Delay-induced stochastic bifurcations in a bistable system under white noise
In this paper, the effects of noise and time delay on stochastic bifurcations are investigated theoretically and numerically in a time-delayed Duffing-Van der Pol oscillator subjected to white noise. Due to the time delay, the random response is not Markovian. Thereby, approximate methods have been...
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| Veröffentlicht in: | Chaos (Woodbury, N.Y.) N.Y.), 2015-08, Vol.25 (8), p.083102-083102 |
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| container_title | Chaos (Woodbury, N.Y.) |
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| creator | Sun, Zhongkui Fu, Jin Xiao, Yuzhu Xu, Wei |
| description | In this paper, the effects of noise and time delay on stochastic bifurcations are investigated theoretically and numerically in a time-delayed Duffing-Van der Pol oscillator subjected to white noise. Due to the time delay, the random response is not Markovian. Thereby, approximate methods have been adopted to obtain the Fokker-Planck-Kolmogorov equation and the stationary probability density function for amplitude of the response. Based on the knowledge that stochastic bifurcation is characterized by the qualitative properties of the steady-state probability distribution, it is found that time delay and feedback intensity as well as noise intensity will induce the appearance of stochastic P-bifurcation. Besides, results demonstrated that the effects of the strength of the delayed displacement feedback on stochastic bifurcation are accompanied by the sensitive dependence on time delay. Furthermore, the results from numerical simulations best confirm the effectiveness of the theoretical analyses. |
| doi_str_mv | 10.1063/1.4927646 |
| format | Article |
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Due to the time delay, the random response is not Markovian. Thereby, approximate methods have been adopted to obtain the Fokker-Planck-Kolmogorov equation and the stationary probability density function for amplitude of the response. Based on the knowledge that stochastic bifurcation is characterized by the qualitative properties of the steady-state probability distribution, it is found that time delay and feedback intensity as well as noise intensity will induce the appearance of stochastic P-bifurcation. Besides, results demonstrated that the effects of the strength of the delayed displacement feedback on stochastic bifurcation are accompanied by the sensitive dependence on time delay. Furthermore, the results from numerical simulations best confirm the effectiveness of the theoretical analyses.</description><identifier>ISSN: 1054-1500</identifier><identifier>EISSN: 1089-7682</identifier><identifier>DOI: 10.1063/1.4927646</identifier><identifier>PMID: 26328553</identifier><language>eng</language><publisher>United States: American Institute of Physics</publisher><subject>Approximation ; BIFURCATION ; Bifurcation theory ; CHAPMAN-KOLMOGOROV EQUATION ; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS ; Computer simulation ; COMPUTERIZED SIMULATION ; Delay ; Economic models ; FEEDBACK ; FOKKER-PLANCK EQUATION ; MARKOV PROCESS ; Markov processes ; NOISE ; Noise intensity ; OSCILLATORS ; PROBABILITY DENSITY FUNCTIONS ; Probability theory ; Qualitative analysis ; RANDOMNESS ; TIME DELAY ; Time dependence ; Time lag ; White noise</subject><ispartof>Chaos (Woodbury, N.Y.), 2015-08, Vol.25 (8), p.083102-083102</ispartof><rights>2015 AIP Publishing LLC.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c341t-8574b4ea491221a6e5e5de261e336375c6b50a26a6919fc68d30a4fc1fe44adc3</citedby><cites>FETCH-LOGICAL-c341t-8574b4ea491221a6e5e5de261e336375c6b50a26a6919fc68d30a4fc1fe44adc3</cites><orcidid>0000-0001-5847-4426</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,780,784,885,27923,27924</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/26328553$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink><backlink>$$Uhttps://www.osti.gov/biblio/22482311$$D View this record in Osti.gov$$Hfree_for_read</backlink></links><search><creatorcontrib>Sun, Zhongkui</creatorcontrib><creatorcontrib>Fu, Jin</creatorcontrib><creatorcontrib>Xiao, Yuzhu</creatorcontrib><creatorcontrib>Xu, Wei</creatorcontrib><title>Delay-induced stochastic bifurcations in a bistable system under white noise</title><title>Chaos (Woodbury, N.Y.)</title><addtitle>Chaos</addtitle><description>In this paper, the effects of noise and time delay on stochastic bifurcations are investigated theoretically and numerically in a time-delayed Duffing-Van der Pol oscillator subjected to white noise. Due to the time delay, the random response is not Markovian. Thereby, approximate methods have been adopted to obtain the Fokker-Planck-Kolmogorov equation and the stationary probability density function for amplitude of the response. Based on the knowledge that stochastic bifurcation is characterized by the qualitative properties of the steady-state probability distribution, it is found that time delay and feedback intensity as well as noise intensity will induce the appearance of stochastic P-bifurcation. Besides, results demonstrated that the effects of the strength of the delayed displacement feedback on stochastic bifurcation are accompanied by the sensitive dependence on time delay. Furthermore, the results from numerical simulations best confirm the effectiveness of the theoretical analyses.</description><subject>Approximation</subject><subject>BIFURCATION</subject><subject>Bifurcation theory</subject><subject>CHAPMAN-KOLMOGOROV EQUATION</subject><subject>CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS</subject><subject>Computer simulation</subject><subject>COMPUTERIZED SIMULATION</subject><subject>Delay</subject><subject>Economic models</subject><subject>FEEDBACK</subject><subject>FOKKER-PLANCK EQUATION</subject><subject>MARKOV PROCESS</subject><subject>Markov processes</subject><subject>NOISE</subject><subject>Noise intensity</subject><subject>OSCILLATORS</subject><subject>PROBABILITY DENSITY FUNCTIONS</subject><subject>Probability theory</subject><subject>Qualitative analysis</subject><subject>RANDOMNESS</subject><subject>TIME DELAY</subject><subject>Time dependence</subject><subject>Time lag</subject><subject>White noise</subject><issn>1054-1500</issn><issn>1089-7682</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><recordid>eNpFkc1Lw0AQxRdRtFYP_gMS8KKH1J39SnKU-gkFL3peNpsJ3ZLuanaD9L83pbWeZhh-PN68R8gV0BlQxe9hJipWKKGOyARoWeWFKtnxdpciB0npGTmPcUUpBcblKTljirNSSj4hi0fszCZ3vhksNllMwS5NTM5mtWuH3prkgo-Z85kZLzGZusMsbmLCdTb4BvvsZ-kSZj64iBfkpDVdxMv9nJLP56eP-Wu-eH95mz8scssFpLyUhagFGlEBY2AUSpQNMgXIueKFtKqW1DBlVAVVa1XZcGpEa6FFIUxj-ZTc7HTD6FRHOxqwSxu8R5s0Y6JkHGCkbnfUVx--B4xJr1202HXGYxiihoJWvBJQyX_BA7oKQ-_HHzQDJoCCADVSdzvK9iHGHlv91bu16TcaqN4WoUHvixjZ673iUK-xOZB_yfNfV9CAew</recordid><startdate>20150801</startdate><enddate>20150801</enddate><creator>Sun, Zhongkui</creator><creator>Fu, Jin</creator><creator>Xiao, Yuzhu</creator><creator>Xu, Wei</creator><general>American Institute of Physics</general><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope><scope>7X8</scope><scope>OTOTI</scope><orcidid>https://orcid.org/0000-0001-5847-4426</orcidid></search><sort><creationdate>20150801</creationdate><title>Delay-induced stochastic bifurcations in a bistable system under white noise</title><author>Sun, Zhongkui ; Fu, Jin ; Xiao, Yuzhu ; Xu, Wei</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c341t-8574b4ea491221a6e5e5de261e336375c6b50a26a6919fc68d30a4fc1fe44adc3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Approximation</topic><topic>BIFURCATION</topic><topic>Bifurcation theory</topic><topic>CHAPMAN-KOLMOGOROV EQUATION</topic><topic>CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS</topic><topic>Computer simulation</topic><topic>COMPUTERIZED SIMULATION</topic><topic>Delay</topic><topic>Economic models</topic><topic>FEEDBACK</topic><topic>FOKKER-PLANCK EQUATION</topic><topic>MARKOV PROCESS</topic><topic>Markov processes</topic><topic>NOISE</topic><topic>Noise intensity</topic><topic>OSCILLATORS</topic><topic>PROBABILITY DENSITY FUNCTIONS</topic><topic>Probability theory</topic><topic>Qualitative analysis</topic><topic>RANDOMNESS</topic><topic>TIME DELAY</topic><topic>Time dependence</topic><topic>Time lag</topic><topic>White noise</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Sun, Zhongkui</creatorcontrib><creatorcontrib>Fu, Jin</creatorcontrib><creatorcontrib>Xiao, Yuzhu</creatorcontrib><creatorcontrib>Xu, Wei</creatorcontrib><collection>PubMed</collection><collection>CrossRef</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>MEDLINE - Academic</collection><collection>OSTI.GOV</collection><jtitle>Chaos (Woodbury, N.Y.)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Sun, Zhongkui</au><au>Fu, Jin</au><au>Xiao, Yuzhu</au><au>Xu, Wei</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Delay-induced stochastic bifurcations in a bistable system under white noise</atitle><jtitle>Chaos (Woodbury, N.Y.)</jtitle><addtitle>Chaos</addtitle><date>2015-08-01</date><risdate>2015</risdate><volume>25</volume><issue>8</issue><spage>083102</spage><epage>083102</epage><pages>083102-083102</pages><issn>1054-1500</issn><eissn>1089-7682</eissn><abstract>In this paper, the effects of noise and time delay on stochastic bifurcations are investigated theoretically and numerically in a time-delayed Duffing-Van der Pol oscillator subjected to white noise. Due to the time delay, the random response is not Markovian. Thereby, approximate methods have been adopted to obtain the Fokker-Planck-Kolmogorov equation and the stationary probability density function for amplitude of the response. Based on the knowledge that stochastic bifurcation is characterized by the qualitative properties of the steady-state probability distribution, it is found that time delay and feedback intensity as well as noise intensity will induce the appearance of stochastic P-bifurcation. Besides, results demonstrated that the effects of the strength of the delayed displacement feedback on stochastic bifurcation are accompanied by the sensitive dependence on time delay. Furthermore, the results from numerical simulations best confirm the effectiveness of the theoretical analyses.</abstract><cop>United States</cop><pub>American Institute of Physics</pub><pmid>26328553</pmid><doi>10.1063/1.4927646</doi><tpages>1</tpages><orcidid>https://orcid.org/0000-0001-5847-4426</orcidid></addata></record> |
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| ispartof | Chaos (Woodbury, N.Y.), 2015-08, Vol.25 (8), p.083102-083102 |
| issn | 1054-1500 1089-7682 |
| language | eng |
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| source | American Institute of Physics (AIP) Journals; Alma/SFX Local Collection |
| subjects | Approximation BIFURCATION Bifurcation theory CHAPMAN-KOLMOGOROV EQUATION CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS Computer simulation COMPUTERIZED SIMULATION Delay Economic models FEEDBACK FOKKER-PLANCK EQUATION MARKOV PROCESS Markov processes NOISE Noise intensity OSCILLATORS PROBABILITY DENSITY FUNCTIONS Probability theory Qualitative analysis RANDOMNESS TIME DELAY Time dependence Time lag White noise |
| title | Delay-induced stochastic bifurcations in a bistable system under white noise |
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