Browsing Articles publicats (Matemàtica) by Title
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Can wild ungulate carcasses provide enough biomass to maintain avian scavenger populations? An empirical assessment using a bioinspired computational model
(Public Library of Science (PLoS), 2011)Background: The reduction in the amount of food available for European avian scavengers as a consequence of restrictive public health policies is a concern for managers and conservationists. Since 2002, the application of ... 
Carrion ecology modelling for vulture conservation : are vulture restaurants needed to sustain the densest breeding population of the African whitebacked vulture?
(Wiley, 2015)As obligate scavengers, vultures are entirely dependent on carrion resources. In this study we model the carrion ecology of an ecosystem in Swaziland which is home to the densest breeding population of the African Whitebacked ... 
Center conditions and limits cycles for bilienard systems
(Texas State University, 2017)In this article we study the center problem for polynomial BiLiénard systems of degree n. Computing the focal values and using Gröbner bases we end the center conditions for such systems for n = 6. We also establish ... 
Center conditions for generalized polynomial Kukles systems
(American Institute of Mathematical Sciences, 2017)In this paper we study the center problem for certain generalized Kukles systems \[ \dot{x}= y, \qquad \dot{y}= P_0(x)+ P_1(x)y+P_2(x) y^2+ P_3(x) y^3, \] where $P_i(x)$ are polynomials of degree $n$, $P_0(0)=0$ and $P_0'(0) ... 
Center conditions for nilpotent cubic systems using Cherkas method
(Elsevier, 2016)In this work we study the center problem of a cubic polynomial differential system with nilpotent linear part. The analysis is based on the application of the Cherkas method to the Takens normal form. The study needs many ... 
Center conditions for polynomial Liénard systems
(Springer International Publishing, 2017)In this paper we study the center problem for polynomial Liénard systems of degree n with damping of degree n. Computing the focal values we find the center conditions for such systems for n=5 and using modular arithmetics ... 
Center cyclicity for some nilpotent singularities including the Z2equivariant class
(World Scientific Publishing, 20211020)This work concerns with polynomial families of real planar vector fields having a monodromic nilpotent singularity. The families considered are those for which the centers are characterized by the existence of a formal ... 
Center cyclicity of a family of quartic polynomial differential system
(Springer, 20160901)In this paper we study the cyclicity of the centers of the quartic polynomial family written in complex notation as z = i z + z z (A z^2 + B z z + C z^2 ), where A,B,C. We give an upper bound for the cyclicity of any ... 
Center cyclicity of Lorenz, Chen and Lü systems
(Elsevier, 20181109)This work provides upper bounds on the cyclicity of the centers on center manifolds in the wellknown Lorenz family, and also in the Chen and Lü families. We prove that at most one limit cycle can be made to bifurcate from ... 
Center problem and νcyclicity of polynomial zeroHopf singularities with nonsingular rotation axis
(Elsevier, 20210602)We consider threedimensional polynomial families of vector fields parameterized by the admissible coefficients having a fixed zeroHopf equilibrium and a nonsingular rotation axis through it. We are interested in the ... 
Center problem for generic degenerate vector fields
(Elsevier, 2022)We generalize the method of construction of an integrating factor for Abel differential equations, developed in Briskin et al. (1998), for any generic monodromic singularity. Here generic means that the vector field has ... 
Center problem for systems with two monomial nonlinearities
(American Institute of Mathematical Sciences, 2016)We study the center problem for planar systems with a linear center at the origin that in complex coordinates have a nonlinearity formed by the sum of two monomials. Our first result lists several centers inside this family. ... 
Center problem for trigonometric Liénard systems
(Elsevier, 2017)We give a complete algebraic characterization of the nondegenerated centers for planar trigonometric Liénard systems. The main tools used in our proof are the classical results of Cherkas on planar analytic Liénard systems ... 
Center problem in the center manifold for quadratic differential systems in R^3
(Elsevier, 2016)Using tools of computer algebra based on the Gröbner basis theory we derive conditions for the existence of a center on a local center manifold for fifteen sevenparameter families of quadratic systems on R 3. To obtain ... 
Center problem with characteristic directions and inverse integrating factors
(Elsevier, 2022)We consider the centerfocus problem for analytic families of planar vector fields having a monodromic singularity with characteristic directions. We give a method to compute the center conditions of the family provided ... 
Centers and isochronous centers for generalized quintic systems
(Elsevier, 2015)In this paper we classify the centers and the isochronous centers of certain polynomial differential systems in R2 of degree d≥5 odd that in complex notation are ż=(λ+i)z(zz̄)d−52(Az5+Bz4z̄+Cz3z̄2+Dz2z̄3+Ezz̄4+Fz̄5), ... 
Centers for a class of generalized quintic polynomial differential systems
(Elsevier, 2014)We classify the centers of the polynomial differential systems in R2 of degree d ≥ 5 odd that in complex notation writes as z˙ = iz + (zz¯)d−5/2 (Az5 + Bz4z¯ + Cz3z¯2 + Dz2z¯3 + Ezz¯4 + Fz¯5), where A, B, C, D, E, F ∈ C ... 
Centers for generalized quintic polynomial differential systems
(Rocky Mountain Mathematics Consortium, 2017)We classify the centers of polynomial differential systems in $R^2$ of odd degree $d \ge 5$, in complex notation, as $\dot{z} = iz + (z \bar z)^(d5)/2(A z^5 + B z^4 \bar z + C z^3 \bar z^2 + D z^2 \bar z^3 + E z \bar z^4 ... 
Centers for the Kukles homogeneous systems with even degree
(Shanghai Normal University & Wilmington Scientific Publisher, 2017)For the polynomial differential system x˙=−y, y˙=x+Qn(x,y), where Qn(x,y) is a homogeneous polynomial of degree n there are the following two conjectures done in 1999. (1) Is it true that the previous system for n≥2 has a ... 
Centers for the Kukles homogeneous systems with odd degree
(London Mathematical Society, 2015)For the polynomial differential system x˙ = −y, y˙ = x+Qn(x; y), where Qn(x; y) is a homogeneous polynomial of degree n there are the following two conjectures done in 1999. (1) Is it true that the previous system for ...