Evolution of Biological Systems in Random Media: Limit Theorems and Stability:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
2003
|
| Schriftenreihe: | Mathematical Modelling: Theory and Applications
18 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The book is devoted to the study of limit theorems and stability of evolving biologieal systems of "particles" in random environment. Here the term "particle" is used broadly to include moleculas in the infected individuals considered in epidemie models, species in logistie growth models, age classes of population in demographics models, to name a few. The evolution of these biological systems is usually described by difference or differential equations in a given space X of the following type and dxt/dt = g(Xt, y), here, the vector x describes the state of the considered system, 9 specifies how the system's states are evolved in time (discrete or continuous), and the parameter y describes the change ofthe environment. For example, in the discrete-time logistic growth model or the continuous-time logistic growth model dNt/dt = r(y)Nt(l-Nt/K(y)), N or Nt is the population of the species at time n or t, r(y) is the per capita n birth rate, and K(y) is the carrying capacity of the environment, we naturally have X = R, X == Nn(X == Nt), g(x, y) = r(y)x(l-xl K(y)) , xE X. Note that n t for a predator-prey model and for some epidemie models, we will have that X = 2 3 R and X = R , respectively. In th case of logistic growth models, parameters r(y) and K(y) normaIly depend on some random variable y |
| Beschreibung: | 1 Online-Ressource (XX, 218 p) |
| ISBN: | 9789401715065 9789048163984 |
| ISSN: | 1386-2960 |
| DOI: | 10.1007/978-94-017-1506-5 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042424251 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s2003 |||| o||u| ||||||eng d | ||
| 020 | |a 9789401715065 |c Online |9 978-94-017-1506-5 | ||
| 020 | |a 9789048163984 |c Print |9 978-90-481-6398-4 | ||
| 024 | 7 | |a 10.1007/978-94-017-1506-5 |2 doi | |
| 035 | |a (OCoLC)864039809 | ||
| 035 | |a (DE-599)BVBBV042424251 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 570.285 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Swishchuk, Anatoly |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Evolution of Biological Systems in Random Media: Limit Theorems and Stability |c by Anatoly Swishchuk, Jianhong Wu |
| 264 | 1 | |a Dordrecht |b Springer Netherlands |c 2003 | |
| 300 | |a 1 Online-Ressource (XX, 218 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Mathematical Modelling: Theory and Applications |v 18 |x 1386-2960 | |
| 500 | |a The book is devoted to the study of limit theorems and stability of evolving biologieal systems of "particles" in random environment. Here the term "particle" is used broadly to include moleculas in the infected individuals considered in epidemie models, species in logistie growth models, age classes of population in demographics models, to name a few. The evolution of these biological systems is usually described by difference or differential equations in a given space X of the following type and dxt/dt = g(Xt, y), here, the vector x describes the state of the considered system, 9 specifies how the system's states are evolved in time (discrete or continuous), and the parameter y describes the change ofthe environment. For example, in the discrete-time logistic growth model or the continuous-time logistic growth model dNt/dt = r(y)Nt(l-Nt/K(y)), N or Nt is the population of the species at time n or t, r(y) is the per capita n birth rate, and K(y) is the carrying capacity of the environment, we naturally have X = R, X == Nn(X == Nt), g(x, y) = r(y)x(l-xl K(y)) , xE X. Note that n t for a predator-prey model and for some epidemie models, we will have that X = 2 3 R and X = R , respectively. In th case of logistic growth models, parameters r(y) and K(y) normaIly depend on some random variable y | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Human genetics | |
| 650 | 4 | |a Epidemiology | |
| 650 | 4 | |a Distribution (Probability theory) | |
| 650 | 4 | |a Population | |
| 650 | 4 | |a Mathematical and Computational Biology | |
| 650 | 4 | |a Probability Theory and Stochastic Processes | |
| 650 | 4 | |a Human Genetics | |
| 650 | 4 | |a Population Economics | |
| 650 | 4 | |a Mathematik | |
| 700 | 1 | |a Wu, Jianhong |e Sonstige |4 oth | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-94-017-1506-5 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027859668 | ||
Datensatz im Suchindex
| _version_ | 1804153101012172800 |
|---|---|
| any_adam_object | |
| author | Swishchuk, Anatoly |
| author_facet | Swishchuk, Anatoly |
| author_role | aut |
| author_sort | Swishchuk, Anatoly |
| author_variant | a s as |
| building | Verbundindex |
| bvnumber | BV042424251 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)864039809 (DE-599)BVBBV042424251 |
| dewey-full | 570.285 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 570 - Biology |
| dewey-raw | 570.285 |
| dewey-search | 570.285 |
| dewey-sort | 3570.285 |
| dewey-tens | 570 - Biology |
| discipline | Biologie Mathematik |
| doi_str_mv | 10.1007/978-94-017-1506-5 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02967nmm a2200493zcb4500</leader><controlfield tag="001">BV042424251</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s2003 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789401715065</subfield><subfield code="c">Online</subfield><subfield code="9">978-94-017-1506-5</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789048163984</subfield><subfield code="c">Print</subfield><subfield code="9">978-90-481-6398-4</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-94-017-1506-5</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)864039809</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042424251</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">570.285</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Swishchuk, Anatoly</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Evolution of Biological Systems in Random Media: Limit Theorems and Stability</subfield><subfield code="c">by Anatoly Swishchuk, Jianhong Wu</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Dordrecht</subfield><subfield code="b">Springer Netherlands</subfield><subfield code="c">2003</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (XX, 218 p)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Mathematical Modelling: Theory and Applications</subfield><subfield code="v">18</subfield><subfield code="x">1386-2960</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">The book is devoted to the study of limit theorems and stability of evolving biologieal systems of "particles" in random environment. Here the term "particle" is used broadly to include moleculas in the infected individuals considered in epidemie models, species in logistie growth models, age classes of population in demographics models, to name a few. The evolution of these biological systems is usually described by difference or differential equations in a given space X of the following type and dxt/dt = g(Xt, y), here, the vector x describes the state of the considered system, 9 specifies how the system's states are evolved in time (discrete or continuous), and the parameter y describes the change ofthe environment. For example, in the discrete-time logistic growth model or the continuous-time logistic growth model dNt/dt = r(y)Nt(l-Nt/K(y)), N or Nt is the population of the species at time n or t, r(y) is the per capita n birth rate, and K(y) is the carrying capacity of the environment, we naturally have X = R, X == Nn(X == Nt), g(x, y) = r(y)x(l-xl K(y)) , xE X. Note that n t for a predator-prey model and for some epidemie models, we will have that X = 2 3 R and X = R , respectively. In th case of logistic growth models, parameters r(y) and K(y) normaIly depend on some random variable y</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Human genetics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Epidemiology</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Distribution (Probability theory)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Population</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematical and Computational Biology</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Probability Theory and Stochastic Processes</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Human Genetics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Population Economics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Wu, Jianhong</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-94-017-1506-5</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027859668</subfield></datafield></record></collection> |
| id | DE-604.BV042424251 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:15Z |
| institution | BVB |
| isbn | 9789401715065 9789048163984 |
| issn | 1386-2960 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027859668 |
| oclc_num | 864039809 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (XX, 218 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Springer Netherlands |
| record_format | marc |
| series2 | Mathematical Modelling: Theory and Applications |
| spelling | Swishchuk, Anatoly Verfasser aut Evolution of Biological Systems in Random Media: Limit Theorems and Stability by Anatoly Swishchuk, Jianhong Wu Dordrecht Springer Netherlands 2003 1 Online-Ressource (XX, 218 p) txt rdacontent c rdamedia cr rdacarrier Mathematical Modelling: Theory and Applications 18 1386-2960 The book is devoted to the study of limit theorems and stability of evolving biologieal systems of "particles" in random environment. Here the term "particle" is used broadly to include moleculas in the infected individuals considered in epidemie models, species in logistie growth models, age classes of population in demographics models, to name a few. The evolution of these biological systems is usually described by difference or differential equations in a given space X of the following type and dxt/dt = g(Xt, y), here, the vector x describes the state of the considered system, 9 specifies how the system's states are evolved in time (discrete or continuous), and the parameter y describes the change ofthe environment. For example, in the discrete-time logistic growth model or the continuous-time logistic growth model dNt/dt = r(y)Nt(l-Nt/K(y)), N or Nt is the population of the species at time n or t, r(y) is the per capita n birth rate, and K(y) is the carrying capacity of the environment, we naturally have X = R, X == Nn(X == Nt), g(x, y) = r(y)x(l-xl K(y)) , xE X. Note that n t for a predator-prey model and for some epidemie models, we will have that X = 2 3 R and X = R , respectively. In th case of logistic growth models, parameters r(y) and K(y) normaIly depend on some random variable y Mathematics Human genetics Epidemiology Distribution (Probability theory) Population Mathematical and Computational Biology Probability Theory and Stochastic Processes Human Genetics Population Economics Mathematik Wu, Jianhong Sonstige oth https://doi.org/10.1007/978-94-017-1506-5 Verlag Volltext |
| spellingShingle | Swishchuk, Anatoly Evolution of Biological Systems in Random Media: Limit Theorems and Stability Mathematics Human genetics Epidemiology Distribution (Probability theory) Population Mathematical and Computational Biology Probability Theory and Stochastic Processes Human Genetics Population Economics Mathematik |
| title | Evolution of Biological Systems in Random Media: Limit Theorems and Stability |
| title_auth | Evolution of Biological Systems in Random Media: Limit Theorems and Stability |
| title_exact_search | Evolution of Biological Systems in Random Media: Limit Theorems and Stability |
| title_full | Evolution of Biological Systems in Random Media: Limit Theorems and Stability by Anatoly Swishchuk, Jianhong Wu |
| title_fullStr | Evolution of Biological Systems in Random Media: Limit Theorems and Stability by Anatoly Swishchuk, Jianhong Wu |
| title_full_unstemmed | Evolution of Biological Systems in Random Media: Limit Theorems and Stability by Anatoly Swishchuk, Jianhong Wu |
| title_short | Evolution of Biological Systems in Random Media: Limit Theorems and Stability |
| title_sort | evolution of biological systems in random media limit theorems and stability |
| topic | Mathematics Human genetics Epidemiology Distribution (Probability theory) Population Mathematical and Computational Biology Probability Theory and Stochastic Processes Human Genetics Population Economics Mathematik |
| topic_facet | Mathematics Human genetics Epidemiology Distribution (Probability theory) Population Mathematical and Computational Biology Probability Theory and Stochastic Processes Human Genetics Population Economics Mathematik |
| url | https://doi.org/10.1007/978-94-017-1506-5 |
| work_keys_str_mv | AT swishchukanatoly evolutionofbiologicalsystemsinrandommedialimittheoremsandstability AT wujianhong evolutionofbiologicalsystemsinrandommedialimittheoremsandstability |