UAB Digital Repository of Documents 9 records found  Search took 0.02 seconds. 
1.
Phase portraits of planar piecewise linear refracting systems : Focus-saddle case / Li, Shimin (Guangdong University of Finance and Economics. School of Mathematics and Statistics (China)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
This paper deals with planar piecewise linear refracting systems with a straight line of separation. Using the Poincaré compactification, we provide the classification of the phase portraits in the Poincaré disc of piecewise linear refracting systems with focus-saddle dynamics.
2020 - 10.1016/j.nonrwa.2020.103153
Nonlinear Analysis: Real World Applications, Vol. 56 (December 2020) , art. 103153  
2.
21 p, 1.9 MB Quantitative analysis of competition models / Chiralt, Cristina (Universitat Jaume I. Departament de Matemàtiques) ; Ferragut, Antoni (Universitat Jaume I. Departament de Matemàtiques) ; Gasull i Embid, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Vindel, Pura (Universitat Jaume I. Departament de Matemàtiques)
We study a 2-species Lotka-Volterra type differential system, modeling competition between two species and having a coexistence equilibrium in the first quadrant. In case that this equilibrium is of saddle type, its stable manifold divides the first quadrant into two zones. [...]
2017 - 10.1016/j.nonrwa.2017.06.001
Nonlinear Analysis: Real World Applications, Vol. 38 (2017) , p. 327-347  
3.
11 p, 698.6 KB Zero-Hopf bifurcation in a Chua system / D. Euzébio, Rodrigo (Universidade Estadual Paulista (Brasil). Departamento de Matemática) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
A zero-Hopf equilibrium is an isolated equilibrium point whose eigenvalues are ±ωi ̸= 0 and 0. In general for a such equilibrium there is no theory for knowing when it bifurcates some small-amplitude limit cycles moving the parameters of the system. [...]
2017 - 10.1016/j.nonrwa.2017.02.002
Nonlinear Analysis: Real World Applications, Vol. 37 (2017) , p. 31-40  
4.
24 p, 563.0 KB Singular solutions for a class of traveling wave equations arising in hydrodynamics / Geyer, Anna (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mañosa, Víctor (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III)
We give an exhaustive characterization of singular weak solutions for ordinary differential equations of the form 12^2 F'(u) =0, where F is an analytic function. Our motivation stems from the fact that in the context of hydrodynamics several prominent equations are reducible to an equation of this form upon passing to a moving frame. [...]
2016 - 10.1016/j.nonrwa.2016.01.009
Nonlinear Analysis: Real World Applications, Vol. 31 (2016) , p. 57-76  
5.
12 p, 1.9 MB Non-uniform continuity of the flow map for an evolution equation modeling shallow water waves of moderate amplitude / Duruk-Mutlubaş, Nilay (Istanbul Kemerburgaz University. Department of Basic Sciences) ; Geyer, Anna (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Matioc, Bogdan-Vasile (Leibniz Universität Hannover(Germany). Institut für Angewandte Mathematik)
We prove that the flow map associated to a model equation for surface waves of moderate amplitude in shallow water is not uniformly continuous in the Sobolev space Hs with s > 3/2. The main idea is to consider two suitable sequences of smooth initial data whose difference converges to zero in Hs, but such that neither of them is convergent. [...]
2014 - 10.1016/j.nonrwa.2013.12.007
Nonlinear Analysis: Real World Applications, Vol. 17 (2014) , p. 322-331  
6.
33 p, 580.2 KB Stability and periodic oscillations in the Moon-Rand systems / Mahdi, Adam (North Carolina State University. Mathematics Department) ; Romanovskii, Valery G. (University of Maribor. Center for Applied Mathematics and Theoretical Physics) ; Shafer, Douglas S. (University of North Carolina at Charlotte. Mathematics Department)
2013 - 10.1016/j.nonrwa.2012.06.005
Nonlinear Analysis: Real World Applications, Vol. 14 (2013) , p. 294-313  
7.
23 p, 558.3 KB Integrability and global dynamics of the May-Leonard model / Blé, Gamaliel (UJAT(México). División Académica de Ciencias Básicas) ; Castellanos, Víctor (UJAT(México). División Académica de Ciencias Básicas) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Quilantán, Ingrid (UJAT(México). División Académica de Ciencias Básicas)
We study when the celebrated May-Leonard model in R3, describing the competition between three species and depending on two positive parameters a and b, is completely integrable; i. e. when a+b = 2 or a = b. [...]
2013 - 10.1016/j.nonrwa.2012.06.004
Nonlinear Analysis: Real World Applications, Vol. 14 (2013) , p. 280-293  
8.
17 p, 370.8 KB On the existence and uniqueness of limit cycles in planar continuous piecewise linear systems without symmetry / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Ordóñez, Manuel (Universidad de Sevilla. E.T.S. Ingeniería) ; Ponce, Enrique (Universidad de Sevilla. E.T.S. Ingeniería)
Some techniques to show the existence and uniqueness of limit cycles, typically stated for smooth vector fields, are extended to continuous piecewise-linear differential systems. New results are obtained for systems with three linearity zones without symmetry and having one equilibrium point in the central region. [...]
2013 - 10.1016/j.nonrwa.2013.02.004
Nonlinear Analysis: Real World Applications, Vol. 14 Núm. 5 (2013) , p. 2002-2012  
9.
6 p, 562.3 KB On the Hopf-zero bifurcation of the Michelson system / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Zhang, Xiang (Shanghai Jiaotong University. Department of Mathematics)
Applying a new result for studying the periodic orbits of a differential system via the averaging theory, we provide the first analytic proof on the existence of a Hopf-zero bifurcation for the Michelson system x2 x˙ = y, y˙ = z, z˙ = c2 − y − , 2 at c = 0. [...]
2011 - 10.1016/j.nonrwa.2010.10.019
Nonlinear Analysis: Real World Applications, Vol. 12 (2011) , p. 1650-1653  

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