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The existence of this limit cycle and its evolution with parameters turn out to be of great importance for the stability and robustness control of this type of power converter. This degenerate situation is obtained from the lack of controllability. El doctor Cristóbal Zaragoza informó, tras 50 minutos de operación, de una cornada en la parte inferior del glúteo con una trayectoria ascendente de 12 centímetros y otra descendente de 5. First, the dimensional issue, since at least a 3D dynamical system must be analyzed; secondly, one must deal with discontinuous models, when a piecewise linear characteristics for the memristor is adopted. We propose for symmetric three-dimensional piecewise linear systems with three zones a unified approach to analyze both Hopf and Hopf-pitchfork bifurcations.

Some theoretical bifurcation results previously obtained by the authors are applied to describe the bifurcation set of a piecewise linear electronic circuit with two state variables. These homoclinic orbits exist both under Shil'nikov 0 1 and sufficiently close to 1 we show that these periodic orbits persist but then they do not accumulate to the homoclinic orbit. Appropriate modifications of the switching decision with the aim of converting undesired attractors into virtual ones are proposed. Also, based upon the bifurcation set obtained, we show the existence of closed surfaces in the 3D state space which are foliated by periodic orbits. Pero su actitud pone de manifiesto el interés desmedido del torero por volver a los ruedos y estar presente en todas las ferias.

Different bifurcations which are responsible for the appearance of crossing limit cycles are detected and parameter regions with none, one, two and three crossing limit cycles are found. Following the Filippov convention, the vector field can be extended to the points in Σ where the two vector fields cannot be concatenated in the natural way, leading to the so called sliding vector field and completing so a Filippov system. Typically, only numerical simulations have been reported and so there is a lack of mathematical results. To characterize this bifurcation, accurate estimates on the amplitude and period of the bifurcating limit cycle are given. We concentrate our attention on the saddle dynamics cases, determining the existence of periodic orbits as well as their stability, and possible bifurcations. Through a rigorous mathematical study, a complete description of the bifurcation set is obtained and the parameter regions where the inverter can work properly is emphasized.

The algorithm is reviewed and some examples, which show that the algorithm is really efficient, are given. Regarding the sliding bifurcation, supercritical cases occur in the regions from 1 to 5 and subcritical ones from 6 to 10. Toñete finalizó lo que el maestro no pudo acabar. The results are applied in the analysis of bifurcation behaviours in an autonomous electronic oscillator.

Numerical simulations corroborate the theoretical predictions, which have been experimentally validated. Such a family is constituted by planar piecewise linear systems with a discontinuity line where the crossing set is maximal and it has two dynamics of focus type. First order plants with a rate-limiter in the feedback loop are considered, leading to discontinuous second order differential systems. The possibility of unsuspected bistable regimes under specific configurations of parameters is also emphasized. The oscillations are associated to a limit cycle that is produced in a second-order subsystem by means of an appropriate feedback law. Que ya había cortado una oreja del primero de su lote.

The bifurcation can be responsible for the abrupt appearance of stable periodic oscillations. These changes are predicted with the proposed methodology The describing function method used normally as a first approximation to study the existence and the stability of periodic orbits is used here to analyze the dependence of periodic orbits on the parameters of autonomous systems. As an application of these results, we study a family of 3D memristor oscilla-tors, for which the characteristic function of the memristor is a cubic polynomial. As an application of these results, we study a family of 3D memristor oscilla-tors, for which the characteristic function of the memristor is a cubic polynomial.

Typically, only numerical simulations have been reported and so there is a lack of mathematical results. Pero, como ocurre con todo hijo de vecino, a veces aciertan y, a veces, no. By adding one parameter that stratifies the 4D dynamics, it is shown that the dynamics in each stratum is topologically equivalent to a 3D continuous piecewise linear dynamical system. The theoretical results are in agreement with numerical simulations. Under some non-degeneracy conditions, a theorem characterizing such bifurcation is stated for the cases of dimension two and three.

This paper includes some new results and a survey of known bifurcations for a family of Filippov systems. It is shown that the described bifurcation scenario appears for appropriate values of parameters in the celebrated Chua's oscillator. Several local and global bifurcations some of them, degenerate are detected and summarized in the corresponding bifurcation diagrams. Un tornillazo de impotencia ensuciaba a veces la faena de amor propio.