Stable Bifurcations in Multi-species Semelparous Population Models
| Autor: | Ryusuke Kon |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Differential equation
Lotka–Volterra equations Leslie matrix 01 natural sciences 010305 fluids & plasmas 010101 applied mathematics Nonlinear system Population model 0103 physical sciences Population cycle Quantitative Biology::Populations and Evolution Applied mathematics 0101 mathematics Basic reproduction number Semelparity and iteroparity Mathematics |
| Zdroj: | Springer Proceedings in Mathematics & Statistics ISBN: 9789811064081 |
| DOI: | 10.1007/978-981-10-6409-8_1 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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