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Articles 112 registres trobats  1 - 10següentfinal  anar al registre:
1.
Hopf bifurcation in 3-dimensional polynomial vector fields / Sanchez Sanchez, Ivan (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this work we study the local cyclicity of some polynomial vector fields in R3. In particular, we give a quadratic system with 11 limit cycles, a cubic system with 31 limit cycles, a quartic system with 54 limit cycles, and a quintic system with 92 limit cycles. [...]
2022 - 10.1016/j.cnsns.2021.106068
Communications in nonlinear science and numerical simulation, Vol. 105 (February 2022) , art. 106068  
2.
Melnikov functions of arbitrary order for piecewise smooth differential systems in Rn and applications / Chen, Xingwu (Sichuan University. Department of Mathematics) ; Li, Tao (Southwestern University of Finance and Economics. School of Economic Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we develop an arbitrary order Melnikov function to study limit cycles bifurcating from a periodic submanifold for autonomous piecewise smooth differential systems in R with two zones separated by a hyperplane. [...]
2022 - 10.1016/j.jde.2022.01.019
Journal of differential equations, Vol. 314 (March 2022) , p. 340-369  
3.
Bifurcations of the Riccati quadratic polynomial differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Lopes, Bruno D. (Universidade Estadual de Campinas. Instituto de Matemática, Estatística e Computação Científica) ; Da Silva, Paulo R. (Universidade Estadual Paulista. Departamento de Matemática)
In this paper, we characterize the global phase portrait of the Riccati quadratic polynomial differential system ẋ = α2(x), ẏ = ky2 + β1(x)y + γ2(x), with (x,y)∈R2, γ2(x) nonzero (otherwise the system is a Bernoulli differential system), k ≠ 0 (otherwise the system is a Liénard differential system), β1(x) a polynomial of degree at most 1, α2(x) and γ2(x) polynomials of degree at most 2, and the maximum of the degrees of α2(x) and ky2 + β1(x)y + γ2(x) is 2. [...]
2021 - 10.1142/S0218127421500942
International Journal of Bifurcation and Chaos, Vol. 31, Issue 6 (May 2021) , art. 2150094  
4.
Dynamical mechanism behind ghosts unveiled in a map complexification / Canela Sánchez, Jordi (Universitat Jaume I. Institut Universitari de Matemàtiques i Aplicacions de Castelló) ; Alsedà i Soler, Lluís (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Fagella Rabionet, Núria (Universitat de Barcelona. Departament de Matemàtiques i Informàtica) ; Sardanyés, Josep (Centre de Recerca Matemàtica)
Complex systems such as ecosystems, electronic circuits, lasers, or chemical reactions can be modelled by dynamical systems which typically experience bifurcations. It is known that transients become extremely long close to bifurcations, also following well-defined scaling laws as the bifurcation parameter gets closer the bifurcation value. [...]
2022 - 10.1016/j.chaos.2021.111780
Chaos, solitons and fractals, Vol. 156 (March 2022) , art. 111780  
5.
13 p, 856.4 KB Limit cycles of piecewise polynomial differential systems with the discontinuity line xy = 0 / Li, Tao (Southwestern University of Finance and Economics. School of Economic Mathematics (China)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we study the maximum number of limit cycles bifurcating from the periodic orbits of the center x. = −y((x + y)/2), y. = x((x + y)/2) with m ≥ 0 under discontinuous piecewise polynomial (resp. [...]
2021 - 10.3934/cpaa.2021136
Communications on pure & applied analysis, Vol. 20, Issue 11 (November 2021) , p. 3887-3909  
6.
Discrete Melnikov functions / Gasull i Embid, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)
We consider non-autonomous N-periodic discrete dynamical systems of the form (Formula presented. ) having when (Formula presented. ) an open continuum of initial conditions such that the corresponding sequences are N-periodic. [...]
2021 - 10.1080/10236198.2021.1970147
Journal of Difference Equations and Applications, (August 2021)  
7.
22 p, 288.8 KB Persistence of periodic traveling waves and Abelian integrals / Gasull i Embid, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Geyer, Anna (Delft University of Technology. Delft Institute of Applied Mathematics) ; Mañosa Fernández, Víctor 1971- (Universitat Politècnica de Catalunya. Departament de Matemàtiques)
It is well known that the existence of traveling wave solutions (TWS) for many partial differential equations (PDE) is a consequence of the fact that an associated planar ordinary differential equation (ODE) has certain types of solutions defined for all time. [...]
2021 - 10.1016/j.jde.2021.05.033
Journal of differential equations, Vol. 293 (August 2021) , p. 48-69
2 documents
8.
New lower bounds of the number of critical periods in reversible centers / Sanchez Sanchez, Ivan (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
In this paper we aim to find the highest number of critical periods in a class of planar systems of polynomial differential equations for fixed degree having a center. We fix our attention to lower bounds of local criticality for low degree planar polynomial centers. [...]
2021 - 10.1016/j.jde.2021.05.013
Journal of differential equations, Vol. 292 (August 2021) , p. 427-460  
9.
35 p, 542.1 KB Simultaneous Bifurcation of Limit Cycles and Critical Periods / Oliveira, Regilene (Universidade de São Paulo. Departamento de Matemática) ; Sanchez Sanchez, Ivan (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
The present work introduces the problem of simultaneous bifurcation of limit cycles and critical periods for a system of polynomial differential equations in the plane. The simultaneity concept is defined, as well as the idea of bi-weakness in the return map and the period function. [...]
2022 - 10.1007/s12346-021-00546-x
Qualitative Theory of Dynamical Systems, Vol. 21, Issue 1 (March 2022) , art. 20  
10.
22 p, 833.4 KB On the birth and death of algebraic limit cycles in quadratic differential systems / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Oliveira, Regilene (Universidade de São Paulo. Instituto de Ciências Matemáticas e Computação. Departamento de Matemática (Brazil)) ; Zhao, Yulin (Sun Yat-sen University. School of Mathematics (People's Republic of China))
In 1958 started the study of the families of algebraic limit cycles in the class of planar quadratic polynomial differential systems. In the present we known one family of algebraic limit cycles of degree 2 and four families of algebraic limit cycles of degree 4, and that there are no limit cycles of degree 3. [...]
2021 - 10.1017/S0956792520000145
European Journal of Applied Mathematics, Vol. 32, Issue 2 (April 2021) , p. 317-336  

Articles : 112 registres trobats   1 - 10següentfinal  anar al registre:
Documents de recerca 1 registres trobats  
1.
132 p, 1.2 MB Dois métodos para a investigação de ciclos limites que bifurcam de centros / Rezende, Alex Carlucci ; Oliveira, Regilene Delazari dos Santos, dir.
Um dos mais investigados problemas na teoria qualitativa dos sistemas dinâmicos no plano é o XVI problema de Hilbert que trata dos ciclos limites. Mais precisamente, a segunda parte do referido problema questiona sobre o número máximo de ciclos limites de um sistema diferencial polinomial plano de grau n. [...]
One of the most investigated problems in the qualitative theory of dynamical systems in the plane is the XVI Hilbert's problem which deals with limit cycles. More precisely, the second part of the problem asks about the maximum number of limit cycles of a polynomial differential system of degree n. [...]

2011  

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