DARBOUX POLYNOMIALS AND ALGEBRAIC INTEGRABILITY OF THE CHEN SYSTEM

DOI10.1142/S0218127407018725zbMath1148.34001MaRDI QIDQ3511079

Tinghua Lü, Xiang Zhang

Publication date: 4 July 2008

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

zbMATH Keywords

Chen systempolynomial vector fieldDarboux polynomialalgebraic integrabilitycharacteristics equationweight homogeneous polynomials

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Symmetries, invariants of ordinary differential equations (34C14) Explicit solutions, first integrals of ordinary differential equations (34A05)

Related Items (20)

Darboux integrability of the simple chaotic flow with a line equilibria differential system ⋮ Invariant algebraic surfaces and impasses ⋮ INVARIANT ALGEBRAIC SURFACES OF THE CHEN SYSTEM ⋮ DYNAMICS OF THE LÜ SYSTEM ON THE INVARIANT ALGEBRAIC SURFACE AND AT INFINITY ⋮ Darboux polynomials and global phase portraits for the \(D_{2}\) vector field ⋮ Chen's attractor exists if Lorenz repulsor exists: The Chen system is a special case of the Lorenz system ⋮ THE CHEN SYSTEM HAVING AN INVARIANT ALGEBRAIC SURFACE ⋮ Invariant algebraic surfaces of the generalized Lorenz system ⋮ Darboux polynomials and rational first integrals of the generalized Lorenz systems ⋮ On Darboux polynomials and rational first integrals of the generalized Lorenz system ⋮ Seeking Darboux polynomials ⋮ Darboux polynomials and rational first integrals of the nonstretching Rolie-Poly model ⋮ POLYNOMIAL FIRST INTEGRALS FOR THE CHEN AND LÜ SYSTEMS ⋮ Rational Integrability of the Maxwell–Bloch System ⋮ Invariant algebraic surfaces of the FitzHugh-Nagumo system ⋮ Heteroclinic, Homoclinic and Closed Orbits in the Chen System ⋮ Jacobi Stability Analysis of the Chen System ⋮ GLOBAL DYNAMICS IN THE POINCARÉ BALL OF THE CHEN SYSTEM HAVING INVARIANT ALGEBRAIC SURFACES ⋮ Normal Forms for Polynomial Differential Systems in ℝ³ Having an Invariant Quadric and a Darboux Invariant ⋮ Dynamics of a 3D autonomous quadratic system with an invariant algebraic surface

Cites Work

• Equations de Pfaff algébriques
• Rational integration of the Lotka-Volterra system
• Sur ĽintÉgration algÉbrique des Équations diffÉrentielles du premier ordre et du premier degrÉ
• YET ANOTHER CHAOTIC ATTRACTOR
• Formal and analytic integrability of the Lorenz system
• Invariant algebraic surfaces of the Lorenz system

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