J. Tomás Lázaro
Polytechnic University of Catalonia
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Featured researches published by J. Tomás Lázaro.
Qualitative Theory of Dynamical Systems | 2002
Amadeu Delshams; Antoni Guillamon; J. Tomás Lázaro
The pseudo-normal form is presented as an alternative to the Birkhoff normal form for a planar vector field with the origin as an equilibrium point. Its convergence is proved for non-zero critical exponents λ,−λ, and some consequences for the center-focus, problem are presented.
Archive | 1999
Amadeu Delshams; J. Tomás Lázaro
It is difficult, in the theory of dynamical systems, to draw a boundary line between conservation laws and symmetries because often their effects on the dynamics can be almost the same. An important example can be the case of motions in Hamiltonian and reversible systems. For instance, it is well-known that the Kolmogorov-Arnol’d-Moser theory applies in both type of systems (see [1, 2, 12, 11]). In the theory of Hamiltonian systems we also have the Nekhoroshev theorem [7], that leads to the concept of effective stability.
Journal of Theoretical Biology | 2019
Joan Fornés; J. Tomás Lázaro; Tomás Alarcón; Santiago F. Elena; Josep Sardanyés
Positive-sense, single-stranded RNA viruses are important pathogens infecting almost all types of organisms. Experimental evidence from distributions of mutations and from viral RNA amplification suggest that these pathogens may follow different RNA replication modes, ranging from the stamping machine replication (SMR) to the geometric replication (GR) mode. Although previous theoretical work has focused on the evolutionary dynamics of RNA viruses amplifying their genomes with different strategies, little is known in terms of the bifurcations and transitions involving the so-called error threshold (mutation-induced dominance of mutants) and lethal mutagenesis (extinction of all sequences due to mutation accumulation and demographic stochasticity). Here we analyze a dynamical system describing the intracellular amplification of viral RNA genomes evolving on a single-peak fitness landscape focusing on three cases considering neutral, deleterious, and lethal mutants. We analytically derive the critical mutation rates causing lethal mutagenesis and error threshold, governed by transcritical bifurcations that depend on parameters α (parameter introducing the mode of replication), replicative fitness of mutants (k1), and on the spontaneous degradation rates of the sequences (ϵ). Our results relate the error catastrophe with lethal mutagenesis in a model with continuous populations of viral genomes. The former case involves dominance of the mutant sequences, while the latter, a deterministic extinction of the viral RNAs during replication due to increased mutation. For the lethal case the critical mutation rate involving lethal mutagenesis is μc=1-ɛ/α. Here, the SMR involves lower critical mutation rates, being the system more robust to lethal mutagenesis replicating closer to the GR mode. This result is also found for the neutral and deleterious cases, but for these later cases lethal mutagenesis can shift to the error threshold once the replication mode surpasses a threshold given by α=ϵ/k1.
Proceedings of the International Conference | 2001
Amadeu Delshams; J. Tomás Lázaro
Since they were introduced by Poincare in his thesis, Normal Forms have become a common and useful tool in the local qualitative study of dynamical systems. Consequently, the literature about this subject is very rich, not only because of the people working on it (Poincare, Dulac, Birkhoff, Stenberg, Chen, Arnold, Moser, Tokarev, Bibikov, Belitskǐi, Bruno, Walcher, Cicogna, Gaeta, Bambusi and many others) but the also the amount of publications (see, for instance 1,2,6,3,7 and references therein). Let us consider a real planar analytic system
Nonlinear Analysis-theory Methods & Applications | 2012
Armengol Gasull; J. Tomás Lázaro; Joan Torregrosa
Discrete and Continuous Dynamical Systems | 2014
Primitivo B. Acosta-Humánez; J. Tomás Lázaro; Juan J. Morales-Ruiz; Chara Pantazi
Journal of Mathematical Analysis and Applications | 2012
Armengol Gasull; J. Tomás Lázaro; Joan Torregrosa
Journal of Differential Equations | 2005
Amadeu Delshams; J. Tomás Lázaro
Computational & Applied Mathematics | 2017
Vanessa Castillo; J. Tomás Lázaro; Josep Sardanyés
arXiv: Dynamical Systems | 2018
Amadeu Delshams; Marina Gonchenko; S. V. Gonchenko; J. Tomás Lázaro