Optimization of fractional-order chaotic cellular neural networks by metaheuristics.

Artificial neural networks have demonstrated to be very useful in solving problems in artificial intelligence. However, in most cases, ANNs are considered integer-order models, limiting the possible applications in recent engineering problems. In addition, when dealing with fractional-order neural networks, almost any work shows cases when varying the fractional order. In this manner, we introduce the optimization of a fractional-order neural network by applying metaheuristics, namely: differential evolution (DE) and accelerated particle swarm optimization (APSO) algorithms. The case study is a chaotic cellular neural network (CNN), for which the main goal is generating fractional orders of the neurons whose Kaplan-Yorke dimension is being maximized. We propose a method based on Fourier transform to evaluate if the generated time series is chaotic or not. The solutions that do not have chaotic behavior are not passed to the time series analysis (TISEAN) software, thus saving execution time. We show the best solutions provided by DE and APSO of the attractors of the fractional-order chaotic CNNs.

FPAA-based implementation of fractional-order chaotic oscillators using first-order active filter blocks.

Fractional-order chaotic oscillators (FOCOs) have been widely studied during the last decade, and some of them have been implemented on embedded hardware like field-programmable gate arrays, which is a good option for fast prototyping and verification of the desired behavior. However, the hardware resources are dependent on the length of the digital word that is used, and this can degrade the desired response due to the finite number of bits to perform computer arithmetic. In this manner, this paper shows the implementation of FOCOs using analog electronics to generate continuous-time chaotic behavior. Charef's method is applied to approximate the fractional-order derivatives as a ratio of two polynomials in the Laplace domain. For instance, two commensurate FOCOs are the cases of study herein, for which we show their dynamical analysis by evaluating their equilibrium points and eigenvalues that are used to estimate the minimum fractional-order that guarantees their chaotic behavior. We propose the use of first-order all-pass and low-pass filters to design the ratio of the polynomials that approximate the fractional-order. The filters are implemented using amplifiers and synthesized on a field-programmable analog array (FPAA) device. Experimental results are in good agreement with simulation results thus demonstrating the usefulness of FPAAs to generate continuous-time chaotic behavior, and to allow reprogramming of the parameters of the FOCOs.

Order type dataset analysis for fiducial markers.

Order Type (OT) describes a point set avoiding the use of metric information. We show that OT is a descriptor which is invariant to Euclidean geometric transformations, change of scale and perspective projection. In this paper we provide the data related to the application of Order Type with sets of 5, 6, 7, and 8 points to build fiducial markers. The OT is represented through a λ -matrix. We provide the set of points which are suitable to solve directly the point matching, because these have a unique associated λ -matrix. We provide maximal perturbation data for all set of points, maximal perturbation is the radius of the circle, centered in each point in the set, inside which each point can be moved without changing its associated OT. Also we provide the scripts to validate the use of OT in fiducial markers.

VHDL Descriptions for the FPGA Implementation of PWL-Function-Based Multi-Scroll Chaotic Oscillators.

Nowadays, chaos generators are an attractive field for research and the challenge is their realization for the development of engineering applications. From more than three decades ago, chaotic oscillators have been designed using discrete electronic devices, very few with integrated circuit technology, and in this work we propose the use of field-programmable gate arrays (FPGAs) for fast prototyping. FPGA-based applications require that one be expert on programming with very-high-speed integrated circuits hardware description language (VHDL). In this manner, we detail the VHDL descriptions of chaos generators for fast prototyping from high-level programming using Python. The cases of study are three kinds of chaos generators based on piecewise-linear (PWL) functions that can be systematically augmented to generate even and odd number of scrolls. We introduce new algorithms for the VHDL description of PWL functions like saturated functions series, negative slopes and sawtooth. The generated VHDL-code is portable, reusable and open source to be synthesized in an FPGA. Finally, we show experimental results for observing 2, 10 and 30-scroll attractors.