Resonance properties and chaotic dynamics of a three-dimensional discrete logistic ecological system within the neighborhoods of bifurcation points
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910934783492096 |
|---|---|
| author | Chen, Yujiang Li, Lin Liu, Lingling Yu, Zhiheng |
| author_facet | Chen, Yujiang Li, Lin Liu, Lingling Yu, Zhiheng |
| contents | In this paper, we delve into the dynamical properties of a class of three-dimensional logistic ecological models. By using the complete discriminant theory of polynomials, we first give a topological classification for each fixed point and investigate the stability of corresponding system near the fixed points. Then employing the bifurcation and normal form theory, we discuss all possible codimension-1 bifurcations near the fixed points, i.e., transcritical, flip, and Neimark-Sacker bifurcations, and further prove that the system can undergo codimension-2 bifurcations, specifically 1:2, 1:3, 1:4 strong resonances and weak resonance Arnold tongues. Additionally, chaotic behaviors in the sense of Marotto are rigorously analyzed. Numerical simulations are conducted to validate the theoretical findings and illustrate the complex dynamical phenomena identified. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_05737 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Resonance properties and chaotic dynamics of a three-dimensional discrete logistic ecological system within the neighborhoods of bifurcation points Chen, Yujiang Li, Lin Liu, Lingling Yu, Zhiheng Dynamical Systems 37G10, 39A28, 58K50, 68W30 In this paper, we delve into the dynamical properties of a class of three-dimensional logistic ecological models. By using the complete discriminant theory of polynomials, we first give a topological classification for each fixed point and investigate the stability of corresponding system near the fixed points. Then employing the bifurcation and normal form theory, we discuss all possible codimension-1 bifurcations near the fixed points, i.e., transcritical, flip, and Neimark-Sacker bifurcations, and further prove that the system can undergo codimension-2 bifurcations, specifically 1:2, 1:3, 1:4 strong resonances and weak resonance Arnold tongues. Additionally, chaotic behaviors in the sense of Marotto are rigorously analyzed. Numerical simulations are conducted to validate the theoretical findings and illustrate the complex dynamical phenomena identified. |
| title | Resonance properties and chaotic dynamics of a three-dimensional discrete logistic ecological system within the neighborhoods of bifurcation points |
| topic | Dynamical Systems 37G10, 39A28, 58K50, 68W30 |
| url | https://arxiv.org/abs/2505.05737 |