Journal: Physica D: Nonlinear Phenomena

Abbreviation

Physica, D, Nonlinear phenom

Publisher

Elsevier

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ISSN

0167-2789
1872-8022

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Publications1 - 10 of 34
  • Resource-consumer dynamics in drylands: Modeling the role of plant–plant facilitation–competition shifts with a piecewise system
    Item type: Journal Article
    Pereira Costa da Cruz, Leonardo; Torregrosa, Joan; Berdugo, Miguel; et al. (2025)
    Physica D: Nonlinear Phenomena
    In drylands, water availability determines plant population densities and whether they cooperate via facilitation or compete. When water scarcity intensifies, plant densities decrease and competition for water surpasses the benefits of soil improvement by facilitator plants, involving an abrupt shift from facilitation to competition. Here, we model this facilitation–competition shift using a piecewise system in a resource species such as grasses studying its impact on a resource-consumer dynamical system. First, the dynamics of each system i.e., competitive and cooperative, are introduced separately for this resource-consumer system. The competitive system, by setting conditions to have a monodromic equilibrium in the first quadrant, has no limit cycles. With a monodromy condition in the same quadrant, the cooperative system only has a hyperbolic, small amplitude limit cycle, allowing for an oscillating coexistence. The dynamic properties of the piecewise system become richer. We here prove the extension of the center-focus problem in this particular case, and from a weak focus of order three, we find 3 limit cycles arising from it. We also study the case assuming continuity in the piecewise system. Finally, we present a special and restricted way of obtaining a limit cycle of small amplitude in a pseudo-Hopf bifurcation type. Our results suggest that abrupt density-dependent functional shifts, such as those described in drylands, could introduce novel dynamical phenomena in population dynamis. Our work also provides a novel theoretical framework to model and investigate population dynamics where ecological interactions change due to density-dependent effects.
  • Geodesic theory of transport barriers in two-dimensional flows
    Item type: Journal Article
    Haller, George; Beron-Vera, Francisco J. (2012)
    Physica D: Nonlinear Phenomena
  • Explicit formulae for the peak time of an epidemic from the SIR model. Which approximant to use?
    Item type: Journal Article
    Kröger, Martin; Turkyilmazoglu, Mustafa; Schlickeiser, Reinhard (2021)
    Physica D: Nonlinear Phenomena
    An analytic evaluation of the peak time of a disease allows for the installment of effective epidemic precautions. Recently, an explicit analytic, approximate expression (MT) for the peak time of the fraction of infected persons during an outbreak within the susceptible–infectious–recovered/removed (SIR) model had been presented and discussed (Turkyilmazoglu, 2021). There are three existing approximate solutions (SK-I, SK-II, and CG) of the semi-time SIR model in its reduced formulation that allow one to come up with different explicit expressions for the peak time of the infected compartment (Schlickeiser and Kröger, 2021; Carvalho and Gonçalves, 2021). Here we compare the four expressions for any choice of SIR model parameters and find that SK-I, SK-II and CG are more accurate than MT as long as the amount of population to which the SIR model is applied exceeds hundred by far (countries, ss, cities). For small populations with less than hundreds of individuals (families, small towns), however, the approximant MT outperforms the other approximants. To be able to compare the various approaches, we clarify the equivalence between the four-parametric dimensional SIR equations and their two-dimensional dimensionless analogue. Using Covid-19 data from various countries and sources we identify the relevant regime within the parameter space of the SIR model.
  • Global uniform symptotic attractive stability of the non autonomous bouncing ball system
    Item type: Journal Article
    Leine, Remco I.; Heimsch, Thomas (2012)
    Physica D: Nonlinear Phenomena
  • The influence of canalization on the robustness of Boolean networks
    Item type: Journal Article
    Kadelka, C.; Kuipers, Jack; Laubenbacher, R. (2017)
    Physica D: Nonlinear Phenomena
  • Corrigendum to "On the structure of acceleration in turbulence" (vol 241, pg 208-2011)
    Item type: Other Journal Item
    Liberzon, Alex; Lüthi, Beat; Holzner, Markus; et al. (2012)
    Physica D: Nonlinear Phenomena
  • Acoustic streaming flows in a cavity
    Item type: Conference Paper
    Sznitman, Josué; Rösgen, Thomas (2008)
    Physica D: Nonlinear Phenomena
  • Particle transport and finite-size effects in Lorentz channels with finite horizons
    Item type: Journal Article
    Cirillo, Emilio N.M.; Colangeli, Matteo; Kröger, Martin; et al. (2025)
    Physica D: Nonlinear Phenomena
    Particle transport is investigated in a finite-size realization of the classical Lorentz gas model. We consider point particles moving at constant speed in a 2D rectangular strip of finite length, filled with circular scatterers sitting at the vertices of a triangular lattice. Particles are injected at the left boundary with a prescribed rate, undergo specular reflections when colliding with the scatterers and the horizontal boundaries of the channel, and are finally absorbed at the left or the right boundary. Thanks to the equivalence with give Correlated Random Walks, in the finite horizon case, we show that the inverse probability that a particle exits through the right boundary depends linearly on the number of cells in the channel. A non-monotonic behavior of such probability as a function of the density of scatterers is also discussed and traced back analytically to the geometric features of a single trap. This way, we do not refer to asymptotic quantities and we accurately quantify the finite size effects. Our deterministic model provides a microscopic support for a variety of phenomenological laws, e.g. the Darcy’s law for porous media and the Ohm’s law in electronic transport.
  • Properties of a simple bilinear stochastic model
    Item type: Journal Article
    Sornette, Didier; Pisarenko, V. F. (2008)
    Physica D: Nonlinear Phenomena
  • Bifurcations of equilibria in non-smooth continuous systems
    Item type: Journal Article
    Leine, R. I. (2006)
    Physica D: Nonlinear Phenomena
Publications1 - 10 of 34