Recently, chaotic behavior has been studied in dynamical systems that generates hidden attractors. Most of these systems have quadratic nonlinearities. This paper introduces a new methodology to develop a family of three-dimensional hidden attractors from the switching of linear systems. This methodology allows to obtain strange attractors with only one stable equilibrium, attractors with an infinite number of equilibria or attractors without equilibrium. The main matrix and the augmented matrix of every linear system are considered in Rouché-Frobenius theorem to analyze the equilibrium of the switching systems. Also, a systematic search assisted by a computer is used to find the chaotic behavior. Basic chaotic properties of the attractors are verified by the Lyapunov exponents.

There are different types of electronic oscillators that have a wide variety of applications in areas such as computing, audio, communication, among others. One of these is the harmonic oscillators that generate an output sinusoidal signal. Due to the advantages of these, this paper proposes a methodology based on an analysis based on the dynamical system theory. This provides undergraduates a useful tool for a better understanding of the harmonic oscillators in order to design and implement accurately this kind of circuits. This tool complements the widely recognized Barkhausen criterion, which is a mathematical condition that must be satisfied by linear feedback oscillators. The analysis based on the dynamical system theory consists of obtaining a state matrix and its eigenvalues from the mathematical model of the oscillator circuits. The eigenvalues are adjusted to get an oscillator system, thus from this way, a set of

Summary This paper introduces an electronic circuit capable of generating a set of functions, some of them known in digital systems as the logical operators AND, OR, XOR, and so on. Using two inputs, u1 and u2, the circuit provides 16 possible output combinations. The main idea of the electronic design is based on an RC network, operational amplifiers, and voltage comparators. On the other hand, mathematically, the stable system response is used as a surface where u1 and u2 are coordinate axes forming a plane, which intersects this surface, and the output y can be seen as a circle surrounding some fixed points over this plane. The mathematical approach on this paper is intended as a groundwork for a multiple input reconfigurable logic gate that could be embedded in more complex systems. The procedure to obtain an XOR gate, represented by the ffalse(6false) function, is explained to illustrate the circuit behavior. Results of the 16 implemented functions are shown in Appendices B and C.