As a simple example of an autonomous motor, the characteristic features of self-motion coupled with the acid-base reaction were numerically and experimentally investigated at the air/aqueous interface. Oscillatory and uniform motion were categorized as a function of the reaction order by numerical computations using a mathematical model that incorporates both the distribution of the surface active layer developed from a material particle as the driving force and the kinetics of the acid-base reaction. The nature of the self-motion was experimentally observed for a boat adhered to a camphor derivative with a mono-or di-carboxylic acid on a phosphate aqueous phase as the base.2

We propose a network of excitable systems that spontaneously initiates and completes loop searching against the removal and attachment of connection links. Network nodes are excitable systems of the FitzHugh-Nagumo type that have three equilibrium states depending on input from other nodes. The attractors of this network are stationary solutions that form loops, except in the case of an acyclic network. Thus, the system is regarded as a loop searching system. To design a system capable of self-recovery (the ability to find a loop when one of the connections in an existing loop is suddenly removed), we have investigated regulatory rules for the interaction between nodes and have used two characteristic properties of nonlinear dynamical systems to provide a solution: postinhibitory rebound phenomena and saddle-node bifurcation.

Various types of interesting pattern dynamics such as self-replicating patterns and spiral patterns have been observed in reaction-diffusion (RD) systems. In recent years, periodically oscillating pulses called breathers have been found in several RD systems. In addition, the transient dynamics from traveling breathers to standing breathers have been numerically investigated, and the existence and stability of breathers have been studied by (semi-)rigorous approaches. However, the mechanism of transient dynamics has yet to be clarified, even using numerical approaches, since the global bifurcation diagram of breathers has not been obtained. In this article, we propose a numerical scheme that enables unstable breathers to be tracked. By using the global bifurcation diagram, we numerically investigate the global behavior of unstable manifolds emanating from the bifurcation point associated with the transient dynamics and clarify the onset mechanism of the transient dynamics.

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