Existence of a singularly degenerate heteroclinic cycle in the Lorenz system and its dynamical consequences. I

DOI10.1007/s10884-004-4290-4zbMath1061.34036OpenAlexW2025846951MaRDI QIDQ1768363

Publication date: 15 March 2005

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10884-004-4290-4

zbMATH Keywords

bifurcation chaotic attractor Lorenz system singularly degenerate heteroclinic cycle

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items

A true three-scroll chaotic attractor coined, Bifurcation analysis and chaos control in Shimizu-Morioka chaotic system with delayed feedback, Double-zero degeneracy and heteroclinic cycles in a perturbation of the Lorenz system, On integrability of the segmented disc dynamo: the effect of mechanical friction, Global dynamical aspects of a generalized Chen-Wang differential system, More Dynamical Properties Revealed from a 3D Lorenz-like System, Bifurcations, ultimate boundedness and singular orbits in a unified hyperchaotic Lorenz-type system, Dynamical analysis of a new autonomous 3-D chaotic system only with stable equilibria, Dynamics at infinity and other global dynamical aspects of Shimizu-Morioka equations, Saddle-type blow-up solutions with computer-assisted proofs: validation and extraction of global nature, Delayed feedback on the 3-D chaotic system only with two stable node-foci, Integrability analysis of the Shimizu-Morioka system, Dynamics of the general Lorenz family, Some new insights into the Liu system, Hidden attractors, singularly degenerate heteroclinic orbits, multistability and physical realization of a new 6D hyperchaotic system, A new finding of the existence of hidden hyperchaotic attractors with no equilibria, HOPF BIFURCATION AND NEW SINGULAR ORBITS COINED IN A LORENZ-LIKE SYSTEM, Study of the Hopf bifurcation in the Lorenz, Chen and Lü systems, COMPLEX DYNAMICS OF A SIMPLE 3D AUTONOMOUS CHAOTIC SYSTEM WITH FOUR-WING, The Hopf bifurcation in the Shimizu-Morioka system, Modeling and analysis of dynamics for a 3D mixed Lorenz system with a damped term, Dynamical analysis of the generalized Sprott C system with only two stable equilibria, AN UNUSUAL 3D AUTONOMOUS QUADRATIC CHAOTIC SYSTEM WITH TWO STABLE NODE-FOCI, Nonlinear analysis in a Lorenz-like system, Geometric treatments and a common mechanism in finite-time singularities for autonomous ODEs, A novel hyperchaotic system with infinitely many heteroclinic orbits coined, Heteroclinic Trajectory and Hopf Bifurcation in an Extended Lorenz System, Nonlinear analysis of a novel three-scroll chaotic system, Comments on ``Dynamics of the general Lorenz family by Y. Liu and W. Pang, On singular orbits and a given conjecture for a 3D Lorenz-like system, On Singular Orbits and Global Exponential Attractive Set of a Lorenz-Type System, The zero-Hopf bifurcations of a four-dimensional hyperchaotic system, Numerical validation of blow-up solutions with quasi-homogeneous compactifications, GLOBAL DYNAMICS IN THE POINCARÉ BALL OF THE CHEN SYSTEM HAVING INVARIANT ALGEBRAIC SURFACES, QUADRATIC VECTOR FIELDS EQUIVARIANT UNDER THE D₂ SYMMETRY GROUP, SINGULAR ORBITS AND DYNAMICS AT INFINITY OF A CONJUGATE LORENZ-LIKE SYSTEM

Cites Work