Shunsuke Horai

Dynamical Calling Behavior Experimentally Observed in Japanese Tree Frogs (Hyla japonica)

We recorded time series data of calls of Japanese tree frogs (Hyla japonica; Nihon-Ama-Gaeru) and examined the dynamics of the experimentally observed data not only through linear time series analysis such as power spectra but also through nonlinear time series analysis such as reconstruction of orbits with delay coordinates and different kinds of recurrence plots, namely the conventional recurrence plot (RP), the iso-directional recurrence plot (IDRP), and the iso-directional neighbors plot (IDNP). The results show that a single frog called nearly periodically, and a pair of frogs called nearly periodically but alternately in almost anti-phase synchronization with little overlap through mutual interaction. The fundamental frequency of the calls of a single frog during the interactive calling between two frogs was smaller than when the same frog first called alone. We also used the recurrence plots to study nonlinear and nonstationary determinism in the transition of the calling behavior. Moreover, we quantified the determinism of the nonlinear and nonstationary dynamics with indices of the ratio R of the number of points in IDNP to that in RP and the percentage PD of contiguous points forming diagonal lines in RP by the recurrence quantification analysis (RQA). Finally, we discuss a possibility of mathematical modeling of the calling behavior and a possible biological meaning of the call alternation.

Parsimonious description for predicting high-dimensional dynamics.

When we observe a system, we often cannot observe all its variables and may have some of its limited measurements. Under such a circumstance, delay coordinates, vectors made of successive measurements, are useful to reconstruct the states of the whole system. Although the method of delay coordinates is theoretically supported for high-dimensional dynamical systems, practically there is a limitation because the calculation for higher-dimensional delay coordinates becomes more expensive. Here, we propose a parsimonious description of virtually infinite-dimensional delay coordinates by evaluating their distances with exponentially decaying weights. This description enables us to predict the future values of the measurements faster because we can reuse the calculated distances, and more accurately because the description naturally reduces the bias of the classical delay coordinates toward the stable directions. We demonstrate the proposed method with toy models of the atmosphere and real datasets related to renewable energy.

FIRM EVIDENCE OF CHAOS FOR HEARTBEATS IN DOGS UNDER CONSTANT FLOW VENTILATION

We show that heartbeats can be chaotic under the influence of the central nerve systems only. By using constant flow ventilation, the heartbeats of dogs were separated from phasic respiratory motion and measured. By using techniques of nonlinear time series analysis, three pieces of evidence are presented for the existence of chaos.