Skip to main content
Erschienen in:
Buchtitelbild

2017 | OriginalPaper | Buchkapitel

Stable Bifurcations in Multi-species Semelparous Population Models

verfasst von : Ryusuke Kon

Erschienen in: Advances in Difference Equations and Discrete Dynamical Systems

Verlag: Springer Singapore

Aktivieren Sie unsere intelligente Suche um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

It is known that the behavior of a nonlinear semelparous Leslie matrix model with the basic reproduction number close to one can be approximated by a solution of a Lotka-Volterra differential equation. Furthermore, even in multi-species cases, a similar approximation works as long as every species is semelparous. This paper gives a mathematical basis to this approximation and shows that Lotka-Volterra equations are helpful to study a certain bifurcation problem of multi-species semelparous population models. With the help of this approximation method, we find an example of coexistence of two biennial populations with temporal segregation. This example provides a new mechanism of producing population cycles.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
1.
2.
Zurück zum Zitat Cushing, J.M., Li, J.: On Ebenman’s model for the dynamics of a population with competing juveniles and adults. Bull. Math. Biol. 51(6), 687–713 (1989)CrossRefMATH Cushing, J.M., Li, J.: On Ebenman’s model for the dynamics of a population with competing juveniles and adults. Bull. Math. Biol. 51(6), 687–713 (1989)CrossRefMATH
5.
Zurück zum Zitat Cushing, J.M., Henson, S.M.: Stable bifurcations in semelparous Leslie models. J. Biol. Dyn. 6, 80–102 (2012)CrossRefMathSciNet Cushing, J.M., Henson, S.M.: Stable bifurcations in semelparous Leslie models. J. Biol. Dyn. 6, 80–102 (2012)CrossRefMathSciNet
6.
Zurück zum Zitat Davydova, N.V., Diekmann, O., van Gils, S.A.: Year class coexistence or competitive exclusion for strict biennials? J. Math. Biol. 46(2), 95–131 (2003)CrossRefMATHMathSciNet Davydova, N.V., Diekmann, O., van Gils, S.A.: Year class coexistence or competitive exclusion for strict biennials? J. Math. Biol. 46(2), 95–131 (2003)CrossRefMATHMathSciNet
7.
Zurück zum Zitat Diekmann, O., van Gils, S.A.: On the cyclic replicator equation and the dynamics of semelparous populations. SIAM J. Appl. Dyn. Syst. 8, 1160–1189 (2009)CrossRefMATHMathSciNet Diekmann, O., van Gils, S.A.: On the cyclic replicator equation and the dynamics of semelparous populations. SIAM J. Appl. Dyn. Syst. 8, 1160–1189 (2009)CrossRefMATHMathSciNet
8.
Zurück zum Zitat Ebenman, B.: Competition between age classes and population dynamics. J. Theor. Biol. 131(4), 389–400 (1988)CrossRefMathSciNet Ebenman, B.: Competition between age classes and population dynamics. J. Theor. Biol. 131(4), 389–400 (1988)CrossRefMathSciNet
9.
Zurück zum Zitat Hardy, G.H., Wright, E.M.: An Introduction to the Theory of Numbers. Oxford University Press, Oxford, sixth edition (2008)MATH Hardy, G.H., Wright, E.M.: An Introduction to the Theory of Numbers. Oxford University Press, Oxford, sixth edition (2008)MATH
10.
Zurück zum Zitat Hofbauer, J.: On the occurrence of limit cycles in the Volterra-Lotka equation. Nonlinear Anal. Theory Methods Appl. 5(9), 1003–1007 (1981)CrossRefMATHMathSciNet Hofbauer, J.: On the occurrence of limit cycles in the Volterra-Lotka equation. Nonlinear Anal. Theory Methods Appl. 5(9), 1003–1007 (1981)CrossRefMATHMathSciNet
11.
Zurück zum Zitat Kon, R.: Invasibility of missing year-classes in leslie matrix models for a semelparous biennial population. In: Proceedings of Czech-Japanese Seminar in Applied Mathematics 2005 of COE Lecturer Note, vol. 3, pp. 77–87. Kyushu Univ. The 21 Century COE Program, Fukuoka (2006) Kon, R.: Invasibility of missing year-classes in leslie matrix models for a semelparous biennial population. In: Proceedings of Czech-Japanese Seminar in Applied Mathematics 2005 of COE Lecturer Note, vol. 3, pp. 77–87. Kyushu Univ. The 21 Century COE Program, Fukuoka (2006)
12.
Zurück zum Zitat Kon, R.: Competitive exclusion between year-classes in a semelparous biennial population. In: Deutsch, A., de la Parra, R.B., de Boer, R.J., Diekmann, O., Jagers, P., Kisdi, E., Kretzschmar, M., Lansky, P., Metz, H. (eds.) Mathematical Modeling of Biological Systems. Volume II, pp. 79–90. Birkhäuser, Boston (2007) Kon, R.: Competitive exclusion between year-classes in a semelparous biennial population. In: Deutsch, A., de la Parra, R.B., de Boer, R.J., Diekmann, O., Jagers, P., Kisdi, E., Kretzschmar, M., Lansky, P., Metz, H. (eds.) Mathematical Modeling of Biological Systems. Volume II, pp. 79–90. Birkhäuser, Boston (2007)
13.
Zurück zum Zitat Kon, R.: Age-structured Lotka-Volterra equations for multiple semelparous populations. SIAM J. Appl. Math. 71(3), 694–713 (2011)CrossRefMATHMathSciNet Kon, R.: Age-structured Lotka-Volterra equations for multiple semelparous populations. SIAM J. Appl. Math. 71(3), 694–713 (2011)CrossRefMATHMathSciNet
14.
Zurück zum Zitat Kon, R.: Permanence induced by life-cycle resonances: the periodical cicada problem. J. Biol. Dyn. 6(2), 855–890 (2012)CrossRef Kon, R.: Permanence induced by life-cycle resonances: the periodical cicada problem. J. Biol. Dyn. 6(2), 855–890 (2012)CrossRef
15.
Zurück zum Zitat Kon, R., Iwasa, Y.: Single-class orbits in nonlinear Leslie matrix models for semelparous populations. J. Math. Biol. 5(5–6), 781–802 (2007)CrossRefMATHMathSciNet Kon, R., Iwasa, Y.: Single-class orbits in nonlinear Leslie matrix models for semelparous populations. J. Math. Biol. 5(5–6), 781–802 (2007)CrossRefMATHMathSciNet
16.
Zurück zum Zitat May, R.M., Leonard, W.J.: Nonlinear aspects of competition between three species. SIAM J. Appl. Math. 29(2), 243–253 (1975)CrossRefMATHMathSciNet May, R.M., Leonard, W.J.: Nonlinear aspects of competition between three species. SIAM J. Appl. Math. 29(2), 243–253 (1975)CrossRefMATHMathSciNet
17.
Metadaten
Titel
Stable Bifurcations in Multi-species Semelparous Population Models
verfasst von
Ryusuke Kon
Copyright-Jahr
2017
Verlag
Springer Singapore
DOI
https://doi.org/10.1007/978-981-10-6409-8_1