Tomomichi Nakamura

We introduce a novel chaotic dynamical system formulated as a second-order difference equation. The model includes one time-delay linear term and one nonlinear term composed of the product of two different time-delay terms. As a result, the nonlinear term gives rise to strange periods. The dynamical behaviors of the model are investigated by the Lyapunov spectrum and bifurcation diagram. We found that the model can have a positive Lyapunov exponent. We also found that while the bifurcation diagram has a typical Arnol’d tongue structure, there are unique shapes that show the progression of overlapping fish hooks in the synchronization region.

Abstract Analysing migration patterns can be used to predict the likelihood of invasion by exotic species, and disease prevalence and spread through contact networks in animals. This paper presents an analytical method for surveying the characteristics of wildlife migration, which can be challenging due to the varying distances and directions that animals travel and the diverse characteristics of different species. To gain a comprehensive understanding of migratory behaviour, it is necessary to integrate migration interrelationships within the populations and correlated migratory modes, e.g., aggregation or dispersed patterns. To achieve this, we propose the SSS-PCA method, which combines the small-shuffle surrogate (SSS) method and principal component analysis (PCA). The SSS-PCA method involves three major steps: (1) applying the SSS method to break down the time-series correlational structure of the movement data with different time frames, (2) obtaining some mobility indicators, e.g., the range and variance of movement, from the original and SSS data with different time frames, and (3) performing PCA on the mobility indicators, and clustering the results. The proposed method can reveal the migration patterns of individuals and the influence of individuals on the whole group. The SSS-PCA method can be used to examine the migration patterns of marine and terrestrial animal species. We suggest that the method can be applied to further studies of various species’ migration data.