{"id":"https://openalex.org/W4409503180","doi":"https://doi.org/10.3390/sym17040604","title":"Modeling the Digestion Process by a Distributed Delay Differential System","display_name":"Modeling the Digestion Process by a Distributed Delay Differential System","publication_year":2025,"publication_date":"2025-04-16","ids":{"openalex":"https://openalex.org/W4409503180","doi":"https://doi.org/10.3390/sym17040604"},"language":"en","primary_location":{"id":"doi:10.3390/sym17040604","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17040604","pdf_url":"https://www.mdpi.com/2073-8994/17/4/604/pdf?version=1744864012","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/17/4/604/pdf?version=1744864012","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100675334","display_name":"Junli Liu","orcid":"https://orcid.org/0000-0003-1157-028X"},"institutions":[{"id":"https://openalex.org/I27599042","display_name":"Xi'an Polytechnic University","ror":"https://ror.org/03442p831","country_code":"CN","type":"education","lineage":["https://openalex.org/I27599042"]},{"id":"https://openalex.org/I4210086011","display_name":"China International Science and Technology Cooperation","ror":"https://ror.org/00bsdxt65","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210086011"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Junli Liu","raw_affiliation_strings":["School of Science, Xi\u2019an Polytechnic University, Xi\u2019an 710048, China","Xi\u2019an International Science and Technology Cooperation Base for Big Data Analysis and Algorithms, Xi\u2019an 710048, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science, Xi\u2019an Polytechnic University, Xi\u2019an 710048, China","institution_ids":["https://openalex.org/I27599042"]},{"raw_affiliation_string":"Xi\u2019an International Science and Technology Cooperation Base for Big Data Analysis and Algorithms, Xi\u2019an 710048, China","institution_ids":["https://openalex.org/I4210086011"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110669899","display_name":"Zhenghua Guo","orcid":null},"institutions":[{"id":"https://openalex.org/I27599042","display_name":"Xi'an Polytechnic University","ror":"https://ror.org/03442p831","country_code":"CN","type":"education","lineage":["https://openalex.org/I27599042"]},{"id":"https://openalex.org/I4210086011","display_name":"China International Science and Technology Cooperation","ror":"https://ror.org/00bsdxt65","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210086011"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhenghua Guo","raw_affiliation_strings":["School of Science, Xi\u2019an Polytechnic University, Xi\u2019an 710048, China","Xi\u2019an International Science and Technology Cooperation Base for Big Data Analysis and Algorithms, Xi\u2019an 710048, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science, Xi\u2019an Polytechnic University, Xi\u2019an 710048, China","institution_ids":["https://openalex.org/I27599042"]},{"raw_affiliation_string":"Xi\u2019an International Science and Technology Cooperation Base for Big Data Analysis and Algorithms, Xi\u2019an 710048, China","institution_ids":["https://openalex.org/I4210086011"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100739679","display_name":"Hui Guo","orcid":"https://orcid.org/0000-0003-0901-1833"},"institutions":[{"id":"https://openalex.org/I27599042","display_name":"Xi'an Polytechnic University","ror":"https://ror.org/03442p831","country_code":"CN","type":"education","lineage":["https://openalex.org/I27599042"]},{"id":"https://openalex.org/I4210086011","display_name":"China International Science and Technology Cooperation","ror":"https://ror.org/00bsdxt65","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210086011"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hui Guo","raw_affiliation_strings":["School of Science, Xi\u2019an Polytechnic University, Xi\u2019an 710048, China","Xi\u2019an International Science and Technology Cooperation Base for Big Data Analysis and Algorithms, Xi\u2019an 710048, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science, Xi\u2019an Polytechnic University, Xi\u2019an 710048, China","institution_ids":["https://openalex.org/I27599042"]},{"raw_affiliation_string":"Xi\u2019an International Science and Technology Cooperation Base for Big Data Analysis and Algorithms, Xi\u2019an 710048, China","institution_ids":["https://openalex.org/I4210086011"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100675334"],"corresponding_institution_ids":["https://openalex.org/I27599042","https://openalex.org/I4210086011"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.0759,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.7695178,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"17","issue":"4","first_page":"604","last_page":"604"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10715","display_name":"Distributed and Parallel Computing Systems","score":0.6966999769210815,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10715","display_name":"Distributed and Parallel Computing Systems","score":0.6966999769210815,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.6295999884605408,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12137","display_name":"Economic theories and models","score":0.5931000113487244,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.6082202792167664},{"id":"https://openalex.org/keywords/digestion","display_name":"Digestion (alchemy)","score":0.5098890066146851},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5032579302787781},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.4701445400714874},{"id":"https://openalex.org/keywords/biological-system","display_name":"Biological system","score":0.3852931261062622},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.36061352491378784},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.22951480746269226},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.15991121530532837},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.14033544063568115},{"id":"https://openalex.org/keywords/chromatography","display_name":"Chromatography","score":0.1386517882347107},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08638566732406616},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.07829496264457703},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07646235823631287}],"concepts":[{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.6082202792167664},{"id":"https://openalex.org/C2781357212","wikidata":"https://www.wikidata.org/wiki/Q5275608","display_name":"Digestion (alchemy)","level":2,"score":0.5098890066146851},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5032579302787781},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.4701445400714874},{"id":"https://openalex.org/C186060115","wikidata":"https://www.wikidata.org/wiki/Q30336093","display_name":"Biological system","level":1,"score":0.3852931261062622},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.36061352491378784},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.22951480746269226},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.15991121530532837},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.14033544063568115},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.1386517882347107},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08638566732406616},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.07829496264457703},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07646235823631287},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3390/sym17040604","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17040604","pdf_url":"https://www.mdpi.com/2073-8994/17/4/604/pdf?version=1744864012","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3390/sym17040604","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17040604","pdf_url":"https://www.mdpi.com/2073-8994/17/4/604/pdf?version=1744864012","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4617610899","display_name":null,"funder_award_id":"2022JM-023","funder_id":"https://openalex.org/F4320336567","funder_display_name":"Natural Science Basic Research Program of Shaanxi Province"},{"id":"https://openalex.org/G8527287743","display_name":null,"funder_award_id":"11801431","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8849881286","display_name":null,"funder_award_id":"2024JC-YBMS-001","funder_id":"https://openalex.org/F4320336567","funder_display_name":"Natural Science Basic Research Program of Shaanxi Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320336567","display_name":"Natural Science Basic Research Program of Shaanxi Province","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4409503180.pdf","grobid_xml":"https://content.openalex.org/works/W4409503180.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W1968742902","https://openalex.org/W2017329746","https://openalex.org/W2027665073","https://openalex.org/W2061796671","https://openalex.org/W2064924936","https://openalex.org/W2079291463","https://openalex.org/W2110178628","https://openalex.org/W2158630456","https://openalex.org/W2280527828","https://openalex.org/W2308473015","https://openalex.org/W2616496375","https://openalex.org/W2765510825","https://openalex.org/W2801331471","https://openalex.org/W2970256545","https://openalex.org/W2971360585","https://openalex.org/W3006644109","https://openalex.org/W3011176355","https://openalex.org/W3049074503","https://openalex.org/W3134794208","https://openalex.org/W3156949438","https://openalex.org/W3183179423","https://openalex.org/W4226257502","https://openalex.org/W4281552090","https://openalex.org/W4317936735","https://openalex.org/W4387822960","https://openalex.org/W4404654881"],"related_works":["https://openalex.org/W108141846","https://openalex.org/W2375823346","https://openalex.org/W2080191072","https://openalex.org/W1982160337","https://openalex.org/W2393943699","https://openalex.org/W166664622","https://openalex.org/W1971380437","https://openalex.org/W2048846564","https://openalex.org/W2363210919","https://openalex.org/W1983548084"],"abstract_inverted_index":{"We":[0,84,146,212],"modified":[1],"the":[2,10,28,42,94,98,104,116,125,135,152,156,160,183,197,210,228,232,245],"work":[3],"of":[4,14,100,106,137,155,200,209,223,227,241],"Wang":[5],"and":[6,12,19,64,97,140],"Zou,":[7],"where":[8],"both":[9,109],"costs":[11],"benefits":[13],"fear":[15,138,153,174,194],"effects":[16],"were":[17,131],"considered,":[18],"a":[20,47,52,60,65,89,173,221],"constant":[21],"time":[22,31,82,141,191],"delay":[23,44,56,192],"was":[24,57,71],"used":[25],"to":[26,34,133,166,205,214,238,244],"represent":[27],"biomass":[29],"conversion":[30],"from":[32,163],"prey":[33,117,157],"predator.":[35],"In":[36,103],"our":[37,169],"work,":[38],"we":[39,75,219,235],"assumed":[40],"that":[41,86,92,148,172,189],"digestion":[43],"is":[45],"not":[46],"constant,":[48],"but":[49],"rather":[50],"follows":[51],"specific":[53],"distribution.":[54],"The":[55],"modeled":[58],"using":[59],"general":[61,67],"kernel":[62,129,201],"function,":[63],"more":[66],"functional":[68,176],"response":[69,177],"function":[70],"also":[72],"employed.":[73],"Then,":[74],"established":[76],"an":[77,149],"integral\u2013differential":[78],"model":[79],"with":[80],"distributed":[81],"delays.":[83],"show":[85],"there":[87],"exists":[88],"delay-dependent":[90],"threshold":[91],"determines":[93],"system\u2019s":[95],"dynamics":[96,162],"presence":[99],"coexistence":[101,107,122,233],"equilibrium.":[102],"absence":[105],"equilibrium,":[108,234],"populations":[110],"tend":[111],"toward":[112],"extinction,":[113],"or":[114,193,196],"only":[115],"population":[118,144],"survives.":[119],"Conversely,":[120],"when":[121,218],"equilibrium":[123],"exists,":[124],"system":[126,161],"persists.":[127],"Four":[128],"functions":[130],"considered":[132],"explore":[134],"effect":[136],"levels":[139],"delays":[142],"on":[143],"dynamics.":[145,185],"found":[147],"increase":[150],"in":[151,181],"level":[154],"may":[158,203],"alter":[159],"periodic":[164],"oscillations":[165],"stability.":[167],"Furthermore,":[168],"findings":[170],"indicate":[171,188],"effect-related":[175],"has":[178],"great":[179],"influence":[180],"shaping":[182],"model\u2019s":[184],"These":[186],"results":[187,208],"ignoring":[190],"effects,":[195],"inappropriate":[198],"use":[199],"functions,":[202],"lead":[204],"inaccurate":[206],"prediction":[207],"model.":[211],"want":[213],"point":[215],"out":[216],"that,":[217],"investigate":[220],"pair":[222],"purely":[224],"imaginary":[225],"roots":[226],"characteristic":[229],"equation":[230],"at":[231],"just":[236],"need":[237],"consider":[239],"one":[240],"them":[242],"due":[243],"symmetry.":[246]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-06-15T08:34:33.830935","created_date":"2025-10-10T00:00:00"}