Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.16749 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916223125553152 |
|---|---|
| author | Herrera, Franco Trofimchuk, Sergei |
| author_facet | Herrera, Franco Trofimchuk, Sergei |
| contents | We continue to study (see arXiv:2401.08618, https://doi.org/10.48550/arXiv.2401.08618) a renewal equation $ϕ(t)=\frak Fϕ_t$ proposed in [C. Barril et al., J. Math. Biology, https://doi.org/10.1007/s00285-024-02084-x] to model trees growth. This time we are considering the case when the per capita reproduction rate $β(x)$ is a non-monotone (unimodal) function of tree's height $x$. Note that the height of some species of trees can impact negatively seed viability, in a kind of autogamy depression. Similarly to previous works, it is also assumed that the growth rate $g(x)$ of an individual of height $x$ is a strictly decreasing function. Here we analyse the connection between dynamics of the associated one-dimensional map $F(b)= {\frak F}b,$ $b \in {\mathbb R}_+$, and the delayed (hence infinite-dimensional) model $ϕ(t)=\frak Fϕ_t$. Our key observation is that this model is of monotone positive feedback type since $F$ is strictly increasing on ${\mathbb R}_+$ independently on the monotonicity properties of $β$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16749 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the global dynamics of a forest model with monotone positive feedback and memory Herrera, Franco Trofimchuk, Sergei Dynamical Systems 45D05, 92D25 We continue to study (see arXiv:2401.08618, https://doi.org/10.48550/arXiv.2401.08618) a renewal equation $ϕ(t)=\frak Fϕ_t$ proposed in [C. Barril et al., J. Math. Biology, https://doi.org/10.1007/s00285-024-02084-x] to model trees growth. This time we are considering the case when the per capita reproduction rate $β(x)$ is a non-monotone (unimodal) function of tree's height $x$. Note that the height of some species of trees can impact negatively seed viability, in a kind of autogamy depression. Similarly to previous works, it is also assumed that the growth rate $g(x)$ of an individual of height $x$ is a strictly decreasing function. Here we analyse the connection between dynamics of the associated one-dimensional map $F(b)= {\frak F}b,$ $b \in {\mathbb R}_+$, and the delayed (hence infinite-dimensional) model $ϕ(t)=\frak Fϕ_t$. Our key observation is that this model is of monotone positive feedback type since $F$ is strictly increasing on ${\mathbb R}_+$ independently on the monotonicity properties of $β$. |
| title | On the global dynamics of a forest model with monotone positive feedback and memory |
| topic | Dynamical Systems 45D05, 92D25 |
| url | https://arxiv.org/abs/2404.16749 |