Department of Mathematics, Bidhan Chandra College, Asansol 713304, Paschim Burdwan, West Bengal, India.
Chaos. 2024 Aug 1;34(8). doi: 10.1063/5.0208457.
In this paper, we report the discovery of some novel dynamical scenarios for quasi-periodic shrimp-shaped structures embedded within chaotic phases in bi-parameter space of a discrete predator-prey system. By constructing high-resolution, two-dimensional stability diagrams based on Lyapunov exponents, we observe the abundance of both periodic and quasi-periodic shrimp-shaped organized domains in a certain parameter space of the system. A comprehensive comparative analysis is conducted to elucidate the similarities and differences between these two types of shrimps. Our analysis reveals that, unlike periodic shrimp, quasi-periodic shrimp induces (i) torus bubbling transition to chaos and (ii) multistability with multi-tori, torus-chaotic, and multi-chaotic coexisting attractors, resulting from the crossing of its two inner antennae. The basin sets of the coexisting attractors are analyzed, and we observe the presence of intriguing basin boundaries. We also verify that, akin to periodic shrimp structures, quasi-periodic shrimps also maintain the three-times self-similarity scaling. Furthermore, we encounter the occurrence of spiral organization for the self-distribution of quasi-periodic shrimps within a large chaotic domain. We believe that these novel findings will significantly enhance our understanding of shrimp-shaped structures and the intricate dynamics exhibited by their distribution in chaotic regimes.
在本文中，我们报告了在离散捕食者-被捕食系统的双参数空间中混沌相中嵌入的准周期虾状结构的一些新颖动力学场景的发现。通过构建基于李雅普诺夫指数的高分辨率二维稳定性图，我们观察到在系统的某个参数空间中存在大量的周期性和准周期性虾状有组织区域。我们进行了全面的比较分析，以阐明这两种虾之间的异同。我们的分析表明，与周期性虾不同，准周期性虾诱导（i）环泡向混沌的转变和（ii）多稳定性，具有多环、环-混沌和多混沌共存吸引子，这是由于其两个内天线的交叉引起的。分析共存吸引子的基区集，我们观察到存在有趣的基区边界。我们还验证了，类似于周期性虾结构，准周期性虾也保持三倍自相似性缩放。此外，我们在大混沌域内遇到了准周期虾的自分布的螺旋组织。我们相信这些新发现将极大地提高我们对虾状结构及其在混沌区分布所表现出的复杂动力学的理解。
