Dynamics of the Lorenz system having an invariant algebraic surface

DOI10.1063/1.2767007zbMath1152.81361OpenAlexW1983674368MaRDI QIDQ3544398

Jinlong Cao, Xiang Zhang

Publication date: 8 December 2008

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.2767007

zbMATH Keywords

singularitieslimit cyclesphase portraits

Mathematics Subject Classification ID

Symmetries, invariants of ordinary differential equations (34C14) Dynamics induced by flows and semiflows (37C10) Surfaces in Euclidean and related spaces (53A05)

Related Items (16)

Invariant algebraic surfaces and impasses ⋮ DYNAMICS OF THE LÜ SYSTEM ON THE INVARIANT ALGEBRAIC SURFACE AND AT INFINITY ⋮ Global dynamical aspects of a generalized Chen-Wang differential system ⋮ Chen's attractor exists if Lorenz repulsor exists: The Chen system is a special case of the Lorenz system ⋮ Global dynamics of the generalized Lorenz systems having invariant algebraic surfaces ⋮ Integrability of 3-dim polynomial systems with three invariant planes ⋮ Comments on ``Global dynamics of the generalized Lorenz systems having invariant algebraic surfaces ⋮ The Lü system is a particular case of the Lorenz system ⋮ Global dynamical behavior of Fitzhugh-Nagumo systems with invariant algebraic surfaces ⋮ Study of the Hopf bifurcation in the Lorenz, Chen and Lü systems ⋮ Darboux polynomials and rational first integrals of the nonstretching Rolie-Poly model ⋮ Invariant algebraic surfaces of the FitzHugh-Nagumo system ⋮ The zero-Hopf bifurcations of a four-dimensional hyperchaotic system ⋮ New Chaotic Regimes in the Lorenz and Chen Systems ⋮ Dynamical analysis of a two prey-one predator system with quadratic self interaction ⋮ Dynamics of a 3D autonomous quadratic system with an invariant algebraic surface

Cites Work

• The Lorenz equations: bifurcations, chaos, and strange attractors
• Integrals of motion and the shape of the attractor for the Lorenz model
• Boundedness, invariant algebraic surfaces and global dynamics for a spectral model of large-scale atmospheric circulation
• Integrals of motion for the Lorenz system
• Formal and analytic integrability of the Lorenz system
• Invariant algebraic surfaces of the Lorenz system
• Integrability, partial integrability, and nonintegrability for systems of ordinary differential equations

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