Dynamical Systems: Qualitative aspects and applications

Dynamical Systems: Qualitative aspects and applications

Organizer: Grupo de Sistemas Dinámicos de la Universidad de Oviedo

Abstract

Results related to population dynamics, neuroscience, fluid mechanics and celestial mechanics are presented. They are examples of the variety of contexts showing a fruitful interaction with the world of dynamical systems. In addition, attention is paid to aspects of Qualitative Theory, from the study of bifurcations to the determinacy of the number of limit cycles exhibited by a differential system, including issues of integrability and global dynamics. This minisymposium offers broad strokes to illustrate the vitality of the research on dynamical systems in our country; 20 years of activities of the DANCE network also give evidence of a great strength.

Keywords: Bifurcation Theory; Applied Dynamical Systems; Global Dynamics


 

Session 1. Monday 11:30 – 13:35. Room A2.

Chair: Fernández-Sánchez, Fernando (Universidad de Sevilla)

Speaker

Organization

Contribution title

Ibáñez, Santiago

Universidad de Oviedo

Self-sustained oscillations and global climate changes

Drubi, Fátima

Universidad de Oviedo

A study of the unfolding of Hopf-Bogdanov-Takens singularities

Rodrigues, Alexandre

Centro de Matemática da Universidade do Porto

Unfolding a Bykov attractor: from an attracting torus to strange attractors

Casas, Pablo S.

Universidad de Oviedo

Homoclinic bifurcations in the unfolding of the nilpotent singularity of codimension 4 in ℝ⁴

 

 

 

 

Session 2. Monday 18:00 – 20:00. Room A2.

Chair: Teruel, Antonio (Universitat de les Illes Balears)

Speaker

Organization

Contribution title

Seara, Tere M.

Universitat Politècnica de Catalunya

Some results about oscillatory orbits

Fernández-Sánchez, Fernando

Universidad de Sevilla

The Falkner-Skan equation revisited

Fernández-García, Soledad

Universidad de Sevilla

Saddle-node bifurcation of canard limit cycles in piecewise linear systems

Carmona, Victoriano

Universidad de Sevilla

Uniqueness of limit cycles in sewing planar piecewise linear systems

 

 

 

 

Session 3. Tuesday 10:30 – 12:10. Room A2.

Chair: Liz, Eduardo (Universidade de Vigo)

Speaker

Organization

Contribution title

Bravo, José Luis

Universidad de Extremadura

Alien limit cycles in Abel equations

Calderón Pérez, Luis Ángel

Universidad de Extremadura

Upper bounds of limit cycles in Abel differential equations with invariant curves

Pérez-González, Set

Universidad de Oviedo

Limit cycles in piecewise linear vector fields having polynomial first integral

     

 

Session 4. Tuesday 12:15 – 13:55. Room A2.

Chair: Bravo, José Luis (Universidad de Extremadura)

Speaker

Organization

Contribution title

Martínez, M. Ángeles

Universidad de Zaragoza

Dynamical systems and cardiac arrhythmia

Pérez, Lucía

Universidad de Oviedo

The Hindmarsh-Rose neuron model: Global homoclinic structure and spike-adding process

Rodero, Ana Livia

Universidade Estadual Paulista

Centers and their cyclicity for linear and quadratic systems defined on  with  as a first integral

 

 

 

 

Session 5. Tuesday 18:00 – 20:00. Room A2.

Chair: Rodríguez, J. Ángel (Universidad de Oviedo)

Speaker

Organization

Contribution title

Peralta-Salas, Daniel

Instituto de Ciencias Matemáticas

Constructing Turing complete Euler flows in dimension 3

Núñez, Carmen

Universidad de Valladolid

R-tipping and saddle-node bifurcation for quadratic nonautonomous ODEs

Liz, Eduardo

Universidade de Vigo

Destabilization and chaos induced by harvesting in discrete-time population models

 

 

 

 

Session 6. Wednesday 10:55 – 12:10. Room A2.

Chair: Ollé, Mercè (Universitat Politècnica de Catalunya)

Speaker

Organization

Contribution title

Palacián, Jesús

Universidad Pública de Navarra

Nonlinear stability of Hamiltonian systems with more than two degrees of freedom: the case of the levitron

Yanguas, Patricia

Universidad Pública de Navarra

The co-orbital motion of two Saturn’s moons

Lanchares, Victor

Universidad de la Rioja

Stability of a one degree of freedom Hamiltonian system in a case of zero quadratic and cubic terms

 

 

Session 7. Thursday 11:30 – 13:35. Room A2.

Chair: Núñez, Carmen (Universidad de Valladolid)

Speaker

Organization

Contribution title

Ollé, Mercè

Universitat Politècnica de Catalunya

Ejection-collision orbits in two degrees of freedom problems

Nicolás, Begoña

Universitat de Barcelona

Invariant manifolds near  and their role in the Sun perturbed Earth-Moon system

Paradela, Jaime

Universitat Politècnica de Catalunya

Oscillatory motions in the Elliptic Isosceles Restricted 3-Body Problem

Giralt, Mar

Universitat Politècnica de Catalunya

Exponentially small splitting of separatrices for  in the restricted 3-body problem

 

 

 

 

Session 8. Thursday 18:00 – 20:00. Room A2.

Chair: Drubi, Fátima  (Universidad de Oviedo)

Speaker

Organization

Contribution title

Rodríguez del Río, Óscar

Universitat Poliècnica de Catalunya

Regularization techniques and ejection-collision orbits in the RTBP

Duarte, Gladston

Universitat de Barcelona

Invariant manifolds near  and  in the planar elliptic restricted three-body problem

Lois-Prados, Cristina

Universidade de Santiago de Compostela

Complex dynamics in discrete- time piecewise-smooth models for populations subject to combinations of constant-quota and threshold harvesting 

 Lombardero, Antón

Universidad de Oviedo 

 Quasi-homogeneous differential systems in R3

 

 

 

 

Session 9. Friday 11:30 – 13:10. Room A2.

Chair: Carmona, Victoriano (Universidad de Sevilla)

Speaker

Organization

Contribution title

Penalva, Jordi

Universitat de les Illes Balears

Bifurcations in a piecewise linear version of the Morris-Lecar neural model

Vigil, Enrique

Universidad de Oviedo

Coexistence of finitely many two-dimensional strange attractors: renormalization scheme and analytic proof

Teruel, Antonio

Universitat de les Illes Balears

Poincaré maps in slow-fast piecewise linear differential systems

 

 

 

 

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