,然后利用离散动力系统的分支理论,在瑞利方程具有Hopf分支的条件下,讨论了差分方程Hopf分支存在的条件及连续系统与其数值逼近间的关系,最后证明了当连续系统产生Hopf分支时,其Euler离散将产生Neimark-Sacker分支,进而得到结论:Euler离散使得方程的Hopf分支性质得以保持。 展开更多
关键词 物价瑞利方程 时滞 EULER方法 HOPF分支 neimark-sacker 数值逼近
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Stability and Neimark-Sacker bifurcation analysis of a food-limited population model with a time delay 被引量:2
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作者 姜晓伟 关治洪 +2 位作者 张先鹤 张顶学 刘峰 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第3期67-71,共5页
In this paper,a kind of discrete delay food-limited model obtained by the Euler method is investigated,where the discrete delay τ is regarded as a parameter.By analyzing the associated characteristic equation,the lin... In this paper,a kind of discrete delay food-limited model obtained by the Euler method is investigated,where the discrete delay τ is regarded as a parameter.By analyzing the associated characteristic equation,the linear stability of this model is studied.It is shown that Neimark-Sacker bifurcation occurs when τ crosses certain critical values.The explicit formulae which determine the stability,direction,and other properties of bifurcating periodic solution are derived by means of the theory of center manifold and normal form.Finally,numerical simulations are performed to verify the analytical results. 展开更多
关键词 food-limited model time delay neimark-sacker bifurcation periodic solution
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离散Leslie-Gower型捕食与被捕食系统的Neimark-Sacker分岔
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作者 朱丽霞 周慧香 《数学理论与应用》 2009年第4期29-32,共4页
本文利用映射的分岔理论讨论了离散Leslie-Gower型捕食与被捕食系统的Neimark-Sacker分岔,并通过数值模拟验证了所得结果的正确性。
关键词 离散动力系统 Leslie-Gower系统 稳定性 neimark-sacker分岔
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