Forthcoming and Online First Articles

International Journal of Dynamical Systems and Differential Equations

International Journal of Dynamical Systems and Differential Equations (IJDSDE)

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International Journal of Dynamical Systems and Differential Equations (2 papers in press)

Regular Issues

  • Pseudo periodicity and pseudo almost periodicity in shifts   Order a copy of this article
    by Meng Hu, Lili Wang 
    Abstract: By means of the shifts operators
    Keywords: Pseudo periodicity; Pseudo almost periodicity; Shift operator; Time scale.
    DOI: 10.1504/IJDSDE.2023.10060882
  • The limit cycles of a class of discontinuous piecewise differential systems   Order a copy of this article
    by Louiza Baymout, Rebiha Benterki, Jaume Llibre 
    Abstract: The determination of the maximum number of limit cycles and their possible positions in the plane is one of the most difficult problems in the qualitative theory of planar differential systems. This problem is related to the second part of the unsolved 16th Hilberts problem. Due to their applications in modelling many natural phenomena, piecewise differential systems have recently attracted big attention. The upper bound number of limit cycles that a class of differential systems may exhibit is typically very difficult to determine. In this work we extend the second part of the 16th Hilberts problem to the planar discontinuous piecewise differential systems separated by a straight line and formed by an arbitrary linear centre and an arbitrary cubic uniform isochronous centre. We provide for this class of piecewise differential systems an upper bound on its maximal number of limit cycles, and we prove that such an upper bound is reached.
    Keywords: Cubic uniform isochronous center; linear center; limit cycle; discontinuous piecewise differential system.
    DOI: 10.1504/IJDSDE.2023.10061493