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Uniqueness of the limit cycles for complex differential equations with two monomials

Autor: M.J. Álvarez, A. Gasull, R. Prohens

We prove that any complex differential equation with two monomials of the form z˙ = azk ¯zl + bzm¯zn, with k, l, m, n non-negative integers and a, b ∈ C, has one limit cycle at most. Moreover, we characterise when such a limit exists and prove t

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6e82e158ccb4bf97e66f53f033c28307
https://ddd.uab.cat/record/267124

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Asymptotic lower bounds on Hilbert numbers using canard cycles

Autor: P. De Maesschalck, M.J. Álvarez, R. Prohens, B. Coll

Publikováno v: Journal of Differential Equations. 268:3370-3391

In this work we give an asymptotic lower bound for the Hilbert number for real planar polynomial differential systems. This lower bound equals, up to leading order, to the best existing one, but the method we provide is new and involves slow-fast sys

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::203009b9e3d00f3facdb1557b5da9a81
https://doi.org/10.1016/j.jde.2019.09.057

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Probability of occurrence of some planar random quasi-homogeneous vector fields

Autor: B. Coll, A. Gasull, R. Prohens

The objective of this work is the study of the probability of occurrence of phase portraits in a family of planar quasi-homogeneous vector fields of quasi degree q, that is a natural extension of planar linear vector fields, which correspond to $$q=1

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::98481d6496ff32b98b7bf1c80657c646
https://ddd.uab.cat/record/274787

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Characterization of the Existence of Non-trivial Limit Cycles for Generalized Abel Equations

Autor: Manuel Montanero Fernández, José Bravo, R. Prohens, M.J. Álvarez

Publikováno v: Qualitative Theory of Dynamical Systems. 20

In this paper, we consider the family of generalized Abel equations of the form $$\begin{aligned} x'=A(t)x^m + B(t) x^n, \end{aligned}$$ where A, B are trigonometric polynomials and $$m,n\in \mathbb {N}$$ . We characterize the existence of non-trivia

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::e8c5f1b35a6911f27f18e68d379975ca
https://doi.org/10.1007/s12346-021-00450-4

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Limit Cycles for two families of cubic systems

Autor: Armengol Gasull, M.J. Álvarez, R. Prohens

Publikováno v: Recercat. Dipósit de la Recerca de Catalunya
instname
Dipòsit Digital de Documents de la UAB
Universitat Autònoma de Barcelona
Recercat: Dipósit de la Recerca de Catalunya
Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)

In this paper we study the number of limit cycles of two families of cubic systems introduced in previous papers to model real phenomena. The first one is motivated by a model of star formation histories in giant spiral galaxies and the second one co

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::258e3faf3bafaf398d51b56c4222130f
http://hdl.handle.net/2072/410453

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Corrigendum to 'Shape and period of limit cycles bifurcating from a class of Hamiltonian period annulus' (Nonlinear Anal. 81 (2013) 130--148)

Autor: Joan Torregrosa, R. Prohens

Publikováno v: Recercat. Dipósit de la Recerca de Catalunya
instname
Recercat: Dipósit de la Recerca de Catalunya
Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Dipòsit Digital de Documents de la UAB
Universitat Autònoma de Barcelona

In our paper (Prohens and Torregrosa, 2013 [1] ) we are concerned with the problem of shape and period of isolated periodic solutions of perturbed analytic radial Hamiltonian vector fields in the plane. Actually, there is a mistake in the formula of

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f1c226450a161b2a7ddb9d64709142ce
http://hdl.handle.net/2072/410517

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Canard Trajectories in 3D piecewise linear systems

Autor: Antonio E. Teruel, R. Prohens

Publikováno v: Recercat: Dipósit de la Recerca de Catalunya
Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Recercat. Dipósit de la Recerca de Catalunya
instname
Dipòsit Digital de Documents de la UAB
Universitat Autònoma de Barcelona

We present some results on singularly perturbed piecewise linear systems, similar to those obtained by the Geometric Singular Perturbation Theory. Unlike the differentiable case, in the piecewise linear case we obtain the global expression of the slo

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fb4134c64e560d62b689728100f5c6cd
http://hdl.handle.net/2072/410547

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Limit cycles bifurcating from a perturbed quartic center

Autor: R. Prohens, Jaume Llibre, B. Coll

We consider the quartic center x ˙ = - yf ( x , y ) , y ˙ = xf ( x , y ) , with f(x, y) = (x + a) (y + b) (x + c) and abc ≠ 0. Here we study the maximum number σ of limit cycles which can bifurcate from the periodic orbits of this quartic center

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2d3a6d09353e9de71ce4137625ad403e
http://hdl.handle.net/2072/410383

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Estimation of Synaptic Activity during Neuronal Oscillations

Autor: R. Prohens, Antonio E. Teruel, Catalina Vich, Antoni Guillamon

Publikováno v: Mathematics
Volume 8
Issue 12
UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)
Mathematics, Vol 8, Iss 2153, p 2153 (2020)

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 membrane potential (or volt

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c2c15a85569311f3fc9ba9104befd201

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