Shrinking shrimp-shaped domains and multistability in the dissipative asymmetric kicked rotor map
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914911978782720 |
|---|---|
| author | Sales, Matheus Rolim Mugnaine, Michele Leonel, Edson Denis Caldas, Iberê L. Szezech Jr, José Danilo |
| author_facet | Sales, Matheus Rolim Mugnaine, Michele Leonel, Edson Denis Caldas, Iberê L. Szezech Jr, José Danilo |
| contents | An interesting feature in dissipative nonlinear systems is the emergence of characteristic domains in parameter space that exhibit periodic temporal evolution, known as shrimp-shaped domains. We investigate the parameter space of the dissipative asymmetric kicked rotor map and show that, in the regime of strong dissipation, the shrimp-shaped domains repeat themselves as the nonlinearity parameter increases while maintaining the same period. We analyze the dependence of the length of each periodic domain with the nonlinearity parameter, revealing that it follows a power law with the same exponent regardless of the dissipation parameter. Additionally, we find that the distance between adjacent shrimp-shaped domains is scaling invariant with respect to the dissipation parameter. Furthermore, we show that for weaker dissipation, a multistable scenario emerges within the periodic domains. We find that as the dissipation gets weaker, the ratio of multistable parameters for each periodic domain increases, and the area of the periodic basin decreases as the nonlinearity parameter increases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_07167 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Shrinking shrimp-shaped domains and multistability in the dissipative asymmetric kicked rotor map Sales, Matheus Rolim Mugnaine, Michele Leonel, Edson Denis Caldas, Iberê L. Szezech Jr, José Danilo Chaotic Dynamics An interesting feature in dissipative nonlinear systems is the emergence of characteristic domains in parameter space that exhibit periodic temporal evolution, known as shrimp-shaped domains. We investigate the parameter space of the dissipative asymmetric kicked rotor map and show that, in the regime of strong dissipation, the shrimp-shaped domains repeat themselves as the nonlinearity parameter increases while maintaining the same period. We analyze the dependence of the length of each periodic domain with the nonlinearity parameter, revealing that it follows a power law with the same exponent regardless of the dissipation parameter. Additionally, we find that the distance between adjacent shrimp-shaped domains is scaling invariant with respect to the dissipation parameter. Furthermore, we show that for weaker dissipation, a multistable scenario emerges within the periodic domains. We find that as the dissipation gets weaker, the ratio of multistable parameters for each periodic domain increases, and the area of the periodic basin decreases as the nonlinearity parameter increases. |
| title | Shrinking shrimp-shaped domains and multistability in the dissipative asymmetric kicked rotor map |
| topic | Chaotic Dynamics |
| url | https://arxiv.org/abs/2408.07167 |