Now showing items 1-10 of 10

    • IconBifurcación Silla-Nodo de Conos Invariantes Vía Bifurcación Foco-Centro-Ciclo Límite  [Article]

      Carmona Centeno, Victoriano; Freire Macías, Emilio; Ponce Núñez, Enrique; Ros Padilla, Francisco Javier (Sema, 2008)
      En este trabajo se considera la existencia de conos invariantes en sistemas dinámicos continuos tridimensionales lineales a trozos, dada la relevancia que estas variedades invariantes tienen en la determinación de la ...
    • IconCanards, Folded Nodes, and Mixed-Mode Oscillations in Piecewise-Linear Slow-Fast Systems  [Article]

      Desroches, Mathieu; Guillamon, Antoni; Ponce Núñez, Enrique; Prohens, Rafael; Rodrigues, Serafim; Teruel Aguilar, Antonio Esteban (Society for Industrial and Applied Mathematics, 2016)
      Canard-induced phenomena have been extensively studied in the last three decades, from both the mathematical and the application viewpoints. Canards in slow-fast systems with (at least) two slow variables, especially ...
    • IconCanonical Discontinuous Planar Piecewise Linear Systems  [Article]

      Freire Macías, Emilio; Ponce Núñez, Enrique; Torres Peral, Francisco (Society of Industrial and Applied Mathematics, 2012)
      The family of Filippov systems constituted by planar discontinuous piecewise linear systems with two half-plane linearity zones is considered. Under generic conditions that amount to the boundedness of the sliding set, ...
    • IconHopf bifurcation from infinity for planar control systems  [Article]

      Llibre Saló, Jaume; Ponce Núñez, Enrique (Universidad Autónoma de Barcelona. Departamento de Matemáticas, 1997)
      Symmetric piecewise linear bi-dimensional systems are very common in control engineering. They constitute a class of non-differentiable vector fields for which classical Hopf bifurcation theorems are not applicable. For ...
    • IconHopf-Like Bifurcations in Planar Piecewise Linear Systems  [Article]

      Freire Macías, Emilio; Ponce Núñez, Enrique; Torres Peral, Francisco (Universitat Autònoma de Barcelona, Servei de Publicacions, 1997)
      Continuous planar piecewise linear systems with two linear zones are considered. Due to their low differentiability specific techniques of analysis must be developed. Several bifurcations giving rise to limit cycles are ...
    • IconNon-hyperbolic boundary equilibrium bifurcations in planar Filippov systems: a case study approach  [Article]

      Di Bernardo, Mario; Pagano, Daniel Juan; Ponce Núñez, Enrique (WorldScientific Open Access, 2008)
      Boundary equilibrium bifurcations in piecewise smooth discontinuous systems are characterized by the collision of an equi- librium point with the discontinuity surface. Generically, these bi- furcations are of codimension ...
    • IconOn the existence and uniqueness of limit cycles in Liénard differential equations allowing discontinuities  [Article]

      Llibre Saló, Jaume; Ponce Núñez, Enrique; Torres Peral, Francisco (IOP Science, 2008)
      In this paper we study the non-existence and the uniqueness of limit cycles for the Liénard differential equation of the form x'' − f(x)x' + g(x) = 0 where the functions f and g satisfy xf(x) > 0 and xg(x) > 0 for x ≠ 0 ...
    • IconStabilization of oscillations through backstepping in high-dimensional systems  [Article]

      Aracil, J.; Gordillo, F.; Ponce Núñez, Enrique (2005-05)
      This paper introduces a method for obtaining stable and robust self-sustained oscillations in a class of single input nonlinear systems of dimension n ≥ 2. The oscillations are associated to a limit cycle that is produced ...
    • IconThe discontinuous matching of two planar linear foci can have three nested limit cycles  [Article]

      Freire Macías, Emilio; Ponce Núñez, Enrique; Torres Peral, Francisco (Universitat Autònoma de Barcelona, Servei de Publicacions, 2014)
      The existence and stability of limit cycles in discontinuous piecewise linear systems obtained by the aggregation of two linear systems of focus type and having only one equilibrium point is considered. By using an adequate ...
    • IconThe Focus-Center-Limit Cycle Bifurcation in Symmetric 3D Piecewise Linear Systems  [Article]

      Freire Macías, Emilio; Ponce Núñez, Enrique; Ros Padilla, Francisco Javier (Society for Industrial and Applied Mathematics, 2005)
      The birth of limit cycles in 3D (three-dimensional) piecewise linear systems for the relevant case of symmetrical oscillators is considered. A technique already used by the authors in planar systems is extended to cope ...