In this paper, it is proved that a monomial derivation d of k[x, y, z] has no Darboux polynomials if and only if d is a strict derivation with a trivial ring of constants, and we give the specific conditions when it h...In this paper, it is proved that a monomial derivation d of k[x, y, z] has no Darboux polynomials if and only if d is a strict derivation with a trivial ring of constants, and we give the specific conditions when it has no Darboux polynomials.展开更多
In this paper, we characterize all of the Darboux polynomials of the L system and prove that the system is not algebraically integrable, using the weight homogeneous polynomials and the method of characteristic curves...In this paper, we characterize all of the Darboux polynomials of the L system and prove that the system is not algebraically integrable, using the weight homogeneous polynomials and the method of characteristic curves for solving linear partial differential equations.展开更多
We study the Hindmarsh-Rose burster which can be described by the differential system x^·=y-x^3＋bx^2＋I-z,y^·=1-5x^2-y,z^·=μ（s（x-x0）-z）where b, I, μ, s, x0 are parameters. We characterize all its...We study the Hindmarsh-Rose burster which can be described by the differential system x^·=y-x^3＋bx^2＋I-z,y^·=1-5x^2-y,z^·=μ（s（x-x0）-z）where b, I, μ, s, x0 are parameters. We characterize all its invariant algebraic surfaces and all its exponential factors for all values of the parameters. We also characterize its Darboux integrability in function of the parameters. These characterizations allow to study the global dynamics of the system when such invariant algebraic surfaces exist.展开更多
In this paper, we study the invariant algebraic surfaces of a system, which generalizes the Lorenz system. Using the weight homogeneous polynomials and the method of characteristic curves for solving linear partial di...In this paper, we study the invariant algebraic surfaces of a system, which generalizes the Lorenz system. Using the weight homogeneous polynomials and the method of characteristic curves for solving linear partial differential equations, we characterize all the Darboux invariants, the irreducible Darboux polynomials, the rational first integrals and the algebraic integrability of this system.展开更多
基金The NSF(11526104)of Chinathe Youth Research Funds(LDGY2015001)from Liaoning University
文摘In this paper, it is proved that a monomial derivation d of k[x, y, z] has no Darboux polynomials if and only if d is a strict derivation with a trivial ring of constants, and we give the specific conditions when it has no Darboux polynomials.
基金supported by the NNSF of China grant No.10231020
文摘In this paper, we characterize all of the Darboux polynomials of the L system and prove that the system is not algebraically integrable, using the weight homogeneous polynomials and the method of characteristic curves for solving linear partial differential equations.
基金partially supported by a MINECO-FEDER(Grant No.MTM2016-77278-P)a MINECO(Grant No.MTM2013-40998-P)+1 种基金an AGAUR(Grant No.2014SGR-568)partially supported by FCT/Portugal through UID/MAT/04459/2013
文摘We study the Hindmarsh-Rose burster which can be described by the differential system x^·=y-x^3＋bx^2＋I-z,y^·=1-5x^2-y,z^·=μ（s（x-x0）-z）where b, I, μ, s, x0 are parameters. We characterize all its invariant algebraic surfaces and all its exponential factors for all values of the parameters. We also characterize its Darboux integrability in function of the parameters. These characterizations allow to study the global dynamics of the system when such invariant algebraic surfaces exist.
基金supported by the NNSF of China (11171191 and 11201266)
文摘In this paper, we study the invariant algebraic surfaces of a system, which generalizes the Lorenz system. Using the weight homogeneous polynomials and the method of characteristic curves for solving linear partial differential equations, we characterize all the Darboux invariants, the irreducible Darboux polynomials, the rational first integrals and the algebraic integrability of this system.
