Mathematical mechanism of state-dependent phase resetting properties of alpha rhythm in the human brain.

It is well-known that 10-Hz alpha oscillations in humans observed by electroencephalogram (EEG) are enhanced when the eyes are closed. Toward explaining this, a previous experimental study using manipulation by transcranial magnetic stimulation (TMS) revealed more global propagation of phase resetting in the eyes-open condition than in the eyes-closed condition in the alpha band. Those results indicate a significant increase of directed information flow across brain networks from the stimulated area to the rest of the brain when the eyes are open, suggesting that sensitivity to environmental changes and external stimuli is adaptively controlled by changing the dynamics of the alpha rhythm.

Model framework for emergence of synchronized oscillations.

Autonomy is an important concept when investigating the mechanism whereby biological systems exhibit flexibility against unpredictable environmental changes. Herein we propose a parameter-tuning algorithm, based on a selection principle, that allows the emergence of synchronization between populations of oscillators through autonomous changes of the intrinsic parameters. With the algorithm, the populations exhibit self-recovery of the synchronized state after the existing synchronized state is broken suddenly; that is, the system chooses appropriate values of the intrinsic parameters to recover the synchronized state.

Neural network model for path-finding problems with the self-recovery property.

The large-scale synchronization of neural oscillations is crucial in the functional integration of brain modules, but the combination of modules changes depending on the task. A mathematical description of this flexibility is a key to elucidating the mechanism of such spontaneous neural activity. We present a model that finds the loop structure of a network whose nodes are connected by unidirectional links.

Current reinforcement model reproduces center-in-center vein trajectory of Physarum polycephalum.

Vein networks span the whole body of the amoeboid organism in the plasmodial slime mould Physarum polycephalum, and the network topology is rearranged within an hour in response to spatio-temporal variations of the environment. It has been reported that this tube morphogenesis is capable of solving mazes, and a mathematical model, named the 'current reinforcement rule', was proposed based on the adaptability of the veins. Although it is known that this model works well for reproducing some key characters of the organism's maze-solving behaviour, one important issue is still open: In the real organism, the thick veins tend to trace the shortest possible route by cutting the corners at the turn of corridors, following a center-in-center trajectory, but it has not yet been examined whether this feature also appears in the mathematical model, using corridors of finite width.

Multistate network for loop searching system with self-recovery property.

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.

Multistate network model for the pathfinding problem with a self-recovery property.

In this study, we propose a continuous model for a pathfinding system. We consider acyclic graphs whose vertices are connected by unidirectional edges. The proposed model autonomously finds a path connecting two specified vertices, and the path is represented by a stable solution of the proposed model.

Three-state network design for robust loop-searching systems.

Self-recovery of function is one of the remarkable properties of biological systems, and its implementation in autonomous distributed systems is highly desirable. In this study, we propose an autonomous distributed system which is capable of searching for closed loops in a network in which nodes are connected by unidirectional paths. A closed loop is defined as a phase synchronization of a group of oscillators belonging to the corresponding nodes.

Tactic direction determined by the interaction between oscillatory chemical waves and rheological deformation in an amoeba.

The survival of an organism can depend upon the direction in which it decides to move in response to changes in external conditions. Here we propose a physicochemical mechanism of the decision process for migration direction in the case of a giant amoebalike Physarum plasmodium. The tactical movement response could be changed by reversal of the phase wave of the rhythmic contractions that occur in any part of the plasmodium body when local stimulation is applied and the frequency of the rhythmic contractions is locally modulated in the stimulated region.

Chaotic motion of propagating pulses in the Gray-Scott model.

Transition routes of propagating pulses in the Gray-Scott model from oscillatory to chaotic motion are investigated by numerical studies. Global bifurcation of the Gray-Scott model gives us information about the onset mechanism of transient dynamics, such as the splitting and extinction of pulses. However, the instability mechanism of oscillatory pulses has not been clarified, even numerically.

Mathematical model for contemplative amoeboid locomotion.

It has recently been reported that even single-celled organisms appear to be "indecisive" or "contemplative" when confronted with an obstacle. When the amoeboid organism Physarum plasmodium encounters the chemical repellent quinine during migration along a narrow agar lane, it stops for a period of time (typically several hours) and then suddenly begins to move again. When movement resumes, three distinct types of behavior are observed: The plasmodium continues forward, turns back, or migrates in both directions simultaneously.

Stabilizing bipedal walking on posts through multiple constraints.

Adaptability of the human locomotion system has been studied from the theoretical viewpoint of dynamical systems. The structure of a dynamical system consists of its time evolution rule, known simply as the dynamics, and its constraints, such as the initial states or boundary conditions that determine future convergent states. Initial state coordination by the system itself is the key to autonomous adaptive mechanisms.

Instability-induced hierarchy in bipedal locomotion.

One of the important features of human locomotion is its instant adaptability to various unpredictable changes of physical and environmental conditions. This property is known as flexibility. Modeling the bipedal locomotion system, we show that initial-state coordination by a global variable which encodes the attractor basins of the system can yield flexibility.

Dynamics of traveling pulses in heterogeneous media.

One of the fundamental issues of pulse dynamics in dissipative systems is clarifying how the heterogeneity in the media influences the propagating manner. Heterogeneity is the most important and ubiquitous type of external perturbation. We focus on a class of one-dimensional traveling pulses, the associated parameters of which are close to drift and/or saddle-node bifurcations.

Scattering of traveling spots in dissipative systems.

One of the fundamental questions for self-organization in pattern formation is how spatial periodic structure is spontaneously formed starting from a localized fluctuation. It is known in dissipative systems that splitting dynamics is one of the driving forces to create many particle-like patterns from a single seed. On the way to final state there occur many collisions among them and its scattering manner is crucial to predict whether periodic structure is realized or not.

Phase-dependent output of scattering process for traveling breathers.

Scattering process between one-dimensional traveling breathers (TBs), i.e., oscillatory traveling pulses, for the complex Ginzburg-Landau equation (CGLE) with external forcing and a three-component activator-substrate-inhibitor model are studied.

Dynamic transitions through scattors in dissipative systems.

Scattering of particle-like patterns in dissipative systems is studied, especially we focus on the issue how the input-output relation is controlled at a head-on collision where traveling pulses or spots interact strongly. It remains an open problem due to the large deformation of patterns at a colliding point. We found that a special type of unstable steady or time-periodic solutions called scattors and their stable and unstable manifolds direct the traffic flow of orbits.

Scattering and separators in dissipative systems.

Scattering of particlelike patterns in dissipative systems is studied, especially we focus on the issue how the input-output relation is controlled at a head-on collision in the one-dimensional(1D) space where traveling pulses interact strongly. It remains an open problem due to the large deformation of patterns at a colliding point. We found that a special type of steady or time-periodic solutions called separators and their stable and unstable manifolds direct the traffic flow of orbits.