Hatsuo Hayashi

Chaotic behavior in the Onchidium giant neuron under sinusoidal stimulation

Abstract The nonperiodic firing of the Onchidium giant neuron under sinusoidal stimulation is investigated. Attractors obtained stroboscopically show that state points on the attractor are mixed by the bakers transformation. The transition function with period three suggests that the nonperiodic oscillation is chaotic.

Chaos in the self-sustained oscillation of an excitable biological membrane under sinusoidal stimulation

Abstract Nonperiodic behavior in self-sustained oscillation of the internodal cell of Nitella was investigated under sinusoidal stimulation. The stroboscopic transformation reveals a single-valued transition function with period three. This suggests that the nonperiodic oscillation is chaotic in the sense of Li and Yorke.

Transition to chaos via intermittency in the onchidium pacemaker neuron

Abstract The nonlinear response of the Onchidium pacemaker neuron to a sinusoidal stimulation was investigated by a stroboscopic mapping. The phase diagram of the response was obtained and the transition from the 1 2 -harmonic oscillation to chaos through the intermittency is pointed out.

Entrained, Harmonic, Quasiperiodic and Chaotic Responses of the Self-Sustained Oscillation of Nitella to Sinusoidal Stimulation

The response of the self-sustained oscillation of the Nitella internodal cell to the sinusoidal stimulation was investigated. The phase diagram was made up from power spectra and stroboscopic representation; there exist entrained, harmonic, quasiperiodic and chaotic oscillations. The stroboscopic mapping of the chaotic oscillation forms a strange attractor and the stroboscopic transition function admits period three. This indicates that there exists chaotic behavior assured by the Li-Yorke theorem.

Chaos in Molluscan Neuron

Irregular responses of Onchidium pacemaker neuron to a sinusoidal current stimulation are classified into three kinds of chaotic oscillations by means of one-dimensional stroboscopic and return maps: chaos, intermittency, and random alternative chaos. Harmonic responses bifurcate to the chaos through the intermittency or the random alternative chaos. All of the chaotic responses are caused by random jumps between two kinds of unstable harmonic responses. Two types of instability exist. Each combination of the two types of instability corresponds to each chaotic response. On the other hand, it is ascertained that spontaneous irregular activities of the neuron are really chaotic. One-dimensional maps of the activities reveal a single-valued function.

NMR Line Width in One-Dimensional Antiferromagnet KCuF3

The NMR line widths of the F 19 nuclei in the α-type KCuF 3 are measured from T N (39.8 K) to 550 K. The widths of F 19 nuclei being on the c -axis extend gradually and tend to saturate as temperature is raised up to 550 K and those of F 19 nuclei being on the a -axes diverge as temperature is lowered to T N . The latter behavior is explained by the three-dimensional behavior of the spin system. In the former case the width near T N is explained by usual exchange narrowing, but there has been no theory which interprets the widths at high temperature. A theory based on Kubo-Tomitas theory is proposed by assuming the one-dimensional diffusion process in the linear chain with a weak interchain exchange interaction. Theory interprets satisfactorily the experimental results.

The Instability in the Membrane Potential of the Nitella Internodal Cell

The excitation phenomena in the Nitella internodal cell was investigated as an example of the phase transition in an open system far from thermal equilibrium. The results observed in the normal medium suggest a hard-mode instability to exist near the threshold potential.

Temperature dependence of the NMR line widths of the 19F nuclei in KCuF3 above TN

Abstract The NMR line widths of 19F nuclei in a one-dimensional antiferromagnet KCuF3 were measured from TN to 550 K. The line widths of 19F nuclei on the a-axes diverge as temperature is decreasing toward TN, which reflect the three-dimensional behavior in the spin system. The widths of 19F on the c-axis increase with increase of temperature and are independent of temperature in the paramagnetic region. The widths at 550 K are interpreted by use of the diffusion process in the linear chain.