Global Period-Doubling Bifurcation of Quadratic Fractional Second Order Difference Equation

We investigate the local stability and the global asymptotic stability of the difference equation xn+1=αxn2+βxnxn-1+γxn-1/Axn2+Bxnxn-1+Cxn-1, n=0,1,… with nonnegative parameters and initial conditions such that Axn2+Bxnxn-1+Cxn-1>0, for all n≥0. We obtain the local stability of the equilibrium fo...

Full description

Saved in:
Bibliographic Details
Published in:Discrete Dynamics in Nature and Society 2014-01, Vol.2014 (2014), p.718-730-266
Main Authors: Kalabusic, Senada, Kulenovic, M.R.S, Mehuljic, M
Format: Article
Language:English
Subjects:
Asymptotic properties
Bifurcation theory
Bifurcations
Colleges & universities
Difference equations
Dynamics
Economic models
Equations, Quadratic
Equilibrium
Initial conditions
Mathematical analysis
Mathematical research
Mathematics
Period doubling
Stability
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-a566t-93e4cf346f2827cc723ec08f92de16e7a762208e94de1b78fa15e2b5924696be3
cites cdi_FETCH-LOGICAL-a566t-93e4cf346f2827cc723ec08f92de16e7a762208e94de1b78fa15e2b5924696be3
container_end_page 730-266
container_issue 2014
container_start_page 718
container_title Discrete Dynamics in Nature and Society
container_volume 2014
creator Kalabusic, Senada
Kulenovic, M.R.S
Mehuljic, M
description We investigate the local stability and the global asymptotic stability of the difference equation xn+1=αxn2+βxnxn-1+γxn-1/Axn2+Bxnxn-1+Cxn-1, n=0,1,… with nonnegative parameters and initial conditions such that Axn2+Bxnxn-1+Cxn-1>0, for all n≥0. We obtain the local stability of the equilibrium for all values of parameters and give some global asymptotic stability results for some values of the parameters. We also obtain global dynamics in the special case, where β=B=0, in which case we show that such equation exhibits a global period doubling bifurcation.
doi_str_mv 10.1155/2014/920410
format article
fullrecord <record><control><sourceid>gale_doaj_</sourceid><recordid>TN_cdi_doaj_primary_oai_doaj_org_article_45d0cfb6bb524414825ba2d054d9ff26</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><galeid>A423816494</galeid><airiti_id>P20160913003_201412_201611170001_201611170001_718_730_266</airiti_id><doaj_id>oai_doaj_org_article_45d0cfb6bb524414825ba2d054d9ff26</doaj_id><sourcerecordid>A423816494</sourcerecordid><originalsourceid>FETCH-LOGICAL-a566t-93e4cf346f2827cc723ec08f92de16e7a762208e94de1b78fa15e2b5924696be3</originalsourceid><addsrcrecordid>eNqFkc9rFTEQxxdRsFZPnoUFL6JsO5nNZjfH2l8WCn2iguAhZJPJM4_tps2-RfzvnfdWKnqRHCYz-cw386MoXgo4EqJpjhGEPNYIUsCj4kAoaKuua78-5jugqgBRPS2eTdMGAKHTeFB8uxxSb4dyRTkmX52luR_iuC7fxzBnZ7cxjWUK5cfZ-syeKy-ydbso53wil0Zf3mRPuTyLIVCm0VF5fj_vE58XT4IdJnrx2x4WXy7OP59-qK5vLq9OT64r2yi1rXRN0oVaqoAdts61WJODLmj0JBS1tlXI1ZKW7PdtF6xoCPtGo1Ra9VQfFleLrk92Y-5yvLX5p0k2mn0g5bWxmWsfyMjGgwu96vsGpRSyw6a36KGRXoeAirXeLFp3Od3PNG3NbZwcDYMdKc2TEQoBJI8ZGX39D7pJc-bBMNXIVgshVcfU0UKtLf8fx5C2PEE-nm4jz49C5PgJ63VCSS054d2S4HKapkzhoSMBZrdls9uyWbbM9NuF_h5Hb3_E_8CvFpgYoWAf4AY6BM3vq-Xdxhy38U8_K1ZRoEUNUO8VBe6MEkK0ACD-dlrRmbYGg0rVvwDZ5MMp</addsrcrecordid><sourcetype>Open Website</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1547911468</pqid></control><display><type>article</type><title>Global Period-Doubling Bifurcation of Quadratic Fractional Second Order Difference Equation</title><source>Wiley Online Library Open Access</source><source>Publicly Available Content (ProQuest)</source><creator>Kalabusic, Senada ; Kulenovic, M.R.S ; Mehuljic, M</creator><contributor>Abu-Saris, Raghib</contributor><creatorcontrib>Kalabusic, Senada ; Kulenovic, M.R.S ; Mehuljic, M ; Abu-Saris, Raghib</creatorcontrib><description>We investigate the local stability and the global asymptotic stability of the difference equation xn+1=αxn2+βxnxn-1+γxn-1/Axn2+Bxnxn-1+Cxn-1, n=0,1,… with nonnegative parameters and initial conditions such that Axn2+Bxnxn-1+Cxn-1&gt;0, for all n≥0. We obtain the local stability of the equilibrium for all values of parameters and give some global asymptotic stability results for some values of the parameters. We also obtain global dynamics in the special case, where β=B=0, in which case we show that such equation exhibits a global period doubling bifurcation.</description><identifier>ISSN: 1026-0226</identifier><identifier>EISSN: 1607-887X</identifier><identifier>DOI: 10.1155/2014/920410</identifier><language>eng</language><publisher>Cairo, Egypt: Hindawi Limiteds</publisher><subject>Asymptotic properties ; Bifurcation theory ; Bifurcations ; Colleges &amp; universities ; Difference equations ; Dynamics ; Economic models ; Equations, Quadratic ; Equilibrium ; Initial conditions ; Mathematical analysis ; Mathematical research ; Mathematics ; Period doubling ; Stability</subject><ispartof>Discrete Dynamics in Nature and Society, 2014-01, Vol.2014 (2014), p.718-730-266</ispartof><rights>Copyright © 2014 Senada Kalabušić et al.</rights><rights>COPYRIGHT 2014 John Wiley &amp; Sons, Inc.</rights><rights>Copyright © 2014 Senada Kalabusic et al. Senada Kalabusic et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-a566t-93e4cf346f2827cc723ec08f92de16e7a762208e94de1b78fa15e2b5924696be3</citedby><cites>FETCH-LOGICAL-a566t-93e4cf346f2827cc723ec08f92de16e7a762208e94de1b78fa15e2b5924696be3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.proquest.com/docview/1547911468/fulltextPDF?pq-origsite=primo$$EPDF$$P50$$Gproquest$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/1547911468?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>314,776,780,25733,27903,27904,36991,36992,44569,74872</link.rule.ids></links><search><contributor>Abu-Saris, Raghib</contributor><creatorcontrib>Kalabusic, Senada</creatorcontrib><creatorcontrib>Kulenovic, M.R.S</creatorcontrib><creatorcontrib>Mehuljic, M</creatorcontrib><title>Global Period-Doubling Bifurcation of Quadratic Fractional Second Order Difference Equation</title><title>Discrete Dynamics in Nature and Society</title><description>We investigate the local stability and the global asymptotic stability of the difference equation xn+1=αxn2+βxnxn-1+γxn-1/Axn2+Bxnxn-1+Cxn-1, n=0,1,… with nonnegative parameters and initial conditions such that Axn2+Bxnxn-1+Cxn-1&gt;0, for all n≥0. We obtain the local stability of the equilibrium for all values of parameters and give some global asymptotic stability results for some values of the parameters. We also obtain global dynamics in the special case, where β=B=0, in which case we show that such equation exhibits a global period doubling bifurcation.</description><subject>Asymptotic properties</subject><subject>Bifurcation theory</subject><subject>Bifurcations</subject><subject>Colleges &amp; universities</subject><subject>Difference equations</subject><subject>Dynamics</subject><subject>Economic models</subject><subject>Equations, Quadratic</subject><subject>Equilibrium</subject><subject>Initial conditions</subject><subject>Mathematical analysis</subject><subject>Mathematical research</subject><subject>Mathematics</subject><subject>Period doubling</subject><subject>Stability</subject><issn>1026-0226</issn><issn>1607-887X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><sourceid>DOA</sourceid><recordid>eNqFkc9rFTEQxxdRsFZPnoUFL6JsO5nNZjfH2l8WCn2iguAhZJPJM4_tps2-RfzvnfdWKnqRHCYz-cw386MoXgo4EqJpjhGEPNYIUsCj4kAoaKuua78-5jugqgBRPS2eTdMGAKHTeFB8uxxSb4dyRTkmX52luR_iuC7fxzBnZ7cxjWUK5cfZ-syeKy-ydbso53wil0Zf3mRPuTyLIVCm0VF5fj_vE58XT4IdJnrx2x4WXy7OP59-qK5vLq9OT64r2yi1rXRN0oVaqoAdts61WJODLmj0JBS1tlXI1ZKW7PdtF6xoCPtGo1Ra9VQfFleLrk92Y-5yvLX5p0k2mn0g5bWxmWsfyMjGgwu96vsGpRSyw6a36KGRXoeAirXeLFp3Od3PNG3NbZwcDYMdKc2TEQoBJI8ZGX39D7pJc-bBMNXIVgshVcfU0UKtLf8fx5C2PEE-nm4jz49C5PgJ63VCSS054d2S4HKapkzhoSMBZrdls9uyWbbM9NuF_h5Hb3_E_8CvFpgYoWAf4AY6BM3vq-Xdxhy38U8_K1ZRoEUNUO8VBe6MEkK0ACD-dlrRmbYGg0rVvwDZ5MMp</recordid><startdate>20140101</startdate><enddate>20140101</enddate><creator>Kalabusic, Senada</creator><creator>Kulenovic, M.R.S</creator><creator>Mehuljic, M</creator><general>Hindawi Limiteds</general><general>Hindawi Puplishing Corporation</general><general>Hindawi Publishing Corporation</general><general>John Wiley &amp; Sons, Inc</general><general>Hindawi Limited</general><scope>188</scope><scope>ADJCN</scope><scope>AHFXO</scope><scope>RHU</scope><scope>RHW</scope><scope>RHX</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>CWDGH</scope><scope>DWQXO</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>P5Z</scope><scope>P62</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>DOA</scope></search><sort><creationdate>20140101</creationdate><title>Global Period-Doubling Bifurcation of Quadratic Fractional Second Order Difference Equation</title><author>Kalabusic, Senada ; Kulenovic, M.R.S ; Mehuljic, M</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a566t-93e4cf346f2827cc723ec08f92de16e7a762208e94de1b78fa15e2b5924696be3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Asymptotic properties</topic><topic>Bifurcation theory</topic><topic>Bifurcations</topic><topic>Colleges &amp; universities</topic><topic>Difference equations</topic><topic>Dynamics</topic><topic>Economic models</topic><topic>Equations, Quadratic</topic><topic>Equilibrium</topic><topic>Initial conditions</topic><topic>Mathematical analysis</topic><topic>Mathematical research</topic><topic>Mathematics</topic><topic>Period doubling</topic><topic>Stability</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kalabusic, Senada</creatorcontrib><creatorcontrib>Kulenovic, M.R.S</creatorcontrib><creatorcontrib>Mehuljic, M</creatorcontrib><collection>Airiti Library</collection><collection>الدوريات العلمية والإحصائية - e-Marefa Academic and Statistical Periodicals</collection><collection>معرفة - المحتوى العربي الأكاديمي المتكامل - e-Marefa Academic Complete</collection><collection>Hindawi Publishing Complete</collection><collection>Hindawi Publishing Subscription Journals</collection><collection>Hindawi Publishing Open Access Journals</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical &amp; Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>Advanced Technologies &amp; Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>Middle East &amp; Africa Database</collection><collection>ProQuest Central</collection><collection>Engineering Research Database</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts – Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>ProQuest advanced technologies &amp; aerospace journals</collection><collection>ProQuest Advanced Technologies &amp; Aerospace Collection</collection><collection>Publicly Available Content (ProQuest)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>DOAJ Directory of Open Access Journals</collection><jtitle>Discrete Dynamics in Nature and Society</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kalabusic, Senada</au><au>Kulenovic, M.R.S</au><au>Mehuljic, M</au><au>Abu-Saris, Raghib</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Global Period-Doubling Bifurcation of Quadratic Fractional Second Order Difference Equation</atitle><jtitle>Discrete Dynamics in Nature and Society</jtitle><date>2014-01-01</date><risdate>2014</risdate><volume>2014</volume><issue>2014</issue><spage>718</spage><epage>730-266</epage><pages>718-730-266</pages><issn>1026-0226</issn><eissn>1607-887X</eissn><abstract>We investigate the local stability and the global asymptotic stability of the difference equation xn+1=αxn2+βxnxn-1+γxn-1/Axn2+Bxnxn-1+Cxn-1, n=0,1,… with nonnegative parameters and initial conditions such that Axn2+Bxnxn-1+Cxn-1&gt;0, for all n≥0. We obtain the local stability of the equilibrium for all values of parameters and give some global asymptotic stability results for some values of the parameters. We also obtain global dynamics in the special case, where β=B=0, in which case we show that such equation exhibits a global period doubling bifurcation.</abstract><cop>Cairo, Egypt</cop><pub>Hindawi Limiteds</pub><doi>10.1155/2014/920410</doi><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 1026-0226
ispartof Discrete Dynamics in Nature and Society, 2014-01, Vol.2014 (2014), p.718-730-266
issn 1026-0226
1607-887X
language eng
recordid cdi_doaj_primary_oai_doaj_org_article_45d0cfb6bb524414825ba2d054d9ff26
source Wiley Online Library Open Access; Publicly Available Content (ProQuest)
subjects Asymptotic properties
Bifurcation theory
Bifurcations
Colleges & universities
Difference equations
Dynamics
Economic models
Equations, Quadratic
Equilibrium
Initial conditions
Mathematical analysis
Mathematical research
Mathematics
Period doubling
Stability
title Global Period-Doubling Bifurcation of Quadratic Fractional Second Order Difference Equation
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-28T05%3A04%3A05IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-gale_doaj_&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Global%20Period-Doubling%20Bifurcation%20of%20Quadratic%20Fractional%20Second%20Order%20Difference%20Equation&rft.jtitle=Discrete%20Dynamics%20in%20Nature%20and%20Society&rft.au=Kalabusic,%20Senada&rft.date=2014-01-01&rft.volume=2014&rft.issue=2014&rft.spage=718&rft.epage=730-266&rft.pages=718-730-266&rft.issn=1026-0226&rft.eissn=1607-887X&rft_id=info:doi/10.1155/2014/920410&rft_dat=%3Cgale_doaj_%3EA423816494%3C/gale_doaj_%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-a566t-93e4cf346f2827cc723ec08f92de16e7a762208e94de1b78fa15e2b5924696be3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=1547911468&rft_id=info:pmid/&rft_galeid=A423816494&rft_airiti_id=P20160913003_201412_201611170001_201611170001_718_730_266&rfr_iscdi=true