Recent Submissions

  • Estimation of synaptic activity during neuronal oscillations 

    Guillamon Grabolosa, Antoni; Vich Llompart, Catalina; Prohens Sastre, Rafel; Teruel Aguilar, Antonio E. (Multidisciplinary Digital Publishing Institute (MDPI), 2020-11-24)
    Article
    Open Access
    In the study of brain connectivity, an accessible and convenient way to unveil local functional structures is to infer the time trace of synaptic conductances received by a neuron by using exclusively information about its ...
  • Canard-induced complex oscillations in an excitatory network 

    Desroches, Mathieu; Guillamon Grabolosa, Antoni; Rinzel, John; Köksal Ersöz, Elif; Tabak, Joël (2020-01-01)
    Article
    Open Access
    In Neuroscience, mathematical modelling involving multiple spatial and temporal scales can unveil complex oscillatory activity such as excitable responses to an input current, subthreshold oscillations, spiking or bursting. ...
  • Darboux integrability and dynamics of the Basener–Ross population model 

    Güngör, Faruk; Llibre Saló, Jaume; Pantazi, Chara (Circolo Matematico di Palermo, 2020)
    Article
    Open Access
    We deal with the Basener and Ross model for the evolution of human population in Easter island. We study the Darboux integrability of this model and characterize all its global dynamics in the Poincaré disc, obtaining 15 ...
  • Exponentially small splitting of separatrices associated to 3D whiskered tori with cubic frequencies 

    Delshams Valdés, Amadeu; Gonchenko, Marina; Gutiérrez Serrés, Pere (2020-01-01)
    Article
    Open Access
    We study the splitting of invariant manifolds of whiskered (hyperbolic) tori with three frequencies in a nearly-integrable Hamiltonian system, whose hyperbolic part is given by a pendulum. We consider a 3-dimensional torus ...
  • On planar polynomial vector fields with elementary first integrals 

    Christopher, Colin; Pantazi, Chara; Llibre Saló, Jaume; Walcher, Sebastian (2019-10-05)
    Article
    Restricted access - publisher's policy
    We show that under rather general conditions a polynomial differential system having an elementary first integral already must admit a Darboux first integral, and we explicitly characterize the vector fields in this class. ...
  • Critical velocity in kink-defect interaction models: rigorous results 

    Martínez-Seara Alonso, M. Teresa; Guàrdia Munarriz, Marcel; Gomide, Otávio M.L. (2020-01-01)
    Article
    Open Access
    In this work we study a model of interaction of kinks of the sine-Gordon equation with a weak defect. We obtain rigorous results concerning the so-called critical velocity derived in [7] by a geometric approach. More ...
  • Study of periodic orbits in periodic perturbations of planar reversible Filippov systems having a twofold cycle 

    Martínez-Seara Alonso, M. Teresa; Novaes, Douglas D.; Teixeira, Marco Antonio; Zeli, Iris O. (2020-01-01)
    Article
    Open Access
    We study the existence of periodic solutions in a class of planar Filippov systems obtained from non-autonomous periodic perturbations of reversible piecewise smooth differential systems. It is assumed that the unperturbed ...
  • A general mechanism of diffusion in hamiltonian systems: qualitative results 

    Gidea, Marian; Llave Canosa, Rafael de la; Martínez-Seara Alonso, M. Teresa (2019-01-01)
    Article
    Open Access
    We present a general mechanism to establish the existence of diffusing orbits in a large class of nearly integrable Hamiltonian systems. Our approach is based on following the “outer dynamics” along homoclinic orbits to a ...
  • The uncoupling limit of identical Hopf bifurcations with an application to perceptual bistability 

    Pérez Cervera, Alberto; Ashwin, Peter; Huguet Casades, Gemma; Rankin, James; Martínez-Seara Alonso, M. Teresa (2019-12-01)
    Article
    Open Access
    We study the dynamics arising when two identical oscillators are coupled near a Hopfbifurcation where we assume a parameter uncouples the system at = 0. Using anormal form forN= 2 identical systems undergoing Hopf bifurcation, ...
  • Hopf-Zero singularities truly unfold chaos 

    Baldomá Barraca, Inmaculada; Ibáñez Mesa, Santiago; Martínez-Seara Alonso, M. Teresa (2020-05-01)
    Article
    Restricted access - publisher's policy
    We provide conditions to guarantee the occurrence of Shilnikov bifurcations in analytic unfoldings of some Hopf-Zero singularities through a beyond all order phenomenon: the exponentially small breakdown of invariant ...
  • Dynamics in a time-discrete food-chain model with strong pressure on preys 

    Lázaro Ochoa, José Tomás; Alsedà, Lluís; Vidiella, Blai; Solé Vicente, Ricard; Sardañés, Josep (2020-05-01)
    Article
    Restricted access - publisher's policy
    Discrete-time dynamics, mainly arising in boreal and temperate ecosystems for species with non-overlapping generations, have been largely studied to understand the dynamical outcomes due to changes in relevant ecological ...
  • A geometric approach to phase response curves and its numerical computation through the parameterization method 

    Pérez Cervera, Alberto; Martínez-Seara Alonso, M. Teresa; Huguet Casades, Gemma (2019-01-01)
    Article
    Open Access
    The phase response curve (PRC) is a tool used in neuroscience that measures the phase shift experienced by an oscillator due to a perturbation applied at different phases of the limit cycle. In this paper, we present a new ...

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