Bifurcation and Chaos of a Discrete-Time Mathematical Model for Tissue Inflammation
Abstract In this paper, the discrete-time mathematical model for tissue inflammation obtained by Euler is investigated in detail. Conditions of the existence for fold bifurcation, flip bifurcation and Hopf bifurcation are derived by using center manifold theorem and bifurcation theory, and chaos in...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Chen, Xianwei [verfasserIn] |
|---|
| Format: |
Artikel |
|---|---|
| Sprache: |
Englisch |
| Erschienen: |
2014 |
|---|
| Schlagwörter: |
|---|
| Anmerkung: |
© Springer Science+Business Media New York 2014 |
|---|
| Übergeordnetes Werk: |
Enthalten in: Journal of dynamics and differential equations - Springer US, 1989, 28(2014), 1 vom: 25. Nov., Seite 281-299 |
|---|---|
| Übergeordnetes Werk: |
volume:28 ; year:2014 ; number:1 ; day:25 ; month:11 ; pages:281-299 |
| Links: |
|---|
| DOI / URN: |
10.1007/s10884-014-9413-y |
|---|
| Katalog-ID: |
OLC2063459649 |
|---|
| LEADER | 01000caa a22002652 4500 | ||
|---|---|---|---|
| 001 | OLC2063459649 | ||
| 003 | DE-627 | ||
| 005 | 20230503135844.0 | ||
| 007 | tu | ||
| 008 | 200819s2014 xx ||||| 00| ||eng c | ||
| 024 | 7 | |a 10.1007/s10884-014-9413-y |2 doi | |
| 035 | |a (DE-627)OLC2063459649 | ||
| 035 | |a (DE-He213)s10884-014-9413-y-p | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rakwb | ||
| 041 | |a eng | ||
| 082 | 0 | 4 | |a 510 |q VZ |
| 084 | |a 17,1 |2 ssgn | ||
| 100 | 1 | |a Chen, Xianwei |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Bifurcation and Chaos of a Discrete-Time Mathematical Model for Tissue Inflammation |
| 264 | 1 | |c 2014 | |
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a ohne Hilfsmittel zu benutzen |b n |2 rdamedia | ||
| 338 | |a Band |b nc |2 rdacarrier | ||
| 500 | |a © Springer Science+Business Media New York 2014 | ||
| 520 | |a Abstract In this paper, the discrete-time mathematical model for tissue inflammation obtained by Euler is investigated in detail. Conditions of the existence for fold bifurcation, flip bifurcation and Hopf bifurcation are derived by using center manifold theorem and bifurcation theory, and chaos in the sense of Marotto is proved by analytical method. Numerical simulations, including bifurcation diagrams, Lyapunov exponents, fractal dimensions, and phase portraits are plotted to perfectly show the consistence with the theoretical analysis. | ||
| 650 | 4 | |a Tissue inflammation | |
| 650 | 4 | |a Fold bifurcation | |
| 650 | 4 | |a Flip bifurcation | |
| 650 | 4 | |a Hopf bifurcation | |
| 650 | 4 | |a Marotto’s chaos | |
| 700 | 1 | |a Yuan, Shaoliang |4 aut | |
| 700 | 1 | |a Jing, Zhujun |4 aut | |
| 700 | 1 | |a Fu, Xiangling |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Journal of dynamics and differential equations |d Springer US, 1989 |g 28(2014), 1 vom: 25. Nov., Seite 281-299 |w (DE-627)165666455 |w (DE-600)1008261-X |w (DE-576)023042591 |x 1040-7294 |7 nnns |
| 773 | 1 | 8 | |g volume:28 |g year:2014 |g number:1 |g day:25 |g month:11 |g pages:281-299 |
| 856 | 4 | 1 | |u https://doi.org/10.1007/s10884-014-9413-y |z lizenzpflichtig |3 Volltext |
| 912 | |a GBV_USEFLAG_A | ||
| 912 | |a SYSFLAG_A | ||
| 912 | |a GBV_OLC | ||
| 912 | |a SSG-OLC-MAT | ||
| 912 | |a SSG-OPC-MAT | ||
| 912 | |a GBV_ILN_32 | ||
| 912 | |a GBV_ILN_40 | ||
| 912 | |a GBV_ILN_70 | ||
| 912 | |a GBV_ILN_2088 | ||
| 912 | |a GBV_ILN_4126 | ||
| 951 | |a AR | ||
| 952 | |d 28 |j 2014 |e 1 |b 25 |c 11 |h 281-299 | ||
| author_variant |
x c xc s y sy z j zj x f xf |
|---|---|
| matchkey_str |
article:10407294:2014----::iuctoadhooaiceeieahmtcloefr |
| hierarchy_sort_str |
2014 |
| publishDate |
2014 |
| allfields |
10.1007/s10884-014-9413-y doi (DE-627)OLC2063459649 (DE-He213)s10884-014-9413-y-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Chen, Xianwei verfasserin aut Bifurcation and Chaos of a Discrete-Time Mathematical Model for Tissue Inflammation 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2014 Abstract In this paper, the discrete-time mathematical model for tissue inflammation obtained by Euler is investigated in detail. Conditions of the existence for fold bifurcation, flip bifurcation and Hopf bifurcation are derived by using center manifold theorem and bifurcation theory, and chaos in the sense of Marotto is proved by analytical method. Numerical simulations, including bifurcation diagrams, Lyapunov exponents, fractal dimensions, and phase portraits are plotted to perfectly show the consistence with the theoretical analysis. Tissue inflammation Fold bifurcation Flip bifurcation Hopf bifurcation Marotto’s chaos Yuan, Shaoliang aut Jing, Zhujun aut Fu, Xiangling aut Enthalten in Journal of dynamics and differential equations Springer US, 1989 28(2014), 1 vom: 25. Nov., Seite 281-299 (DE-627)165666455 (DE-600)1008261-X (DE-576)023042591 1040-7294 nnns volume:28 year:2014 number:1 day:25 month:11 pages:281-299 https://doi.org/10.1007/s10884-014-9413-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_32 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2088 GBV_ILN_4126 AR 28 2014 1 25 11 281-299 |
| spelling |
10.1007/s10884-014-9413-y doi (DE-627)OLC2063459649 (DE-He213)s10884-014-9413-y-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Chen, Xianwei verfasserin aut Bifurcation and Chaos of a Discrete-Time Mathematical Model for Tissue Inflammation 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2014 Abstract In this paper, the discrete-time mathematical model for tissue inflammation obtained by Euler is investigated in detail. Conditions of the existence for fold bifurcation, flip bifurcation and Hopf bifurcation are derived by using center manifold theorem and bifurcation theory, and chaos in the sense of Marotto is proved by analytical method. Numerical simulations, including bifurcation diagrams, Lyapunov exponents, fractal dimensions, and phase portraits are plotted to perfectly show the consistence with the theoretical analysis. Tissue inflammation Fold bifurcation Flip bifurcation Hopf bifurcation Marotto’s chaos Yuan, Shaoliang aut Jing, Zhujun aut Fu, Xiangling aut Enthalten in Journal of dynamics and differential equations Springer US, 1989 28(2014), 1 vom: 25. Nov., Seite 281-299 (DE-627)165666455 (DE-600)1008261-X (DE-576)023042591 1040-7294 nnns volume:28 year:2014 number:1 day:25 month:11 pages:281-299 https://doi.org/10.1007/s10884-014-9413-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_32 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2088 GBV_ILN_4126 AR 28 2014 1 25 11 281-299 |
| allfields_unstemmed |
10.1007/s10884-014-9413-y doi (DE-627)OLC2063459649 (DE-He213)s10884-014-9413-y-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Chen, Xianwei verfasserin aut Bifurcation and Chaos of a Discrete-Time Mathematical Model for Tissue Inflammation 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2014 Abstract In this paper, the discrete-time mathematical model for tissue inflammation obtained by Euler is investigated in detail. Conditions of the existence for fold bifurcation, flip bifurcation and Hopf bifurcation are derived by using center manifold theorem and bifurcation theory, and chaos in the sense of Marotto is proved by analytical method. Numerical simulations, including bifurcation diagrams, Lyapunov exponents, fractal dimensions, and phase portraits are plotted to perfectly show the consistence with the theoretical analysis. Tissue inflammation Fold bifurcation Flip bifurcation Hopf bifurcation Marotto’s chaos Yuan, Shaoliang aut Jing, Zhujun aut Fu, Xiangling aut Enthalten in Journal of dynamics and differential equations Springer US, 1989 28(2014), 1 vom: 25. Nov., Seite 281-299 (DE-627)165666455 (DE-600)1008261-X (DE-576)023042591 1040-7294 nnns volume:28 year:2014 number:1 day:25 month:11 pages:281-299 https://doi.org/10.1007/s10884-014-9413-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_32 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2088 GBV_ILN_4126 AR 28 2014 1 25 11 281-299 |
| allfieldsGer |
10.1007/s10884-014-9413-y doi (DE-627)OLC2063459649 (DE-He213)s10884-014-9413-y-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Chen, Xianwei verfasserin aut Bifurcation and Chaos of a Discrete-Time Mathematical Model for Tissue Inflammation 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2014 Abstract In this paper, the discrete-time mathematical model for tissue inflammation obtained by Euler is investigated in detail. Conditions of the existence for fold bifurcation, flip bifurcation and Hopf bifurcation are derived by using center manifold theorem and bifurcation theory, and chaos in the sense of Marotto is proved by analytical method. Numerical simulations, including bifurcation diagrams, Lyapunov exponents, fractal dimensions, and phase portraits are plotted to perfectly show the consistence with the theoretical analysis. Tissue inflammation Fold bifurcation Flip bifurcation Hopf bifurcation Marotto’s chaos Yuan, Shaoliang aut Jing, Zhujun aut Fu, Xiangling aut Enthalten in Journal of dynamics and differential equations Springer US, 1989 28(2014), 1 vom: 25. Nov., Seite 281-299 (DE-627)165666455 (DE-600)1008261-X (DE-576)023042591 1040-7294 nnns volume:28 year:2014 number:1 day:25 month:11 pages:281-299 https://doi.org/10.1007/s10884-014-9413-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_32 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2088 GBV_ILN_4126 AR 28 2014 1 25 11 281-299 |
| allfieldsSound |
10.1007/s10884-014-9413-y doi (DE-627)OLC2063459649 (DE-He213)s10884-014-9413-y-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Chen, Xianwei verfasserin aut Bifurcation and Chaos of a Discrete-Time Mathematical Model for Tissue Inflammation 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2014 Abstract In this paper, the discrete-time mathematical model for tissue inflammation obtained by Euler is investigated in detail. Conditions of the existence for fold bifurcation, flip bifurcation and Hopf bifurcation are derived by using center manifold theorem and bifurcation theory, and chaos in the sense of Marotto is proved by analytical method. Numerical simulations, including bifurcation diagrams, Lyapunov exponents, fractal dimensions, and phase portraits are plotted to perfectly show the consistence with the theoretical analysis. Tissue inflammation Fold bifurcation Flip bifurcation Hopf bifurcation Marotto’s chaos Yuan, Shaoliang aut Jing, Zhujun aut Fu, Xiangling aut Enthalten in Journal of dynamics and differential equations Springer US, 1989 28(2014), 1 vom: 25. Nov., Seite 281-299 (DE-627)165666455 (DE-600)1008261-X (DE-576)023042591 1040-7294 nnns volume:28 year:2014 number:1 day:25 month:11 pages:281-299 https://doi.org/10.1007/s10884-014-9413-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_32 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2088 GBV_ILN_4126 AR 28 2014 1 25 11 281-299 |
| language |
English |
| source |
Enthalten in Journal of dynamics and differential equations 28(2014), 1 vom: 25. Nov., Seite 281-299 volume:28 year:2014 number:1 day:25 month:11 pages:281-299 |
| sourceStr |
Enthalten in Journal of dynamics and differential equations 28(2014), 1 vom: 25. Nov., Seite 281-299 volume:28 year:2014 number:1 day:25 month:11 pages:281-299 |
| format_phy_str_mv |
Article |
| institution |
findex.gbv.de |
| topic_facet |
Tissue inflammation Fold bifurcation Flip bifurcation Hopf bifurcation Marotto’s chaos |
| dewey-raw |
510 |
| isfreeaccess_bool |
false |
| container_title |
Journal of dynamics and differential equations |
| authorswithroles_txt_mv |
Chen, Xianwei @@aut@@ Yuan, Shaoliang @@aut@@ Jing, Zhujun @@aut@@ Fu, Xiangling @@aut@@ |
| publishDateDaySort_date |
2014-11-25T00:00:00Z |
| hierarchy_top_id |
165666455 |
| dewey-sort |
3510 |
| id |
OLC2063459649 |
| language_de |
englisch |
| fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2063459649</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230503135844.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200819s2014 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10884-014-9413-y</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2063459649</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s10884-014-9413-y-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">17,1</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Chen, Xianwei</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Bifurcation and Chaos of a Discrete-Time Mathematical Model for Tissue Inflammation</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2014</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer Science+Business Media New York 2014</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract In this paper, the discrete-time mathematical model for tissue inflammation obtained by Euler is investigated in detail. Conditions of the existence for fold bifurcation, flip bifurcation and Hopf bifurcation are derived by using center manifold theorem and bifurcation theory, and chaos in the sense of Marotto is proved by analytical method. Numerical simulations, including bifurcation diagrams, Lyapunov exponents, fractal dimensions, and phase portraits are plotted to perfectly show the consistence with the theoretical analysis.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Tissue inflammation</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Fold bifurcation</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Flip bifurcation</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Hopf bifurcation</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Marotto’s chaos</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Yuan, Shaoliang</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Jing, Zhujun</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Fu, Xiangling</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Journal of dynamics and differential equations</subfield><subfield code="d">Springer US, 1989</subfield><subfield code="g">28(2014), 1 vom: 25. Nov., Seite 281-299</subfield><subfield code="w">(DE-627)165666455</subfield><subfield code="w">(DE-600)1008261-X</subfield><subfield code="w">(DE-576)023042591</subfield><subfield code="x">1040-7294</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:28</subfield><subfield code="g">year:2014</subfield><subfield code="g">number:1</subfield><subfield code="g">day:25</subfield><subfield code="g">month:11</subfield><subfield code="g">pages:281-299</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1007/s10884-014-9413-y</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_32</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_40</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2088</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4126</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">28</subfield><subfield code="j">2014</subfield><subfield code="e">1</subfield><subfield code="b">25</subfield><subfield code="c">11</subfield><subfield code="h">281-299</subfield></datafield></record></collection>
|
| author |
Chen, Xianwei |
| spellingShingle |
Chen, Xianwei ddc 510 ssgn 17,1 misc Tissue inflammation misc Fold bifurcation misc Flip bifurcation misc Hopf bifurcation misc Marotto’s chaos Bifurcation and Chaos of a Discrete-Time Mathematical Model for Tissue Inflammation |
| authorStr |
Chen, Xianwei |
| ppnlink_with_tag_str_mv |
@@773@@(DE-627)165666455 |
| format |
Article |
| dewey-ones |
510 - Mathematics |
| delete_txt_mv |
keep |
| author_role |
aut aut aut aut |
| collection |
OLC |
| remote_str |
false |
| illustrated |
Not Illustrated |
| issn |
1040-7294 |
| topic_title |
510 VZ 17,1 ssgn Bifurcation and Chaos of a Discrete-Time Mathematical Model for Tissue Inflammation Tissue inflammation Fold bifurcation Flip bifurcation Hopf bifurcation Marotto’s chaos |
| topic |
ddc 510 ssgn 17,1 misc Tissue inflammation misc Fold bifurcation misc Flip bifurcation misc Hopf bifurcation misc Marotto’s chaos |
| topic_unstemmed |
ddc 510 ssgn 17,1 misc Tissue inflammation misc Fold bifurcation misc Flip bifurcation misc Hopf bifurcation misc Marotto’s chaos |
| topic_browse |
ddc 510 ssgn 17,1 misc Tissue inflammation misc Fold bifurcation misc Flip bifurcation misc Hopf bifurcation misc Marotto’s chaos |
| format_facet |
Aufsätze Gedruckte Aufsätze |
| format_main_str_mv |
Text Zeitschrift/Artikel |
| carriertype_str_mv |
nc |
| hierarchy_parent_title |
Journal of dynamics and differential equations |
| hierarchy_parent_id |
165666455 |
| dewey-tens |
510 - Mathematics |
| hierarchy_top_title |
Journal of dynamics and differential equations |
| isfreeaccess_txt |
false |
| familylinks_str_mv |
(DE-627)165666455 (DE-600)1008261-X (DE-576)023042591 |
| title |
Bifurcation and Chaos of a Discrete-Time Mathematical Model for Tissue Inflammation |
| ctrlnum |
(DE-627)OLC2063459649 (DE-He213)s10884-014-9413-y-p |
| title_full |
Bifurcation and Chaos of a Discrete-Time Mathematical Model for Tissue Inflammation |
| author_sort |
Chen, Xianwei |
| journal |
Journal of dynamics and differential equations |
| journalStr |
Journal of dynamics and differential equations |
| lang_code |
eng |
| isOA_bool |
false |
| dewey-hundreds |
500 - Science |
| recordtype |
marc |
| publishDateSort |
2014 |
| contenttype_str_mv |
txt |
| container_start_page |
281 |
| author_browse |
Chen, Xianwei Yuan, Shaoliang Jing, Zhujun Fu, Xiangling |
| container_volume |
28 |
| class |
510 VZ 17,1 ssgn |
| format_se |
Aufsätze |
| author-letter |
Chen, Xianwei |
| doi_str_mv |
10.1007/s10884-014-9413-y |
| dewey-full |
510 |
| title_sort |
bifurcation and chaos of a discrete-time mathematical model for tissue inflammation |
| title_auth |
Bifurcation and Chaos of a Discrete-Time Mathematical Model for Tissue Inflammation |
| abstract |
Abstract In this paper, the discrete-time mathematical model for tissue inflammation obtained by Euler is investigated in detail. Conditions of the existence for fold bifurcation, flip bifurcation and Hopf bifurcation are derived by using center manifold theorem and bifurcation theory, and chaos in the sense of Marotto is proved by analytical method. Numerical simulations, including bifurcation diagrams, Lyapunov exponents, fractal dimensions, and phase portraits are plotted to perfectly show the consistence with the theoretical analysis. © Springer Science+Business Media New York 2014 |
| abstractGer |
Abstract In this paper, the discrete-time mathematical model for tissue inflammation obtained by Euler is investigated in detail. Conditions of the existence for fold bifurcation, flip bifurcation and Hopf bifurcation are derived by using center manifold theorem and bifurcation theory, and chaos in the sense of Marotto is proved by analytical method. Numerical simulations, including bifurcation diagrams, Lyapunov exponents, fractal dimensions, and phase portraits are plotted to perfectly show the consistence with the theoretical analysis. © Springer Science+Business Media New York 2014 |
| abstract_unstemmed |
Abstract In this paper, the discrete-time mathematical model for tissue inflammation obtained by Euler is investigated in detail. Conditions of the existence for fold bifurcation, flip bifurcation and Hopf bifurcation are derived by using center manifold theorem and bifurcation theory, and chaos in the sense of Marotto is proved by analytical method. Numerical simulations, including bifurcation diagrams, Lyapunov exponents, fractal dimensions, and phase portraits are plotted to perfectly show the consistence with the theoretical analysis. © Springer Science+Business Media New York 2014 |
| collection_details |
GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_32 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2088 GBV_ILN_4126 |
| container_issue |
1 |
| title_short |
Bifurcation and Chaos of a Discrete-Time Mathematical Model for Tissue Inflammation |
| url |
https://doi.org/10.1007/s10884-014-9413-y |
| remote_bool |
false |
| author2 |
Yuan, Shaoliang Jing, Zhujun Fu, Xiangling |
| author2Str |
Yuan, Shaoliang Jing, Zhujun Fu, Xiangling |
| ppnlink |
165666455 |
| mediatype_str_mv |
n |
| isOA_txt |
false |
| hochschulschrift_bool |
false |
| doi_str |
10.1007/s10884-014-9413-y |
| up_date |
2024-07-03T19:07:28.164Z |
| _version_ |
1803586002659311616 |
| fullrecord_marcxml |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2063459649</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230503135844.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200819s2014 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10884-014-9413-y</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2063459649</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s10884-014-9413-y-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">17,1</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Chen, Xianwei</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Bifurcation and Chaos of a Discrete-Time Mathematical Model for Tissue Inflammation</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2014</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer Science+Business Media New York 2014</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract In this paper, the discrete-time mathematical model for tissue inflammation obtained by Euler is investigated in detail. Conditions of the existence for fold bifurcation, flip bifurcation and Hopf bifurcation are derived by using center manifold theorem and bifurcation theory, and chaos in the sense of Marotto is proved by analytical method. Numerical simulations, including bifurcation diagrams, Lyapunov exponents, fractal dimensions, and phase portraits are plotted to perfectly show the consistence with the theoretical analysis.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Tissue inflammation</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Fold bifurcation</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Flip bifurcation</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Hopf bifurcation</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Marotto’s chaos</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Yuan, Shaoliang</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Jing, Zhujun</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Fu, Xiangling</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Journal of dynamics and differential equations</subfield><subfield code="d">Springer US, 1989</subfield><subfield code="g">28(2014), 1 vom: 25. Nov., Seite 281-299</subfield><subfield code="w">(DE-627)165666455</subfield><subfield code="w">(DE-600)1008261-X</subfield><subfield code="w">(DE-576)023042591</subfield><subfield code="x">1040-7294</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:28</subfield><subfield code="g">year:2014</subfield><subfield code="g">number:1</subfield><subfield code="g">day:25</subfield><subfield code="g">month:11</subfield><subfield code="g">pages:281-299</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1007/s10884-014-9413-y</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_32</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_40</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2088</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4126</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">28</subfield><subfield code="j">2014</subfield><subfield code="e">1</subfield><subfield code="b">25</subfield><subfield code="c">11</subfield><subfield code="h">281-299</subfield></datafield></record></collection>
|
| score |
7.399866 |