Persona:
Franco Leis, Daniel

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0000-0002-9819-5664
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Franco Leis
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Daniel
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2020 - 20255
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Mostrando 1 - 5 de 5
  • Miniatura
    Publicación
    Long-run economic growth in the delay spatial Solow model
    (Taylor&Francis, 2022-09-01) Franco Leis, Daniel; Perán Mazón, Juan Jacobo; Segura, Juan
    This paper analyses the long-term dynamics of the Solow model with spatial dependence of the physical capital, time delay and pollution effect due to capital accumulation. Previous studies not including spatial dependence showed that the dynamics can be cyclic or chaotic, in which cases the description of the long-run system’s behaviour becomes difficult or unfeasible. We provide sufficient conditions for the existence of a delay-independent global attractor and an easy way to estimate it. We also introduce new and extend known results for the existence of a global attractor in the absence of spatial dependence. Additionally, we complement known global stability results for a family of difference equations with applications in different fields.
  • Miniatura
    Publicación
    Persistency and stability of a class of nonlinear forced positive discrete-time systems with delays
    (Elsevier, 2024-06-14) Franco Leis, Daniel; Guiver, Chris; Logemann, Hartmut; Perán Mazón, Juan Jacobo; Elsevier
    Persistence, excitability and stability properties are considered for a class of nonlinear, forced, positive discrete-time systems with delays. As will be illustrated, these equations arise in a number of biological and ecological contexts. Novel sufficient conditions for persistence, excitability and stability are presented. Further, similarities and differences between the delayed equations considered presently and their corresponding undelayed versions are explored, and some striking differences are noted. It is shown that recent results for a corresponding class of positive, nonlinear delay-differential (continuous-time) systems do not carry over to the discrete-time setting. Detailed discussion of three examples from population dynamics is provided.
  • Miniatura
    Publicación
    New insights into the combined effect of dispersal and local1 dynamics in a two-patch population model
    (Elsevier, 2024-09-17) Franco Leis, Daniel; Perán Mazón, Juan Jacobo; Segura, Juan
    Understanding the effect of dispersal on fragmented populations has drawn the attention of ecologists and managers in recent years, and great efforts have been made to understand the impact of dispersal on the total population size. All previous numerical and theoretical findings determined that the possible response scenarios of the overall population size to increasing dispersal are monotonic or hump-shaped, which has become a common assumption in ecology. Against this, we show in this paper that many other response scenarios are possible by using a simple two-patch discrete-time model. This fact evidences the interplay of local dynamics and dispersal and has significant consequences from a management perspective that will be discussed.
  • Miniatura
    Publicación
    On the global attractor of delay differential equations with unimodal feedback not satisfying the negative Schwarzian derivative condition
    (Electronic Journal of Qualitative Theory of Differential Equations, 2020-12-21) Franco Leis, Daniel; Guiver, Chris; Logemann, Harmut; Perán Mazón, Juan Jacobo; Kriszrin, Tibor; Webb, Jeff R. L.
    We study the size of the global attractor for a delay differential equation with unimodal feedback. We are interested in extending and complementing a dichotomy result by Liz and Röst, which assumed that the Schwarzian derivative of the nonlinear feedback is negative in a certain interval. Using recent stability results for difference equations, we obtain a stability dichotomy for the original delay differential equation in the situation wherein the Schwarzian derivative of the nonlinear term may change sign. We illustrate the applicability of our results with several examples.
  • Miniatura
    Publicación
    Dynamic properties of a class of forced positive higher-order scalar difference equations: persistency, stability and convergence
    (Taylor and Francis Group, 2025-02-17) Franco Leis, Daniel; Guiver, Chris; Logemann, Hartmut; Perán Mazón, Juan Jacobo; https://orcid.org/0000-0001-5496-7362
    Persistency, stability and convergence properties are considered for a class of nonlinear, forced, positive, scalar higher-order difference equations. Sufficient conditions for these properties to hold are derived, broadly in terms of the interplay of the linear and nonlinear components of the difference equations. The convergence results presented include asymptotic response properties when the system is subject to (asymptotically) almost periodic forcing. The equations under consideration arise in a number of ecological and biological contexts, with the Allen-Clark population model appearing as a special case. We illustrate our results by several examples from population dynamics.