Global dynamics of the generalized Lorenz systems having invariant algebraic surfaces

DOI10.1016/j.physd.2012.10.011zbMath1338.37038OpenAlexW1964879541MaRDI QIDQ1948078

Xiang Zhang, Kesheng Wu

Publication date: 30 April 2013

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physd.2012.10.011

zbMATH Keywords

limit cycleglobal dynamicsinvariant algebraic surfacegeneralized Lorenz systemblow-up and Poincaré compactification

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Invariant manifold theory for dynamical systems (37D10) Complex behavior and chaotic systems of ordinary differential equations (34C28) Invariant manifolds for ordinary differential equations (34C45)

Related Items

Integrability analysis of Muthuswamy-Chua-Ginoux system, Integrability and linearizability of symmetric three-dimensional quadratic systems, Superluminal periodic orbits in the Lorenz system, 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, Center cyclicity of Lorenz, Chen and Lü systems, Invariant algebraic surfaces of the FitzHugh-Nagumo system, Comments on ``Dynamics of the general Lorenz family by Y. Liu and W. Pang, The zero-Hopf bifurcations of a four-dimensional hyperchaotic system, Integrability and bifurcation of a three-dimensional circuit differential system, Dynamics of a 3D autonomous quadratic system with an invariant algebraic surface

Cites Work

• Unnamed Item
• Darboux polynomials and rational first integrals of the generalized Lorenz systems
• Global dynamics of the Rikitake system
• The Lorenz equations: bifurcations, chaos, and strange attractors
• Integrals of motion and the shape of the attractor for the Lorenz model
• Qualitative theory of planar differential systems
• Ši'lnikov chaos in the generalized Lorenz canonical form of dynamical systems
• GLOBAL DYNAMICS OF THE LORENZ SYSTEM WITH INVARIANT ALGEBRAIC SURFACES
• Global dynamics of the Rössler system with conserved quantities
• Bounded Polynomial Vector Fields
• A UNIFIED LORENZ-TYPE SYSTEM AND ITS CANONICAL FORM
• On the global dynamics of the Rabinovich system
• Dynamics of the Lorenz system having an invariant algebraic surface
• Dynamics at infinity and the existence of singularly degenerate heteroclinic cycles in the Lorenz system
• Integrals of motion for three-dimensional non-Hamiltonian dynamical systems
• YET ANOTHER CHAOTIC ATTRACTOR
• Deterministic Nonperiodic Flow
• BRIDGE THE GAP BETWEEN THE LORENZ SYSTEM AND THE CHEN SYSTEM
• A NEW CHAOTIC ATTRACTOR COINED
• Invariant algebraic surfaces of the Lorenz system
• Integrability, partial integrability, and nonintegrability for systems of ordinary differential equations
• THE CHEN SYSTEM HAVING AN INVARIANT ALGEBRAIC SURFACE
• The topological structure of the Rabinovich system having an invariant algebraic surface