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The dynamics of retrieval processes in a system composed of coupled circle maps is studied by means of a statistical method and numerical simulations. Phase patterns are embedded in coupling parameters so that the system may work as an associative memory system. A parameter, which is an amplification factor multiplied to all the coupling strengths, is introduced for investigating the effect of the strength of the coupling nonlinearity on the behavior of the system concerned. The statistical method provides a set of time evolution equations representing the macroscopic behavior. It is found that the storage capacity is considerably enhanced by the introduced amplification factor. It is also shown that the system exhibits macroscopic chaotic oscillations when the strength of the coupling is sufficiently large. Moreover, the clustering is observed, as in other types of the globally coupled nonlinear systems.

Electric characteristics of hybrid polymer membranes composed of two lipid species were studied, where one lipid species is positively charged in aqueous solution and the other is negatively charged. As a result, it was found that the hybrid membranes responded to taste substances in different ways according to the molar mixing ratio of these two kinds of lipids, and also showed different response characteristics from those of the single-lipid membranes. The membranes with the mixing ratio around 50% exhibited the largest responses to HCl (sourness) and monosodium glutamate (umami). Moreover, good quantitative agreements with the observed data on the response electric potential were obtained using a theory describing both the changes in surface electric potential and surface charge density with taste substances.

It is clarified that the coupled oscillator system, which has the output of the phase coherency, can learn mapping from specified phase patterns to specified phase coherencies. The system considered here has the output unit which is a group of oscillators coupled both to the other oscillators of the system and also to the mean field generated by the output unit itself. It is analytically and numerically shown that the system can learn the above specified mapping. The effect of the distribution of the natural frequency of oscillators on the dynamics of the system is also investigated. It is shown that the system exhibits oscillatory and complex (chaotic) output when the phase pattern sufficiently different from the learned patterns is input into the system.

Responses to periodic signals in the oscillator network are studied numerically. The network used here is globally coupled oscillators with distributed natural frequencies of the oscillatory elements. The ability of the temporal-pattern recognition in the system is studied using the learning rule which changes the distribution of the natural frequencies. It is found that the coherency representing the order of the system exhibits the periodic and complex behaviors. The periodic response of the coherency is observed in the case where the input signal is similar to the learned signal. The behavior of the coherency becomes complex; i.e., the number of the degrees of freedom of the behavior increases with the decrease in the similarity of the input signal to the learned signal. Moreover, the long transient process is observed after turning off the input.

A theoretical model is presented for reproducing chaotic behaviors observed experimentally in the DOPH (dioleyl phosphate) membrane system with external periodic stimulation. The model describes the self-sustained oscillation of the membrane potential of the DOPH membrane by taking into account the effect of applied AC electric current. The route to chaos was classified as break-down of quasi-periodicity, although it was unclear experimentally. Effects of the change in the phenomenological parameters in the theoretical model on the attractor were also investigated. It was shown that some dynamic bifurcation properties can change much more sensitively than average quantities as the mean frequency. The change of the attractor was discussed in relation to the interaction of DOPH molecules with taste substances by comparing with experimental results.

The mechanism of the oscillatory electric potential of a dioleyl phosphate (DOPH) layer in a single hole sandwiched by two KCl solutions, 100 mM and 5 mM, was investigated using two types of cells for axial and transverse observations. It was discovered that the electrical oscillation was related to a macroscopic behavior of the interfaces between DOPH and KCl solutions caused by a chemically driven surface tension effect.

A spatial pattern of electric potential in the growing root was studied with a usual microelectrode and a multi-electrode measuring apparatus, which made possible a simultaneous measurement of electric potentials along the root. The pattern of surface electric potential disappeared along the entire root length when air surrounding the plant was replaced with nitrogen gas for about 2 h. Disappearance of a large peak of surface potential around 10 mm from the root tip preceded both the decrease in the growth speed and the change in pH of the aqueous medium to neutral in the elongation region, while this region showed a localized acidification in normal conditions. Supply of air recovered the spatial patterns of electric potential and pH. Proton accumulation within the cell wall following activation of H + pumps was suggested to participate directly in the growth.

Effects of a distribution of natural frequencies of oscillatory elements constituting a phase memory system are investigated theoretically. It is found that the distribution causes considerable effects on the storage capacity (α c ) and on the dynamics of the retrieval states. The obtained state diagram shows the decrease of α c with the introduction of the distribution. The distribution also leads to an oscillation of the overlap.

An equation for self-oscillations with small amplitudes near hard-mode instabilities is derived by means of a reductive perturbation approach. The present equation can be used to discuss both normally and invertedly bifurcating cases, bacause the present equation is equivalent to each set of equations resulting from reductive perturbations up to the fifth order, in spite of the difference of expansion parameters for reductive perturbations according as the types of bifurcations. In this paper, an explicit expression of the present equation is given for the FitzHugh-Nagumo model, while the present method can be used generally for hard-mode instabilities. Some typical behavior of hard-mode instabilities is also discussed with the aid of the present equation.

A theory is presented for an appearance of band-type pattern of electric potential accompanied with electric current surrounding a unit or many-cell system of a cylindrical shape. A flux continuity at the membrane is reduced to a nonlinear equation composed of passive and active fluxes through a diffusion equation for protons. Another equation concerns the concentration of a diffusive substance weakening the pump activity. It is shown that, when an external parameter is varied from the homogeneous state, a symmetry breaking along a longitudinal axis usually appears before the one along a circumferential direction. A TDGL equation for spatial modes, which can describe both normally and invertedly bifurcating cases, is derived. An observation of hysteretic bands of chloroplasts in the green alga Acetabularia is discussed within the present theoretical scheme.

An early stage of development of a rhizoid in Fucus eggs is described theoretically by taking account of a stabilizing effect of Ca 2+ on membranes of the rhizoid. Basic equations are coupled ones for a length of the rhizoid, a concentration of Ca 2+ and a concentration of membrane-creating molecules accumulated in the rhizoid region. The present theory can explain the observed fact that an illumination of light becomes effective on the growth of rhizoid, only when the time after fertilization exceeds a certain threshold value. An effect of the number of neighboring eggs on the speed of rhizoid formation is discussed with the aid of the present equations, and the result agrees with the observed tendency.

A spatial pattern of the electric potential formed by a characean internodal cell is investigated experimentally. A multi-electrode measuring system is used to pursue the dynamic properties of the pattern. It is shown that periodic low-potential regions are formed after the entire transient increase over the cell when the light is imposed on. Under constant illumination an electric oscillation is found. These experimental data are also discussed by the use of a spectrum analysis; the formation of the pattern is a bifurcation phenomenon of soft-mode instability realizing far from equilibrium, accompanied by sharpening of spectrum of a particular wave mode. A long-range coherence extending over 1 cm is also shown to exist in the high-potential region, where protons are extruded by H + -ATPase molecules existing within the membrane.

Self-sustained oscillations of membrane potential in an artificial model membrane, where dioleyl phosphate (DOPH) is infiltrated into pores of a Millipore filter, are investigated both experimentally and theoretically. Spike-like self-oscillations with an extremely long period of about one hour were observed for membranes with large adsorbed amounts of DOPH in the absence of external forces such as electric current and pressure gradient. On the basis of a previously-presented model that DOPH molecules make transitions among three phases composed of oil droplets, spherical micelles and multi- or bilayer leaflets, the occurrence of self-oscillations is explained well by taking account of an accumulation and a release of salt in a pore of the filter.

For an artificial membrane in which dioleyl phosphate (DOPH) is infiltrated into pores of Millipore filter, a relaxation of electric caracitance of the membrane in a solution was investigated after an abrupt change of salt concentration. Relaxation curves of sigmoid types were observed after an increase of salt concentration, while the curves were of exponential types after a decrease. These facts suggest us that hysteresis loops of electric capacitance or this membrane observed for a cyclic variation of salt concentration belong to a different type from the usual ones originating from the first-order phase transition. It is shown that these electric characteristics of the membranes can be explained well on the basis of a model that dioleyl phosphate molecules make transitions among three phases composed of droplets, spherical micells and multi- or bilayer leaflets.

La resistivite electrique d'un film de phosphate de dioleyl a l'interface entre des solutions de KCl a SmM et 100 mM est etudiee en fonction des transitions de phase