{"id":"https://openalex.org/W2084874702","doi":"https://doi.org/10.1155/2012/857134","title":"Dynamical Behavior of a Stochastic Ratio\u2010Dependent Predator\u2010Prey System","display_name":"Dynamical Behavior of a Stochastic Ratio\u2010Dependent Predator\u2010Prey System","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2084874702","doi":"https://doi.org/10.1155/2012/857134","mag":"2084874702"},"language":"en","primary_location":{"id":"doi:10.1155/2012/857134","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/857134","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/857134.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2012/857134.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100555131","display_name":"Zheng Wu","orcid":null},"institutions":[{"id":"https://openalex.org/I143868143","display_name":"Anhui University","ror":"https://ror.org/05th6yx34","country_code":"CN","type":"education","lineage":["https://openalex.org/I143868143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zheng Wu","raw_affiliation_strings":["School of Mathematical Science, Anhui University, Hefei 230039, China","School of Mathematical Science, Anhui University, Hefei 230039"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Science, Anhui University, Hefei 230039, China","institution_ids":["https://openalex.org/I143868143"]},{"raw_affiliation_string":"School of Mathematical Science, Anhui University, Hefei 230039","institution_ids":["https://openalex.org/I143868143"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079468288","display_name":"Hao Huang","orcid":"https://orcid.org/0000-0001-9336-883X"},"institutions":[{"id":"https://openalex.org/I143868143","display_name":"Anhui University","ror":"https://ror.org/05th6yx34","country_code":"CN","type":"education","lineage":["https://openalex.org/I143868143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hao Huang","raw_affiliation_strings":["School of Mathematical Science, Anhui University, Hefei 230039, China","School of Mathematical Science, Anhui University, Hefei 230039"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Science, Anhui University, Hefei 230039, China","institution_ids":["https://openalex.org/I143868143"]},{"raw_affiliation_string":"School of Mathematical Science, Anhui University, Hefei 230039","institution_ids":["https://openalex.org/I143868143"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050632045","display_name":"Lianglong Wang","orcid":"https://orcid.org/0000-0002-0667-7755"},"institutions":[{"id":"https://openalex.org/I143868143","display_name":"Anhui University","ror":"https://ror.org/05th6yx34","country_code":"CN","type":"education","lineage":["https://openalex.org/I143868143"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Lianglong Wang","raw_affiliation_strings":["School of Mathematical Science, Anhui University, Hefei 230039, China","School of Mathematical Science, Anhui University, Hefei 230039"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Science, Anhui University, Hefei 230039, China","institution_ids":["https://openalex.org/I143868143"]},{"raw_affiliation_string":"School of Mathematical Science, Anhui University, Hefei 230039","institution_ids":["https://openalex.org/I143868143"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5050632045"],"corresponding_institution_ids":["https://openalex.org/I143868143"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.6293,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.76023807,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"2012","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},"topics":[{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9891999959945679,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T11764","display_name":"Evolution and Genetic Dynamics","score":0.9846000075340271,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7383305430412292},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5810839533805847},{"id":"https://openalex.org/keywords/comparison-theorem","display_name":"Comparison theorem","score":0.4833528697490692},{"id":"https://openalex.org/keywords/predation","display_name":"Predation","score":0.4686927795410156},{"id":"https://openalex.org/keywords/ecology","display_name":"Ecology","score":0.157352477312088},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.05925145745277405}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7383305430412292},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5810839533805847},{"id":"https://openalex.org/C2779396167","wikidata":"https://www.wikidata.org/wiki/Q5156040","display_name":"Comparison theorem","level":2,"score":0.4833528697490692},{"id":"https://openalex.org/C188382862","wikidata":"https://www.wikidata.org/wiki/Q170430","display_name":"Predation","level":2,"score":0.4686927795410156},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.157352477312088},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.05925145745277405}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2012/857134","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/857134","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/857134.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1355495125","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jam/1355495125","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:857134","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2012/857134.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:bb3c70f03d4c45b9a3a1c87685d90e66","is_oa":true,"landing_page_url":"https://doaj.org/article/bb3c70f03d4c45b9a3a1c87685d90e66","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2012 (2012)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2012/857134","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/857134","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/857134.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1029389215","display_name":null,"funder_award_id":"10771001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1088186637","display_name":null,"funder_award_id":"05025104","funder_id":"https://openalex.org/F4320321106","funder_display_name":"Ministry of Education of the People's Republic of China"},{"id":"https://openalex.org/G1131884569","display_name":null,"funder_award_id":"20113401110001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1196026329","display_name":null,"funder_award_id":"20113401110001","funder_id":"https://openalex.org/F4320321106","funder_display_name":"Ministry of Education of the People's Republic of China"},{"id":"https://openalex.org/G1246316609","display_name":null,"funder_award_id":"KJJQ1101","funder_id":"https://openalex.org/F4320321106","funder_display_name":"Ministry of Education of the People's Republic of China"},{"id":"https://openalex.org/G1306027491","display_name":null,"funder_award_id":"11126177","funder_id":"https://openalex.org/F4320321435","funder_display_name":"Anhui University"},{"id":"https://openalex.org/G1560518294","display_name":null,"funder_award_id":"201134","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2250743307","display_name":null,"funder_award_id":"11126177","funder_id":"https://openalex.org/F4320321106","funder_display_name":"Ministry of Education of the People's Republic of China"},{"id":"https://openalex.org/G2736795742","display_name":null,"funder_award_id":"090416237","funder_id":"https://openalex.org/F4320321106","funder_display_name":"Ministry of Education of the People's Republic of China"},{"id":"https://openalex.org/G2802911279","display_name":null,"funder_award_id":"Young","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2948042475","display_name":null,"funder_award_id":"01134","funder_id":"https://openalex.org/F4320321106","funder_display_name":"Ministry of Education of the People's Republic of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3502624587","display_name":null,"funder_award_id":"KJJQ1101","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3669891833","display_name":null,"funder_award_id":"11126177","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3752594195","display_name":null,"funder_award_id":"KJ2009A49","funder_id":"https://openalex.org/F4320321106","funder_display_name":"Ministry of Education of the People's Republic of China"},{"id":"https://openalex.org/G3891938370","display_name":null,"funder_award_id":"KJ2009A49","funder_id":"https://openalex.org/F4320321435","funder_display_name":"Anhui University"},{"id":"https://openalex.org/G391238517","display_name":null,"funder_award_id":", and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4364602779","display_name":null,"funder_award_id":"KJ2009A49","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4616082893","display_name":null,"funder_award_id":"10771001","funder_id":"https://openalex.org/F4320321435","funder_display_name":"Anhui University"},{"id":"https://openalex.org/G4781520999","display_name":null,"funder_award_id":"2012SQRL021","funder_id":"https://openalex.org/F4320321106","funder_display_name":"Ministry of Education of the People's Republic of China"},{"id":"https://openalex.org/G4993178436","display_name":null,"funder_award_id":"10771001","funder_id":"https://openalex.org/F4320321106","funder_display_name":"Ministry of Education of the People's Republic of China"},{"id":"https://openalex.org/G5155168512","display_name":null,"funder_award_id":"2012SQRL021","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5309650252","display_name":null,"funder_award_id":"1208085QA15","funder_id":"https://openalex.org/F4320321106","funder_display_name":"Ministry of Education of the People's Republic of China"},{"id":"https://openalex.org/G5555576097","display_name":null,"funder_award_id":"090416237","funder_id":"https://openalex.org/F4320321435","funder_display_name":"Anhui University"},{"id":"https://openalex.org/G5881558632","display_name":null,"funder_award_id":"20103401120002","funder_id":"https://openalex.org/F4320321106","funder_display_name":"Ministry of Education of the People's Republic of China"},{"id":"https://openalex.org/G5904795463","display_name":null,"funder_award_id":"20113401110001","funder_id":"https://openalex.org/F4320321435","funder_display_name":"Anhui University"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6141874152","display_name":null,"funder_award_id":"05025104","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6335744364","display_name":null,"funder_award_id":"090416237","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G719274466","display_name":null,"funder_award_id":"20103401120002","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7608752429","display_name":null,"funder_award_id":"Talent","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G807070257","display_name":null,"funder_award_id":"211 Project","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8119036938","display_name":null,"funder_award_id":"KJJQ1101","funder_id":"https://openalex.org/F4320321435","funder_display_name":"Anhui University"},{"id":"https://openalex.org/G8212061402","display_name":null,"funder_award_id":"20103401120002","funder_id":"https://openalex.org/F4320321435","funder_display_name":"Anhui University"},{"id":"https://openalex.org/G8237826462","display_name":null,"funder_award_id":"2012SQRL021","funder_id":"https://openalex.org/F4320321435","funder_display_name":"Anhui University"},{"id":"https://openalex.org/G8295110571","display_name":null,"funder_award_id":"1208085QA15","funder_id":"https://openalex.org/F4320321435","funder_display_name":"Anhui University"},{"id":"https://openalex.org/G8792948398","display_name":null,"funder_award_id":"05025104","funder_id":"https://openalex.org/F4320321435","funder_display_name":"Anhui University"},{"id":"https://openalex.org/G969775218","display_name":null,"funder_award_id":"1208085QA15","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321106","display_name":"Ministry of Education of the People's Republic of China","ror":"https://ror.org/01mv9t934"},{"id":"https://openalex.org/F4320321435","display_name":"Anhui University","ror":"https://ror.org/05th6yx34"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2084874702.pdf","grobid_xml":"https://content.openalex.org/works/W2084874702.grobid-xml"},"referenced_works_count":38,"referenced_works":["https://openalex.org/W609447776","https://openalex.org/W1586658033","https://openalex.org/W1597176843","https://openalex.org/W1607503834","https://openalex.org/W1971865379","https://openalex.org/W1972487182","https://openalex.org/W1983878692","https://openalex.org/W1983989607","https://openalex.org/W1985856465","https://openalex.org/W2000380602","https://openalex.org/W2004509489","https://openalex.org/W2004728046","https://openalex.org/W2008403791","https://openalex.org/W2011794160","https://openalex.org/W2017032949","https://openalex.org/W2019468701","https://openalex.org/W2021856992","https://openalex.org/W2025572774","https://openalex.org/W2030774769","https://openalex.org/W2037562767","https://openalex.org/W2045010624","https://openalex.org/W2045434011","https://openalex.org/W2065478543","https://openalex.org/W2071369760","https://openalex.org/W2073927055","https://openalex.org/W2079337490","https://openalex.org/W2094032066","https://openalex.org/W2095278975","https://openalex.org/W2133988428","https://openalex.org/W2150145189","https://openalex.org/W2172222153","https://openalex.org/W2316904041","https://openalex.org/W2474031850","https://openalex.org/W2797485658","https://openalex.org/W2799664482","https://openalex.org/W3140228646","https://openalex.org/W4232610721","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W4376636461","https://openalex.org/W2431956656","https://openalex.org/W2115185993","https://openalex.org/W2564087297","https://openalex.org/W2118545552","https://openalex.org/W4376099541","https://openalex.org/W1874274327","https://openalex.org/W4379615226","https://openalex.org/W4236132388"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,36],"concerned":[3],"with":[4,10],"a":[5,28],"stochastic":[6,18,50],"ratio\u2010dependent":[7,34],"predator\u2010prey":[8],"model":[9,35],"varible":[11],"coefficients.":[12],"By":[13],"the":[14,21,24,33,45],"comparison":[15],"theorem":[16],"of":[17,27,32],"equations":[19],"and":[20,49],"It\u00f4":[22],"formula,":[23],"global":[25],"existence":[26],"unique":[29],"positive":[30],"solution":[31],"obtained.":[37],"Besides,":[38],"some":[39],"results":[40],"are":[41],"established":[42],"such":[43],"as":[44],"stochastically":[46],"ultimate":[47],"boundedness":[48],"permanence":[51],"for":[52],"this":[53],"model.":[54]},"counts_by_year":[{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-13T07:58:08.660418","created_date":"2025-10-10T00:00:00"}