This paper presents a nonlinear model of human brain activity in response to visual stimuli according to Blood-Oxygen-Level-Dependent (BOLD) signals scanned by functional Magnetic Resonance Imaging (fMRI). A BOLD signal often contains a low frequency signal component (trend), which is usually removed by detrending because it is considered a part of noise. However, such detrending could destroy the dynamics of the BOLD signal and ignore an essential component in the response. This paper shows a model that, in the absence of detrending, can predict the BOLD signal with smaller errors than existing models. The presented model also has low Schwarz information criterion, which implies that it will be less likely to overfit the experimental data. Comparison between the various types of artificial trends suggests that the trends are not merely the result of noise in the BOLD signal.

Phase structure of nonlinear dynamical system is governed by the vector field and decides the trajectories. Accordingly, the power spectra of trajectories include the structural field effect on the phase space. In this paper, we develop a method for analyzing phase structure using power spectra of trajectories and reconstitute a potential function in the system.

In this paper, we propose a variational method to derive the coefficients of piecewise-linear (PWL) models able to accurately approximate nonlinear functions, which are vector fields of autonomous dynamical systems described by continuous-time state-space models dependent on parameters. Such dynamical systems admit limit cycles, and the supercritical Hopf bifurcation normal form is chosen as an example of a system to be approximated. The robustness of the approximations is checked, with a view to circuit implementations.

A merged analog-digital circuit architecture is proposed for implementing intelligence in SoC systems. Pulse modulation signals are introduced for time-domain massively parallel analog signal processing, and also for interfacing analog and digital worlds naturally within the SoC VLSI chip. Principles and applications of pulse-domain linear arithmetic processing are explored, and the results are expanded to the nonlinear signal processing, including an arbitrary chaos generation and continuous-time dynamical systems with nonlinear oscillation. Silicon implementations of the circuits employing the proposed architecture are fully described.

We investigate bifurcations of the periodic solution observed in a phase converter circuit. The system equations can be considered as a nonlinear coupled system with Duffing's equation and an equation describing a parametric excitation circuit. In this system there are two types of solutions. One is with x = y = 0 which is the same as the solution of Duffing's equation (correspond to uncoupled case), another solution is with xy0. We obtain bifurcation sets of both solutions and discuss how does the coupling change the bifurcation structure. From numerical analysis we obtain a codimension two bifurcation which is intersection of double period-doubling bifurcations. Pericdic solutions generated by these bifurcations become chaotic states through a cascade of codimension three bifurcations which are intersections of D-type of branchings and period-doubling bifurcations.

We propose an equivalent circuit model described by the Rössler equation. Then we can consider a coupled Rössler system with a physical meaning on the connection. We consider an oscillatory circuit such that two identical Rössler circuits are coupled by a resistor. We have studied three routes to entirely and almost synchronized chaotic attractors from phase-locked periodic oscillations. Moreover, to simplify understanding of synchronization phenomena in the coupled Rössler system, we investigate a mutually coupled map that shows analogous locking properties to the coupled Rössler System.