This paper presents circuit techniques using pulse-width and pulse-phase modulation (PWM/PPM) approaches for VLSI implementation of nonlinear dynamical systems. The proposed circuits implement discrete-time continuous-state dynamics by means of analog processing in a time domain, and also approximately implement continuous-time dynamics. Arbitrary nonlinear transformation functions are generated by the process in which a PPM signal samples a voltage or current source whose waveform in the time domain has the same shape as the desired transformation function. Because a shared arbitrary nonlinear voltage or current waveform generator can be constructed by digital circuits and D/A converters, high flexibility and real-time controllability are achieved. By using one of these new techniques, we have designed and fabricated a CMOS chaos circuit with arbitrary 1-D maps using a 0.6 µm CMOS process, and demonstrate from the experimental results that the new chaos circuit successfully generated various chaos with 7.5-7.8 bit precision by using logistic, tent and chaotic-neuron maps.

In this paper, an adaptive bound reduced-form genetic algorithm (ABRGA) to tune the control points of B-spline neural networks is proposed. It is developed not only to search for the optimal control points but also to adaptively tune the bounds of the control points of the B-spline neural networks by enlarging the search space of the control points. To improve the searching speed of the reduced-form genetic algorithm (RGA), the ABRGA is derived, in which better bounds of control points of B-spline neural networks are determined and paralleled with the optimal control points searched. It is shown that better efficiency is obtained if the bounds of control points are adjusted properly for the RGA-based B-spline neural networks.

We propose a new intelligent blind source separation algorithm for the mixture of sub-Gaussian and super-Gaussian sources. The algorithm consists of an update equation of the separating matrix and an adjustment equation of nonlinear functions. To verify the validity of the proposed algorithm, we compare the proposed algorithm with extant methods.

A simple algorithm is proposed for representing nonseparable functions by equivalent separable functions. In this algorithm, functions are first represented by computational graphs, which are directed graphs representing the computational process of the functions. Then, the vertices of the computational graphs are searched in preorder or postorder, and the transformation to separable forms is performed at the places where it is necessary. By this repetition of the transformation, nonseparable functions are represented by separable functions automatically. The proposed algorithm will be useful in various fields of science and engineering because funcutions of one variable are easy to deal with.

Separability is a valuable property of nonlinear mappings. By exploiting this property, computational complexity of many numerical algorithms can be substantially reduced. In this letter, a new algorithm is presented that detects the separability of nonlinear mappings using the concept of "computational graph". A hybrid algorithm using both the top-down search and the bottom-up search is proposed. It is shown that this hybrid algorithm is advantageous in detecting the separability of nonlinear simultaneous functions.