The pendulum equation with a periodic impulsive force is investigated. This model described by a second order differential equation is also derived from dynamics of the stepping motor. In this paper, firstly, we analyze bifurcation phenomena of periodic solutions observed in a generalized pendulum equation with a periodic impulsive force. There exist two topologically different kinds of solution which can be chaotic by changing system parameters. We try to stabilize an unstable periodic orbit embedded in the chaotic attractor by small perturbations for the parameters. Secondly, we investigate the intermittent drive characteristics of two-phase hybrid stepping motor. We suggest that the unstable operations called pull-out are caused by bifurcations. Finally, we proposed a control method to avoid the pull-out by changing the repetitive frequency and stepping rate.

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.

It is important to analyze a tracking or synchronizing process in Spread Spectrum (SS) receiving system. The most common SS tracking system considered here consists of pseudorandom (PN) generator, Lowpass Filter (LPE) and Voltage Controlled Oscillator (VCO). The SS receiver is to track or synchronize its local PN generator to the received PN waveform by VCO. The fundamental equation of the system is known by a second order nonlinear differential equation in terms of phase difference between local PN generator and received PN waveform. The differential equation is nonautonoumous due to PN function of time t with period T. Picking up the gain of VCO as the main parameter in the system we show that the system has bifurcation from the normal oscillation through subharmonic oscillation to finally chaos. In the final case, chaos is confirmed by investigating maximum Liapunov number and both stable and unstable manifolds.

Secure communications via chaotic synchronization is experimentally demonstrated using 3-pieces of commercial integrated circuit phase-locked loops, MC14046. Different from the conventional chaotic synchronization secure communication systems where one channel is used, our system uses two channels to send one signal to be concealed. Namely, one channel is used to send a synchronizing chaotic signal. The other channel is used to send the informational signal superimposed on the chaotic masking signal at transmitter side. The synchronizing chaotic signal is applied as a common input to two identical PLL's located at both transmitter and receiver sides. It has been shown previously by us that the VCO inputs of almost identical two PLL's driven by a common chaotic signal become chaotic, and synchronized with each other. This synchronization is only possible for those who knows exact internal configuration and exact parameter values of the PLL at transmitter side. Therefore, we can use the synchronized VCO input signal as a masking signal which can be used as a key for secure communications. The advantage of this method compared to the previous one channel method is that informational signal frequency range does not affect the quality of recovered signal. Our experiments demonstrate good masking and recovery characteristics for sinusoidal, triangular, and square waves.

In this paper, we propose algorithm of deterministic nonlinear prediction, or a modified version of the method of analogues which was originally proposed by E.N. Lorenz (J. Atom. Sci., 26, 636-646, 1969), and apply it to the artificial time series data produced from nonlinear dynamical systems and further corrupted by superimposed observational noise. The prediction performance of the present method are investigated by calculating correlation coefficients, root mean square errors and signature errors and compared with the prediction algorithm of local linear approximation method. As a result, it is shown that the prediction performance of the proposed method are better than those of the local linear approximation especially in case that the amount of noise is large.

The number of solutions of a nonlinear equation x = sgn(Wx) is discussed. The equation is derived for the determination of equilibrium points of a kind of Hopfield neural networks. We impose some conditions on W. The conditions correspond to the case where a Hopfield neural network has n neurons arranged on a ring, each neuron has connections only from k preceding neurons and the magnitude of k connections decrease as the distance between two neurons increases. We show that the maximum number of solutions for the above case is extremely few and is independent of the number of neurons, n, if k is less than or equal to 4. We also show that the number of solutions generally increases exponentially with n by considering the case where k = n-1.

We present a framework for the unsupervised segmentation of time series. It applies to non-stationary signals originating from different dynamical systems which alternate in time, a phenomenon which appears in many natural systems. In our approach, predictors compete for data points of a given time series. We combine competition and evolutionary inertia to a learning rule. Under this learning rule the system evolves such that the predictors, which finally survive, unambiguously identify the underlying processes. The segmentation achieved by this method is very precise and transients are included, a fact, which makes our approach promising for future applications.

Cellular Neural Networks (CNNs) are nonlinear dynamic array processors with mainly local interconnections. In most of the applications, the local interconnection pattern, called cloning template, is translation invariant. In this paper, an optimal ring-coding method for rotation invariant description of given set of objects, is introduced. The design methodology of the templates based on the ring-codes and the synthesis of CNN analogic algorithms to detect standing and moving objects in a rotationally invariant way, discussed in detail. It is shown that the algorithms can be implemented using the CNN Universal Machine, the recently invented analogic visual microprocessor. The estimated time performance and the parallel detecting capability is emphasized, the limitations are also thoroughly investigated.

In order to provide a fuzzy system with learning function, numerous studies are being carried out to combine fuzzy systems and neural networks. The self-tuning methods using the descent method have been proposed. The constructive and the destructive methods are more powerful than other methods using neural networks (or descent method). On the other hand the destructive method is superior in the number of rules and inference error and inferior in learning speed to the constructive method. In this paper, we propose a new learning method combining the constructive and the destructive methods. The method is superior in the number of rules, inference error and learning speed to the destructive method. However, it is inferior in learning speed to the constructive method. Therefore, in order to improve learning speed of the proposed method, simplified learning methods are proposed. Some numerical examples are given to show the validity of the proposed methods.

In this paper a priori estimation method is presented for calculating solution of convex optimization problems (COP) with some equality and/or inequality constraints by so-called Newton type homotopy method. The homotopy method is known as an efficient algorithm which can always calculate solution of nonlinear equations under a certain mild condition. Although, in general, it is difficult to estimate a priori computational complexity of calculating solution by the homotopy method. In the presented papers, a sufficient condition is considered for linear homotopy, under which an upper bound of the complexity can be estimated a priori. For the condition it is seen that Urabe type convergence theorem plays an important role. In this paper, by introducing the results, it is shown that under a certain condition a global minimum of COP can be always calculated, and that computational complexity of the calculation can be a priori estimated. Suitability of the estimation for analysing COP is also discussed.

This paper describes an MOS charge-mode version of a T-Model neural-based PCM encoder. The neural-based PCM encoding networks are designed, simulated and implemented using MOS charge-mode circuits. Simulation results are given for both the T-Model and the Hopfield model CMOS charge-mode PCM encoders, and demonstrate the T-Model neural-based one performs the PCM encoding perfectly, while the Hopfield one fails to.

In this paper, a new switched-current auto-tuning filter is proposed. Switched-current (SI) is a current-mode analog sampled-data circuit technique. An SI circuit can be realized using only standard digital CMOS technologies, and is capable of realizing high frequency circuits. The proposed filter is composed of SI-OTA (operational transconductance amplifier) integrators. The gain of an SI-OTA integrator can be electronically controlled by the bias current. The proposed filter is a current controlled filter (CCF) and a PLL technique was used as its tuning method. A 2nd-order SI auto-tuning low-pass filter with 100kHz cutoff frequency was designed assuming a 2µm CMOS process. The characteristics of this SI filter and its tuning characteristics were confirmed by SPICE simulations.

This paper proposes a new algorithm called the fast Projection algorithm, which reduces the computational complexity of the Projection algorithm from (p+1)L+O(p³) to 2L+20p (where L is the length of the estimation filter and p is the projection order.) This algorithm has properties that lie between those of NLMS and RLS, i.e. less computational complexity than RLS but much faster convergence than NLMS for input signals like speech. The reduction of computation consists of two parts. One concerns calculating the pre-filtering vector which originally took O(p³) operations. Our new algorithm computes the pre-filtering vector recursively with about 15p operations. The other reduction is accomplished by introducing an approximation vector of the estimation filter. Experimental results for speech input show that the convergence speed of the Projection algorithm approaches that of RLS as the projection order increases with only a slight extra calculation complexity beyond that of NLMS, which indicates the efficiency of the proposed fast Projection algorithm.

The main purpose of this paper is to give a new representation method of the convergence characteristics of the LMS algorithm using tap-input vectors. The described representation method is an extended version of the interpretation method based on the orthogonal projection. Using this new representation, we can express the convergence characteristics in terms of tap-input vectors instead of the eigenvalues of the input signal. From this representation, we consider a general method for improving the convergence speed.

This paper is concerned with synthesizing VLSI array processors from iterative algorithms. Our primary objective is to obtain the highest processor efficiency but not the shortest completion time. Unlike most of the previous work that assumes the index space of the given iterative algorithm to be boundless, the proposed method takes into account the effects of the boundaries of the index space. Due to this consideration, the pseudo-dependence relations are excluded, and most of the independent computations can therefore be uniformly grouped. With the method described in this paper, the index space is partitioned into equal-size blocks and the corresponding computations are systematically and uniformly mapped into processing elements. The synthesized VLSI array processors possess the attractive feature of very high processor efficiency, which, in general, is superior to what is derived from the conventional linear transformation methods.

One of the major open issues in neural network research includes a Network Designing Problem (NDP): find a polynomial-time procedure that produces minimal structures (the minimum intermediate size, thresholds and synapse weights) of multilayer threshold feed-forward networks so that they can yield outputs consistent with given sample sets of input-output data. The NDP includes as a sub-problem a Network Training Problem (NTP) where the intermediate size is given. The NTP has been studied mainly by use of iterative algorithms of network training. This paper, making use of both rate distortion theory in information theory and linear algebra, solves the NDP mathematically rigorously. On the basis of this mathematical solution, it furthermore develops a mathematical solution Procedure to the NDP that computes the minimal structure straightforwardly from the sample set. The Procedure precisely attains the minimum intermediate size, although its computational time complexity can be of non-polynomial order at worst cases. The paper also refers to a polynomial-time shortcut to the Procedure for practical use that can reach an approximately minimum intermediate size with its error measurable. The shortcut, when the intermediate size is pre-specified, reduces to a promising alternative as well to current network training algorithms to the NTP.

On a simple model, the quality of the security tag is simulated theoretically and experimentally. A simple correction makes both results correspond exactly and a simulation formula is provided. By using novel insulating film, a small-sized tag of high quality is developed.

In this work, a statistical analysis is performed for a simple constrained high-order Yule-Walker (YW) tone frequency estimator obtained from the first equation of the constrained high-order YW equations. Explicit expressions for its estimation bias and variance are efficiently derived by virtue of a Taylor series expansion technique. Especially, being explicit in terms of frequency, data length and Signal-to-Noise Ratio (SNR) value, the resulting bias expression can not be obtained by using the asymptotic analyses used for the parameter estimation methods. The obtained expressions are compared with their counterparts of the Pisarenko tone frequency estimator. Simulations are performed to support the theoretical results.

The controllability and the stability of the blood clotting system are examined with the linear system analysis. The dynamic behavior of the clotting system consisting of a cascade of ten proteolytic reactions of the clotting factors with multiple positive feed back and feed forward loops is represented by the rate equations in a system of non linear ordinary differential equations with 35 variables. The time courses of concentration change in every factor are revealed by numerical integration of the rate equations. Linearization of the rate equations based on the dynamic behavior of the chemical species relevant to the nonlinear terms leads to the linear systems analysis of the clotting system to clarify the essential features of blood coagulation. It follows from the analysis that the clotting system is uncontrollable regardless of changes in any system parameters and control input and that all the chemical species of the system are uncontrollable so that the sequential reactions in the cascade proceed irreversibly, once they are activated. More over by the analysis of the eigen values, the clotting reaction as a total system was shown to be unstable which was insensitive to changes in the system parameters. These characteristic natures of clotting system must be derived in the sequential cascade reaction pattern and the inherent multiple positive feed back and feed forward regulation.

This paper presents a new learning method to improve noise tolerance in Fuzzy ART. The two weight vectors: the top-down weight vector and the bottom-up weight vector are differently updated by a weighted sum and a fuzzy AND operation. This method effectively resolves the category proliferation problem without increasing the training epochs in noisy environments.

In this study, we propose a system of N Wien-bridge oscillators with the same natural frequency coupled by one resistor, and investigate synchronization phenomena in the proposed system. Because the structure of the system is different from that of LC oscillators systems proposed in our previous works, this system cannot exhibit N-phase oscillations but 3-phase and in-phase oscillations. Also in this system, we can get an extremely large number of steady phase states by changing the initial states. In particular, when N is not so large, we can get more phase states in this system than that of the LC oscillators systems. Because this system does not include any inductors and is strong against phase error this system is much more suitable for applications on VLSI compared with coupled system of van der Pol type LC oscillators.