Persona: Franco Leis, Daniel
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dfranco@ind.uned.es
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0000-0002-9819-5664
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Franco Leis
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Daniel
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11 resultados
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Publicación Long-run economic growth in the delay spatial Solow model(Taylor&Francis, 2022-09-01) Franco Leis, Daniel; Perán Mazón, Juan Jacobo; Segura, JuanThis 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.Publicación Adaptive threshold harvesting and the suppression of transients(Elsevier, 2016-04-21) Segura, Juan; Hilker, Frank M.; Franco Leis, DanielFluctuations in population size are in many cases undesirable, as they can induce outbreaks and extinctions or impede the optimal management of populations. We propose the strategy of adaptive threshold harvesting (ATH) to control fluctuations in population size. In this strategy, the population is harvested whenever population size has grown beyond a certain proportion in comparison to the previous generation. Taking such population increases into account, ATH intervenes also at smaller population sizes than the strategy of threshold harvesting. Moreover, ATH is the harvesting version of adaptive limiter control (ALC) that has recently been shown to stabilize population oscillations in both experiments and theoretical studies. We find that ATH has similar stabilization properties as ALC and thus offers itself as a harvesting alternative for the control of pests, exploitation of biological resources, or when restocking interventions required from ALC are unfeasible. We present numerical simulations of ATH to illustrate its performance in the presence of noise, lattice effect, and Allee effect. In addition, we propose an adjustment to both ATH and ALC that restricts interventions when control seems unnecessary, i.e. when population size is too small or too large, respectively. This adjustment cancels prolonged transients.Publicación Dispersal in multi-patch metapopulations: the impact of patch number and network topology(ELSEVIER, 2026-02-21) Segura, Juan; Marvá, Marcos; Franco Leis, Daniel; Agencia Estatal de Investigación, Spain; European Regional Development Fund, EUHabitat fragmentation is a leading cause of biodiversity loss, and efforts to enhance connectivity through, for example, biological corridors are a common conservation strategy to mitigate it. However, understanding the effects of dispersal variation on the total biomass of spatially structured populations is still far from being well understood. For the simplest situation, i.e., a population occupying a habitat divided into two patches, recent studies have shown that there are only four possible response scenarios to increased connectivity in discrete- and continuous-time models under Beverton-Holt and logistic local dynamics, respectively. This paper explores whether the number of patches in a metapopulation influences the number of response scenarios to increased dispersal. We will show that for given local dynamics the number of possible response scenarios significantly increases when the number of patches increases from two to three. Moreover, the paper revisits the problem of how network topology affects total biomass dynamics for low dispersal rates. We will show that the previous claim that bidirectional connectivity always increases biomass at low dispersal rates when connecting sources is false. Indeed, we will prove that transiting from a chain topology to a ring topology can either increase or decrease the total biomass for low dispersal rates if one considers more realistic production functions or if the probability of using a concrete path is not the same in the whole metapopulation.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/0000-0001-5496-7362Persistency, 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.Publicación Degenerate Period Adding Bifurcation Structure of One-Dimensional Bimodal Piecewise Linear Maps(Society for Industrial and Applied Mathematics (SIAM), 2020-01-01) Segura, Juan; Hilker, Frank M.; Franco Leis, DanielMotivated by a problem in the management of ecological populations, we study the bifurcation structure known as period adding structure for a family of one-dimensional bimodal piecewise linear maps. This structure is rather degenerate compared to the general case usually addressed in the literature. The degeneracy affects both the type of border collision bifurcations constituting the bifurcation structure and the number and location of the bifurcation points in the parameter space. We provide rigorous theoretical results that yield a complete description of the degenerate border collision bifurcations and a full determination of the bifurcation structure. This allows us to extend partial results previously reported about a similar problem. From an ecological point of view, we provide numerical simulations showing potential risks and opportunities associated with the bifurcation structure studied here. Moreover, we provide examples of applications of our results to some well-known population models, showing that the period adding structure ranges from very simple to very intricate.Publicación On the global attractor of delay differential equations with unimodal feedback not satisfying the negative Schwarzian derivative condition(University of Szeged , 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.Publicación Dynamics of the discrete Seno population model: Combined effects of harvest timing and intensity on population stability(ELSEVIER, 2017-08-01) Franco Leis, Daniel; Logemann, Hartmut; Perán Mazón, Juan Jacobo; Segura, JuanThe paper contains new results on the impact of harvesting times and intensities on the stability properties of Seno population models. It is proved that sufficiently high harvest intensities are stabilizing for any harvesting time in the sense that they create a positive equilibrium that attracts all positive solutions. Moreover, in the special case that the nonlinearity in the Seno model is a Ricker function, we derive a global stability result independent of timing and valid for low to medium harvesting efforts. The proof is based on a characterization of those harvesting intensities which guarantee a negative Schwarzian derivative for all harvesting times. Finally, we rigorously show that timing can be stabilizing as well as destabilizing by itself. In particular, a recent conjecture formulated by Cid et al. (2014) [1] is shown to be false.Publicación New insights into the combined effect of dispersal and local1 dynamics in a two-patch population model(Elsevier, 2024-12-07) Franco Leis, Daniel; Perán Mazón, Juan Jacobo; Segura, JuanUnderstanding 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.Publicación One way or another: Combined effect of dispersal and asymmetry on total realized asymptotic population abundance(ELSEVIER, 2024-07-01) Segura, Juan; Franco Leis, Daniel; Agencia Estatal de Investigación, Spain; European Regional Development Fund, EUUnderstanding the consequences on population dynamics of the variability in dispersal over a fragmented habitat remains a major focus of ecological and environmental inquiry. Dispersal is often asymmetric: wind, marine currents, rivers, or human activities produce a preferential direction of dispersal between connected patches. Here, we study how this asymmetry affects population dynamics by considering a discrete-time two-patch model with asymmetric dispersal. We conduct a rigorous analysis of the model and describe all the possible response scenarios of the total realized asymptotic population abundance to a change in the dispersal rate for a fixed symmetry level. In addition, we discuss which of these scenarios can be achieved just by restricting mobility in one specific direction. Moreover, we also report that changing the order of events does not alter the population dynamics in our model, contrary to other situations discussed in the literature.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 JacoboPersistence, 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.