2025年04月13日 星期日

广西师范大学学报（自然科学版） ›› 2024, Vol. 42 ›› Issue (6): 53-66.doi: 10.16088/j.issn.1001-6600.2024030604

• “污水处理”专栏 • 上一篇    下一篇

饮用水处理中藻类混凝消除技术的现状与趋势——基于CiteSpace的可视化分析

刘洋1,2*, 张毅杰1,2, 章延1,2, 李玲3, 孔祥铭3, 李红3   

  1. 1.河南省水生态毒理与健康防护国际联合实验室(河南师范大学),河南 新乡 453007;
    2.河南师范大学 生命科学学院,河南 新乡 453007;
    3.新乡首创水务有限责任公司 水质检测中心,河南 新乡 453004
  • 收稿日期:2024-03-06 修回日期:2024-05-22 出版日期:2024-12-30 发布日期:2024-12-30
  • 通讯作者: 刘洋(1983—),男,河南新乡人,河南师范大学副教授,博士。E-mail: ly@htu.edu.cn
  • 基金资助:
    河南省国际科技合作项目(232102521014);国家重点研发计划“政府间国际科技创新合作”重点专项(2021YFE0112000)

Current Status and Trends of Algal Coagulation Elimination Technology in Drinking Water Treatment: a Visual Analysis Based on CiteSpace

LIU Yang1,2*, ZHANG Yijie1,2, ZHANG Yan1,2, LI Ling3, KONG Xiangming3, LI Hong3   

  1. 1. Henan International Joint Laboratory of Aquatic Ecotoxicology and Health Protection (Henan Normal University), Xinxiang Henan 453007, China;
    2. College of Life Sciences, Henan Normal University, Xinxiang Henan 453007, China;
    3. Xinxiang Capital Water Service Co., Ltd., Water Quality Testing Center, Xinxiang Henan 453004, China
  • Received:2024-03-06 Revised:2024-05-22 Online:2024-12-30 Published:2024-12-30

PDF (PC)

3

摘要： 水体富营养化导致湖库藻类大量生长,给饮用水处理工艺带来潜在影响。为准确把握本领域最新研究和发展趋势,借助CiteSpace科学计量软件,对中国知网(CNKI)和Web of Science(WOS)核心数据库中收录的1999年至2023年有关饮用水藻类混凝的文献进行详细分析,结果表明:①在统计区间内,CNKI数据库关于饮用水藻类混凝总发文量和平均发文量均高于WOS数据库,就发文趋势来看,二者发文量均稳中有升;②CNKI数据库高产作者发文量远低于WOS数据库高产作者发文量,且CNKI数据库没有形成高产核心作者群;③WOS数据库发文机构以高校和科研院所为主,缺乏与地方企业的联系;CNKI数据库发文机构的合作关系具有明显地域关系,跨地域合作能力较弱,不利于后续研究的开展;④2个数据库研究内容主要包含饮用水、饮用水处理、富营养化、预氧化和消毒副产物等,但侧重点不同,WOS数据库包含细胞完整性、溶解有机碳、中度预氧化等细胞代谢分子水平的研究;CNKI数据库主要关注膜污染、强化混凝、二氧化氯、混凝和预氧化等物理化学除藻技术的研究,两者结合可以完善饮用水混凝除藻领域的理论框架,使研究的深度和广度不断增强。尽管目前饮用水藻类混凝领域已有丰富的实践经验和理论基础,但在研究深度与合作方面仍有不足,综合化、环保化、智能化是未来的发展趋势。

关键词: 饮用水, 藻类, 混凝, 消除, CiteSpace, 研究进展

Abstract: Algae blooms in lake and reservoir caused by eutrophication has a potential impact on the drinking water treatment process. In order to accurately grasp the latest research and development trend in this field, CiteSpace bibliometrics software was used to analyze the literature on algal coagulation in drinking water from 1999 to 2023 in the core database of the China National Knowledge Infrastructure (CNKI) and Web of Science(WOS) in detail. The results showed that: ① Within the statistical interval, the total number and average number of published papers on algae coagulation in drinking water in the CNKI database were higher than those in the WOS database. Additionally, the number of published papers in both databases was observed to be stable and gradually increasing over time. ② The publication volume of high-yield authors in the CNKI database was significantly lower compared with high-yield authors in the WOS database. Additionally, the CNKI database have not established a high-yield core author group. ③ Publishing institutions in the WOS database primarily consist of universities and research institutes, with limited connections to local enterprises. On the other hand, the cooperation relationships among CNKI database publishing institutions showed clear regional affiliations, but their ability for cross-regional collaboration was weak, which may hinder the advancement of future research. ④ The research content of the two databases mainly includes drinking water, drinking water treatment, eutrophication, pre-oxidation, and disinfection by-products, with a different focus. The WOS database primarily concentrates on molecular-level research of cell metabolism, covering topics such as cell integrity, dissolved organic carbon, and moderate pre-oxidation. While the CNKI database focuses on physical and chemical algae removal technologies like membrane fouling, enhanced coagulation, chlorine dioxide, coagulation, and pre-oxidation. Combining the findings from both databases can enhance the theoretical framework in the field of drinking water coagulation and algae removal, thereby enriching the depth and breadth of the research. Although there was a wealth of practical experience and theoretical basis in the field of algae coagulation in drinking water, there are still shortcomings in the depth of research and cooperation. And integration, environmental protection and intelligence are the trend of future development.

Key words: drinking water, algae, coagulation, elimination, CiteSpace, research progress

中图分类号:  TU991.2

[1] 张利平, 夏军, 胡志芳. 中国水资源状况与水资源安全问题分析[J]. 长江流域资源与环境, 2009, 18(2): 116-120. DOI: 10.3969/j.issn.1004-8227.2009.02.004.
[2] 赵珂艺, 张宁宁, 薛洁怡, 等. 重金属超富集植物研究CiteSpace可视化分析[J]. 广西师范大学学报(自然科学版), 2023, 41(3): 191-209. DOI: 10.16088/j.issn.1001-6600.2022030701.
[3] 黄群芳, 国超旋, 李娜, 等. 富春江库区高温热浪变化特征及对藻类水华潜在影响研究[J]. 环境科学研究, 2022, 35(2): 530-539. DOI: 10.13198/j.issn.1001-6929.2021.11.31.
[4] 梁炜, 贾秋放, 华一江. 藻类污染对太湖流域饮用水水质的影响[J]. 江苏预防医学, 2001,12(1): 1-2. DOI: 10.3969/j.issn.1006-9070.2001.01.001.
[5] 黄祖亚. 福建省饮用水源藻类危害态势及其对策研究[J]. 水利科技, 2011(1): 1-5.
[6] 凌艳晨, 苏宇亮, 胡克武, 等. 珠海市饮用水水源藻类问题分析与解决方案[J]. 南水北调与水利科技, 2021,19(4): 729-738. DOI: 10.13476/j.cnki.nsbdqk.2021.0076.
[7] 李亚男, 田立平, 王丰科, 等. 强化气浮除藻及其联用工艺研究进展[J]. 净水技术, 2020, 39(10): 102-108. DOI: 10.15890/j.cnki.jsjs.2020.10.016
[8] 陈昕, 胡胜华, 陈晓飞, 等. 蓝藻水华应急处置方法与技术研究进展[J]. 环境科学与技术, 2023, 46(5): 108-116. DOI: 10.19672/j.cnki.1003-6504.0143.23.338.
[9] 刘佩蕊, 洪喻, 谢兴. 藻华防控方法及灭活与捕获新技术研究进展[J]. 环境科学与技术, 2021, 44(2): 171-185. DOI: 10.19672/j.cnki.1003-6504.2021.02.022.
[10] 薛舒心, 唐彪, 董泽樟, 等. 净水厂除藻技术和新型抑藻材料的研究进展[J]. 生物学杂志, 2023, 40(1): 98-103. DOI: 10.3969/j.issn.2095-1736.2023.01.098.
[11] 胡赡方, 黄庆, 赖涵, 等. 预氧化混凝去除原水中铜绿微囊藻及同步控制消毒副产物生成[J]. 净水技术, 2023, 42(5): 60-67. DOI: 10.15890/j.cnki.jsjs.2023.05.009.
[12] 罗云龙, 洪伟业, 周萍. 牛尾岭水库藻类状况及水处理措施探讨[J]. 轻工科技, 2019, 35(6): 86-87, 145.
[13] 汤仲恩, 种云霄, 吴启堂, 等. 3种沉水植物对5种富营养化藻类生长的化感效应[J]. 华南农业大学学报, 2007, 28(4): 42-46. DOI: 10.3969/j.issn.1001-411X,2007.04.011.
[14] 范振强, 崔福义, 马华, 等. 放养鲢鱼预处理高藻原水的除藻效能及特性[J]. 环境科学, 2008, 29(3): 632-637. DOI: 10.13227/j.hjkx.2008.03.049.
[15] 毛嘉欣, 陈皓若, 李丰, 等. 生态型水源水库浮游甲壳类群落结构对水环境因子和生物因子的响应[J]. 环境科学学报, 2024, 44(4): 401-410. DOI: 10.13671/j.hjkxxb.2023.0331.
[16] MEYER N, BIGALKE A, KAULFUß A, et al. Strategies and ecological roles of algicidal bacteriay[J]. FEMS Microbiology Reviews, 2017, 41(6): 880-899. DOI: 10.1093/femsre/fux029.
[17] 邬长友. 紫外/过硫酸盐预氧化强化混凝同步除藻和三氯酚[J]. 中国给水排水, 2023, 39(1): 45-48. DOI: 10.19853/j.zgjsps.1000-4602.2023.01.007.
[18] 杨柳崴, 王妍, 赵瑞, 等. 磁性混凝剂在水处理中的应用研究进展[J]. 土木与环境工程学报(中英文), 2022, 44(6): 181-192. DOI: 10.11835/j.issn.2096-6717.2021.187.
[19] 徐双成, 高熠璇, 胡昕如, 等. 预氧化耦合超滤工艺净化处理含藻水研究进展[J]. 净水技术, 2023, 42(6): 7-13, 21. DOI: 10.15890/j.cnki.jsjs.2023.06.002.
[20] GHERNAOUT D, ELBOUGHDIRI N. Electrochemically and ultrasonically-enhanced coagulation for algae removal[J]. Green and Sustainable Chemistry, 2023, 13(2): 73-109. DOI: 10.4236/gsc.2023.132006.
[21] 李东鹏, 杨岚, 赵晓祥, 等. 光催化抑藻材料的研究进展[J]. 环境化学, 2023, 42(11): 3951-3964. DOI: 10.7524/j.issn.0254-6108.2023051802.
[22] 童凌晨, 李强, 岳鹏鹏. 基于CiteSpace的喀斯特土壤有机碳研究进展[J]. 广西师范大学学报(自然科学版), 2022, 40(4): 22-34. DOI: 10.16088/j.issn.1001-6600.2021052502.
[23] 李仁辉, 王广, 诸战诞, 等. 蓝藻溶藻细菌研究现状的可视化分析[J]. 河南师范大学学报(自然科学版), 2024,52(2): 111-122. DOI: 10.16366/j.cnki.1000-2367.2023.02.28.0003.
[24] XU H Z, PEI H Y, JIN Y, et al. Characteristics of water obtained by dewatering cyanobacteria-containing sludge formed during drinking water treatment, including C-, N-disinfection byproduct formation[J]. Water Research, 2017, 111: 382-392. DOI: 10.1016/j.watres.2017.01.021.
[25] MA C X, XU H Z, ZHANG L, et al. Use of fluorescence excitation-emission matrices coupled with parallel factor analysis tomonitor C- and N-DBPs formation in drinking water recovered from cyanobacteria-laden sludge dewatering[J]. Science of the Total Environment, 2018, 640/641: 609-618. DOI: 10.1016/j.scitotenv.2018.05.369.
[26] MA C X, PEI H Y, HU W R, et al. The enhanced reduction of C- and N-DBP formation in treatment of source water containing Microcystis aeruginosa using a novel CTSAC composite coagulant[J]. Science of The Total Environment, 2017, 579: 1170-1178. DOI: 10.1016/j.scitotenv.2016.11.099.
[27] PEI H Y, XU H Z, XIAO H D, et al. Using a novel hydrogen-terminated porous Si wafer to enhance Microcystis aeruginosa effective removal by chitosan at a low dosage[J]. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2016, 499: 88-96. DOI: 10.1016/j.colsurfa.2016.04.015.
[28] JIN Y, XU H Z, MA C X, et al. Using photocatalyst powder to enhance the coagulation and sedimentation of cyanobacterial cells and enable the sludge to be self-purified under visible light[J]. Water Research, 2018, 143: 550-560. DOI: 10.1016/j.watres.2018.07.015.
[29] CHENG X X, LIAN J C, REN Z X, et al. Coupling sodium percarbonate (SPC) oxidation and coagulation for membrane fouling mitigation in algae-laden water treatment[J]. Water Research, 2021, 204: 117622. DOI: 10.1016/J.WATRES.2021.117622.
[30] JIN Y, CHEN F Y, XU B, et al. Iron-based technology coupling moderate preoxidation with hybrid coagulation for highly effective removal and moderate growth inhibition of Oscillatoria in drinking water treatment plants[J]. Journal of Environmental Chemical Engineering, 2022, 10(3): 107723. DOI: 10.1016/J.JECE.2022.107723.
[31] JIN Y, LI P J, XU B, et al. A novel technology using iron in a coupled process of moderate preoxidation-hybrid coagulation to remove cyanobacteria in drinking water treatment plants[J]. Journal of Cleaner Production, 2022, 342: 130947. DOI: 10.1016/J.JCLEPRO.2022.130947.
[32] PIVOKONSKY M, SAFARIKOVA J, BARESOVA M, et al. A comparison of the character of algal extracellular versus cellular organic matter produced by cyanobacterium, diatom and green alga[J]. Water Research, 2014, 51: 37-46. DOI: 10.1016/j.watres.2013.12.022.
[33] NACERADSKA J, PIVOKONSKA L, PIVOKONSKY M. On the importance of pH value in coagulation[J].Journal of Water Supply Research and Technology-Aqua, 2019, 68(3): 222-230. DOI: 10.2166/aqua.2019.155.
[34] CERMAKOVA L, KOPECKA I, PIVOKONSKY M, et al. Removal of cyanobacterial amino acids in water treatment by activated carbon adsorption[J]. Separation and Purification Technology, 2017, 173: 330-338. DOI: 10.1016/j.seppur.2016.09.043.
[35] BARESOVA M, PIVOKONSKY M, NOVOTNA K, et al. An application of cellular organic matter to coagulation of cyanobacterial cells (Merismopedia tenuissima) [J]. Water Research, 2017, 122: 70-77. DOI: 10.1016/j.watres.2017.05.070.
[36] PIVOKONSKY M, NACERADSKA J, BRABENEC T, et al. The impact of interactions between algal organic matter and humic substances on coagulation[J]. Water Research, 2015, 84: 278-285. DOI:10.1016/j.watres.2015.07.047.
[37] BAREŠOVÁ M, NAČERADSKÁ J, NOVOTNÁ K, et al. The impact of preozonation on the coagulation of cellular organic matter produced by Microcystis aeruginosa and its toxin degradation[J]. Journal of Environmental Sciences China, 2020, 98: 124-133. DOI: 10.1016/j.jes.2020.05.031.
[38] NOVOTNÁ K, PIVOKONSKÝ M, PROKOPOVÁ M, et al. Consequences of ozonation for the limited coagulation of non-proteinaceous AOM and formation of aldehydes as ozonation by-products[J]. Journal of Environmental Chemical Engineering, 2020, 8(6): 104455. DOI: 10.1016/j.jece.2020.104455.
[39] BAREŠOVÁ M, NAČERADSKÁ J, KOPECKÁ I, et al. Coagulation mechanisms for removal of peptides and proteins produced by phytoplankton[J]. Chemicke Listy, 2015, 109(2): 98-104.
[40] SRIVASTAVA J, SINGH N. Effective removal of microorganisms and biostimulants of wasterwater by the application of various electrolytes[J]. Clean—Soil, Air, Water, 2007, 35(2): 151-155. DOI: 10.1002/clen.200600021.
[41] HUANG W W, CHU H Q,DONG B Z. Characteristics of algogenic organic matter generated under different nutrient conditions and subsequent impact on microfiltration membrane fouling[J]. Desalination, 2012, 293: 104-111. DOI: 10.1016/j.desal.2012.03.001.
[42] SCHMIDT W, BORNMANN K, IMHOF L, et al. Assessing drinking water treatment systems for safety against cyanotoxin breakthrough using maximum tolerablevalues[J]. Environmental Toxicology, 2008,23(3): 337-345. DOI: 10.1002/tox.20341.
[43] SANO D, ISHIFUJI S, SATO Y, et al. Identification and characterization of coagulation inhibitor proteins derived from cyanobacterium Microcystis aeruginosa[J]. Chemosphere, 2011, 82(8): 1096-1102. DOI: 10.1016/j.chemosphere.2010.12.005.
[44] ZHANG G M, WANG B, ZHANG P Y, et al. Removal of algae by sonication-coagulation[J]. Journal of Environmental Science and Health, Part A, 2006, 41(7): 1379-1390. DOI: 10.1080/10934520600657156.
[45] GE F, WU X Z, WANG N, et al. Effects of iron and manganese on the formation of HAAs upon chlorinating Chlorella vulgaris[J]. Journal of Hazardous Materials, 2011, 189(1/2): 540-545. DOI: 10.1016/j.jhazmat.2011.02.076.
[46] ZHOU S Q, SHAO Y S,GAO N Y, et al. Removal of Microcystis aeruginosa by potassium ferrate (VI): impacts on cells integrity, intracellular organic matter release and disinfection by-products formation[J]. Chemical Engineering Journal, 2014, 251: 304-309. DOI: 10.1016/j.cej.2014.04.081.
[47] 黄晓东, 孙伟, 庄汉平, 等. 强化混凝处理微污染源水[J]. 中国给水排水, 2002,18(12): 45-47.
[48] 吴思聪, 延克军, 郭恒超, 等. 交变电磁场强化混凝对河水中藻类去除的研究[J]. 水处理技术, 2014, 40(11): 28-31. DOI: 10.16796/j.cnki.1000-3770.2014.11.006.
[49] 尹卫红, 宋向阳, 张湛军, 等. 郑州市白庙水厂混凝沉淀除藻的研究[J]. 工业用水与废水, 2000, 31(4): 7-9.
[50] 刘海龙, 杨栋, 赵智勇, 等. 高藻原水预臭氧强化混凝除藻特性研究[J]. 环境科学, 2009, 30(7): 1914-1919. DOI: 10.13227/j.hjkx.2009.07.008.
[51] 王付林, 王晓昌, 黄廷林, 等. 高锰酸钾和氯对高藻水的氧化助凝作用[J]. 中国给水排水, 2004,20(3): 9-11.
[52] 李晓东, 蔡国庆, 马军. 水中有机成分及其对饮用水水质的影响[J]. 给水排水, 1999, 25(5): 12-14.
[53] 马华, 崔福义, 范振强, 等. 净水厂处理前端放养鲢鱼对藻类的去除特性及相关因素研究[J]. 给水排水, 2012, 48(11): 34-38. DOI: 10.13789/j.cnki.wwe1964.2012.11.027.
[54] 乔瑞平, 李楠, 漆新华, 等. UV/H2O2催化氧化去除微囊藻毒素-LR[J]. 安全与环境学报, 2005,5(2): 46-49.
[55] 池秀静, 魏晓妹, 李洪源. 高锰酸钾复合药剂与粉末活性炭联用组合对微污染源水的强化混凝效能[J]. 水土保持通报, 2002,22(1): 10-13. DOI: 10.13961/j.cnki.stbctb.2002.01.003.
[56] 王威, 邓华, 胡乐宁, 等. 赤泥-海藻酸钠水凝胶对水中Pb(Ⅱ)的吸附性能[J]. 广西师范大学学报(自然科学版), 2023, 41(5): 105-115. DOI: 10.16088/j.issn.1001-6600.2022110901.
[57] 李俊生, 李嘉慧, 车春波, 等. 光催化氧化技术处理废水中抗生素的研究进展[J]. 水处理技术, 2024, 50(2): 14-19, 25. DOI: 10.16796/j.cnki.1000-3770.2024.02.003.
[1] 朱格格, 黄安书, 覃盈盈. 基于Web of Science的国际红树林研究发展态势分析[J]. 广西师范大学学报（自然科学版）, 2024, 42(5): 1-12.
[2] 何静, 冯元柳, 邵靖雯. 基于CiteSpace的多源数据融合研究进展[J]. 广西师范大学学报（自然科学版）, 2024, 42(5): 13-27.
[3] 翟言豪, 王燕舞, 李强, 李景坤. 基于CiteSpace的三维荧光光谱技术对内陆水体中溶解性有机质研究的进展[J]. 广西师范大学学报（自然科学版）, 2024, 42(3): 34-46.
[4] 董淑龙, 马姜明, 辛文杰. 景观视觉评价研究进展与趋势——基于CiteSpace的知识图谱分析[J]. 广西师范大学学报（自然科学版）, 2023, 41(5): 1-13.
[5] 赵珂艺, 张宁宁, 薛洁怡, 李广娈, 李艺, 于方明, 刘可慧. 重金属超富集植物研究CiteSpace可视化分析[J]. 广西师范大学学报（自然科学版）, 2023, 41(3): 191-209.
[6] 张小丽, 陈泽柠, 武正军. 蜥蜴与气候变化的研究热点演变分析——基于Web of Science数据库[J]. 广西师范大学学报（自然科学版）, 2022, 40(5): 332-341.
[7] 童凌晨, 李强, 岳鹏鹏. 基于CiteSpace的喀斯特土壤有机碳研究进展[J]. 广西师范大学学报（自然科学版）, 2022, 40(4): 22-34.
[8] 官晓金, 赵珂艺, 刘世玲, 李艺, 于方明, 李春明, 刘可慧. 近30年全球锰污染植物修复研究进展——基于CiteSpace的可视化分析[J]. 广西师范大学学报（自然科学版）, 2021, 39(5): 44-57.
[9] 宾石玉, 廖芳, 杜雪松, 许艺兰, 王鑫, 武霞, 林勇. 罗非鱼耐寒性能研究进展[J]. 广西师范大学学报（自然科学版）, 2021, 39(1): 10-16.
[10] 金乐, 吉民. 新型靶向CT造影剂的研究进展[J]. 广西师范大学学报（自然科学版）, 2017, 35(3): 83-88.
[11] 丁晓剑, 丁冉. 基于SVR-RFE的作战方案评估指标选择方法[J]. 广西师范大学学报（自然科学版）, 2015, 33(4): 43-48.
Viewed
Full text
3
HTML PDF
Just accepted Online first Issue Just accepted Online first Issue
0 0 0 0 0 3

  From local
  Times 3
  Rate 100%

Abstract
Just accepted Online first Issue
0 0 72

Cited
  Shared   
  Discussed   
[1] 邢伟, 高晋芳, 颜七笙, 周其华. 具有非线性传染率及脉冲免疫接种的SIQR传染病模型[J]. 广西师范大学学报（自然科学版）, 2017, 35(2): 58 -65 .
[2] 王永真, 余黄生, 吴佃华. (6×v,{3,4},1,Q)光正交码的构造[J]. 广西师范大学学报（自然科学版）, 2016, 34(3): 62 -67 .
[3] 李谊纯, 董德信, 王一兵. 北仑河口及其邻近海域物质输运滞留时间研究[J]. 广西师范大学学报（自然科学版）, 2015, 33(2): 56 -63 .
[4] 汪国海, 施泽攀, 李生强, 周岐海. 基于红外相机技术的赤麂活动模式分析[J]. 广西师范大学学报（自然科学版）, 2015, 33(3): 117 -122 .
[5] 李青, 王露雨, 张祖绪, 陈会明. 贵州梵净山国家级自然保护区蜘蛛两新种记述(蛛形纲:蜘蛛目)[J]. 广西师范大学学报（自然科学版）, 2018, 36(4): 119 -123 .
[6] 阳丽, 孔令江. 微纳米球形颗粒之间的毛细力研究[J]. 广西师范大学学报（自然科学版）, 2012, 30(1): 1 -4 .
[7] 赵鑫, 宋英强, 胡月明, 刘轶伦, 朱阿兴. 基于多源开放数据的城乡居民点空间布局优化[J]. 广西师范大学学报（自然科学版）, 2020, 38(1): 26 -40 .
[8] 覃玉月, 刘晓波, 徐照隆, 莫土香, 李俊, 杨瑞云. 广豆根内生真菌Xylaria sp. GDGJ-368代谢产物研究[J]. 广西师范大学学报（自然科学版）, 2020, 38(5): 71 -77 .
[9] 杨迪, 方扬鑫, 周彦. 基于MEB和SVM方法的新类别分类研究[J]. 广西师范大学学报（自然科学版）, 2022, 40(1): 57 -67 .
[10] 王涵, 张映辉. 模拟趋化现象的三维双曲-抛物系统的最优衰减率[J]. 广西师范大学学报（自然科学版）, 2022, 40(2): 125 -131 .
版权所有 © 广西师范大学学报（自然科学版）编辑部
地址：广西桂林市三里店育才路15号　邮编：541004
电话：0773-5857325　E-mail: gxsdzkb@mailbox.gxnu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发