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.

After the brief review on nonlinear phenomena in chemistry, our attention is focused on two oscillatory systems which are typical examples of nonlinear, nonequilibrium chemical oscillations: (1) oscillation at membrane and at interface as a model of self-oscillation of a living cell, and (2) interference and entrainment between chemical oscillations, as an example of a spatio-temporal self-organization of multicellular organisms.

Bifurcations of phase-locked modes for diffusively coupled van der Pol equations are investigated. It is known that in-phase and out-of-phase modes are typically observed in the system if two oscillatory equations are identical. There have been many studies on the behavior of diffusively coupled equations of van der Pol type. Many of these, however, persist in the limits of weakly nonlinearity and weak coupling. In this paper we study global feature of bifurcation sets of the modes under relatively wide range of variation of system parameters: coefficient of nonlinear term, parameter related to the frequency of the uncoupled equations, diffusion coefficient and so on.

A suggestion for creating an excitable/oscillatory field with solid-state material is proposed. In essence, the idea is to make a spatial array of "mesoscopic particles" with the characteristics of a first-order phase transition. A theoretical computation shows that an auto-wave, or excitable wave, is generated in such an excitable field. A simple example of using this system as a diode in information flow is given.