New shrimp-shaped structure unlocks research avenues in nonlinear dynamics
New shrimp-shaped structure unlocks research avenues in nonlinear dynamics lead image
In nonlinear dynamical systems, ‘shrimp’ refers to a structure of regular oscillations embedded in a chaotic regime in bi-parameter space. Extensive research has been done on shrimps and their organization, both theoretically and experimentally, however, researchers mainly found periodic shrimps. N. C. Pati found that shrimps could also be quasi-periodic, consisting of more than one periodic component. This discovery will open new research avenues.
Pati explores the similarities and differences between periodic and quasi-periodic shrimps, finding that while their geometrical features are similar, their underlying dynamics are markedly different. For example, while periodic shrimp manifests a period-bubbling transition to chaos via the creation and annihilation of an infinite sequence of period-doubling bubbles, quasi-periodic shrimp exhibits a transition to chaos via a finite, torus-bubbling mechanism.
“Both shrimp types exhibit multistability due to the intersection of their inner antennae,” Pati said. “However, the nature of the coexisting attractors is different. Periodic shrimp exhibits periodic-periodic, periodic-chaotic, and chaotic-chaotic coexisting attractors. Conversely, quasi-periodic shrimp displays multi-tori, torus-chaotic, and multi-chaotic coexisting attractors. We also identified the existence of spiral connections for the self-organization of the quasi-periodic shrimps within chaotic domains in certain parameter space of the system.”
To identify and analyze the quasi-periodic shrimp, Pati conducted comprehensive numerical simulations, dividing each of the associated parameter planes into a grid of 1000 x 1000 equispaced points. He then used the Wolf algorithm to calculate the Lyanupov exponents — a well-known quantifying measure of asymptotic behavior of dynamical systems —for each grid point, using a color code to highlight regions of different stability.
Future research includes experimental validation and further exploring the analytical aspects of quasi-periodic shrimp as well as new transitional patterns for quasi-periodic shrimp organization.
Source: “Spiral organization of quasi-periodic shrimp-shaped domains in a discrete predator-prey system,” by N. C. Pati, Chaos (2024). The article can be accessed at https://doi.org/10.1063/5.0208457 .
