La seva activitat de recerca està dirigida al desenvolupament de mètodes analítics i numèrics per sistemes dinàmics, gaudint de lideratge científic en diversos temes, com la integrabilitat, els objectes invariants, la teoria K.A.M. (Kolmogorov-Arnold-Moser), els camps vectorials plans i les aplicacions a neurociència, mètode de Poincaré-Melnikov, escissió exponencialment petita de separatrius, difusió, mecànica celest i astrodinàmica.
La qualitat d'aquesta activitat es reflecteix tant en la qualitat i quantitat de publicacions, algunes d'elles en col·laboració amb grups internacionals de primera línia, com en la gestió científica desenvolupada, plasmada en l'organització de múltiples esdeveniments (congressos i jornades , programes de recerca, xarxes temàtiques, etc.), la participació en diversos comitès editorials de revistes de prestigi reconegut, així com en una àmplia formació doctoral.

Su actividad de investigación está dirigida al desarrollo de métodos analíticos y numéricos para sistemas dinámicos, disfrutando de liderazgo científico en diversos temas, como la integrabilidad, los objetos invariantes, la teoría K.A.M. (Kolmogorov-Arnold-Moser), los campos vectoriales planos y las aplicaciones a neurociencia, método de Poincaré-Melnikov, escisión exponencialmente pequeña de separatrices, difusión, mecánica celeste y astrodinámica.
La calidad de esta actividad se refleja tanto en la calidad y cantidad de publicaciones, algunas de ellas en colaboración con grupos internacionales de primera línea, como en la gestión científica desarrollada, plasmada en la organización de múltiples eventos (congresos y jornadas, programas de investigación, redes temáticas, etc.), la participación en diversos comités editoriales de revistas de prestigio reconocido, así como en una amplia formación doctoral.

The UPC dynamical systems group is composed by 20 full time doctors and 3 predocs.

Its research activity is addressed to the development of analytical and numerical methods
for dynamical systems, holding a scientific leading position in several subjects, namely integrability,
invariant objects, KAM theory, planar vector fields and applications to neuroscience, Poincaré-Melnikov
method, exponentially small splitting of separatrices, non-smooth systems, celestial mechanics and astrodynamics.

The quality of this activity is reflected in the quantity and quality of the publications, some of them in
collaboration with cutting edge international research groups as well as in scientific management, leading
to the organization of several events (conferences and meetings, research programs, themed networks, etc),
the participation in several editorial boards of highly regarded journals and a large number of doctoral students.

The UPC dynamical systems group is composed by 20 full time doctors and 3 predocs.

Its research activity is addressed to the development of analytical and numerical methods
for dynamical systems, holding a scientific leading position in several subjects, namely integrability,
invariant objects, KAM theory, planar vector fields and applications to neuroscience, Poincaré-Melnikov
method, exponentially small splitting of separatrices, non-smooth systems, celestial mechanics and astrodynamics.

The quality of this activity is reflected in the quantity and quality of the publications, some of them in
collaboration with cutting edge international research groups as well as in scientific management, leading
to the organization of several events (conferences and meetings, research programs, themed networks, etc),
the participation in several editorial boards of highly regarded journals and a large number of doctoral students.

Recent Submissions

  • Regularisation in ejection-collision orbits of the RTBP 

    Ollé Torner, Mercè; Rodríguez del Río, Óscar; Soler Villanueva, Jaume (2018)
    Conference report
    Open Access
    Numerical explorations confirm well-known analytical results on the ex-istence of ejection-collision orbits in the restricted three-body problem for veryrestrictive values of the Jacobi constantC. For different values ...
  • 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 ...

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