Tomoyuki Miyaji

Computational Ability of Cells based on Cell Dynamics and Adaptability

Learning how biological systems solve problems could help to design new methods of computation. Information processing in simple cellular organisms is interesting, as they have survived for almost 1 billion years using a simple system of information processing. Here we discuss a well-studied model system: the large amoeboid Physarum plasmodium. This amoeba can find approximate solutions for combinatorial optimization problems, such as solving a maze or a shortest network problem. In this report, we describe problem solving by the amoeba, and the computational methods that can be extracted from biological behaviors. The algorithm designed based on Physarum is both simple and useful.

A Four-Leaf Chaotic Attractor of a Three-Dimensional Dynamical System

A three-dimensional autonomous dynamical system proposed by Pehlivan is untypical in simultaneously possessing both unbounded and chaotic solutions. Here, this topic is studied in some depth, both numerically and analytically. We find, by standard methods, that four-leaf chaotic orbits result from a period-doubling cascade; we identify unstable fixed points and both stable and unstable periodic orbits; and we examine how initial data determines whether orbits approach infinity or a stable periodic orbit. Further, we describe and apply a strict numerical verification method that rigorously proves the existence of sequences of period doublings.

Bifurcation structure of a car-following model with nonlinear dependence on the relative velocity

ABSTRACT Understanding the stability of solutions of mathematical models of traffic flow is important for alleviating jams as these are considered stable inhomogeneous solutions of traffic models. Traffic jams can be alleviated by destabilizing these solutions. Solution stability can be studied with the aid of bifurcation analysis, which has been used to describe the global bifurcation structure of a car-following model that exhibits bistable behavior and loss of stability due to Hopf bifurcations. However, previous studies on bifurcation analysis for traffic models have not considered the relative velocity effect, which is important in real-world traffic scenarios. This study analytically derives linear stability conditions and numerically investigates the global bifurcation structure of a car-following model with nonlinear dependence on the relative velocity (the STNN model), which exhibits multistable states. Moreover, the relative velocity drastically changes the bifurcation structure. This supports implementation of (semi-)automatic driving systems as a means to alleviate traffic jams.

An Analyzable Method for Constructing a Cellular Automaton from a Continuous System

We propose an analyzable method of constructing a cellular automaton (CA) which simulates a given partial differential equation (PDE). We follow the study by Kawaharada and Iima who proposed a procedure for empirical construction of a CA from a given dataset. Their procedure is applicable for any spatiotemporal dataset, including numerical solutions of a PDE, in principle. However, the resultant CA is hardly identified a priori in a theoretical manner. An advantage of our proposed is that it is capable of being analyzed mathematically. The key is to design a minimal set of numerical experiments for collecting the spatiotemporal dataset for use in this procedure. We apply the proposed method to numerical solutions of three PDEs: the diffusion equation, the advection equation, and the Burgers equation. We discuss the difference with the existing method and the asymptotic convergence of the local rule depending on the amount of data, exploiting the advantage of the proposed method.

Proper Choice of Spatio-Temporal Scale and Dataset Subsampling for Empirical CA Construction

Here, we consider an appropriate data subsampling procedure for empirical construction of cellular automata (CA). Empirical CA construction is a statistical method to determine a rule of CA by using a given dataset, and this method can be applied to any spatio-temporal datasets in principle. The methodology of constructing the rule was showed by Kawaharada and Iima [5], however it has yet to be developed as a fully convincing method to capture a tendency of space-time patterns of the dataset. In this study, we develop a new procedure to determine the rule by choosing the appropriate spatio-temporal scale to subsample the dataset for more effective empirical CA construction. Using some datasets of numerical solutions of partial differential equations, we illustrate the necessity of the subsampling and elucidate the validity of the new method for the empirical CA construction.

Computer-Aided Bifurcation Analysis for a Novel Car-Following Model with Relative Velocity Effect

The global behaviour of mathematical models for traffic flow is important in order to understand their characteristics because of the bistable property observed in real traffic. This bi-stability can be discussed in a bifurcation analysis. In fact, bifurcation analysis of optimal velocity models in several studies has revealed the global bifurcation structure of the model, which shows a loss of stability due to the Hopf bifurcation and bistable property. Shamoto et al. proposed a novel car-following model with relative velocity effect (STNN model), which was not introduced into the optimal velocity model, but is important in real traffic scenarios. They discussed the linear stability of homogeneous traffic flow; however, they did not reveal the global bifurcation structure of the STNN model. In this paper, we numerically investigated the global bifurcation structure of the STNN model and observed that the strength of the relative velocity effect drastically changes the bifurcation structure. This result provides a possibility of implementing (semi-)automatic driving systems to alleviate traffic jams.