Existence of heteroclinic orbits of the Shil'nikov type in a 3D quadratic autonomous chaotic system

DOI10.1016/j.jmaa.2005.09.087zbMath1162.34037OpenAlexW2040909363MaRDI QIDQ819029

Guan-Rong Chen, Zuo-huan Zheng

Publication date: 22 March 2006

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2005.09.087

zbMATH Keywords

invariant setheteroclinic orbitbehavior of trajectoryShil'nikov map

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Complex behavior and chaotic systems of ordinary differential equations (34C28) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (19)

Comment on ``Existence of heteroclinic and homoclinic orbits in two different chaotic dynamical systems ⋮ Role of logistic and Ricker's maps in appearance of chaos in autonomous quadratic dynamical systems ⋮ On novel conditions of chaotic attractors existence in autonomous polynomial dynamical systems ⋮ Chen's attractor exists if Lorenz repulsor exists: The Chen system is a special case of the Lorenz system ⋮ Research of chaotic dynamics of 3D autonomous quadratic systems by their reduction to special 2D quadratic systems ⋮ Existence of a new three-dimensional chaotic attractor ⋮ Comment on `Šilnikov-type orbits of Lorenz-family systems' ⋮ SHIL'NIKOV HETEROCLINIC ORBITS IN A CHAOTIC SYSTEM ⋮ Comment on ``Existence of heteroclinic orbits of the Shil'nikov type in a 3D quadratic autonomous chaotic system ⋮ Author's reply to: ``Comment on `Existence of heteroclinic orbits of the Shil'nikov type in a 3D quadratic autonomous chaotic system' ⋮ HOMOCLINIC SHADOWING AND ITS APPLICATION TO CHAOTIC SYSTEMS ⋮ The Lü system is a particular case of the Lorenz system ⋮ Shil'nikov homoclinic orbits in a new chaotic system ⋮ General Method of Construction of Implicit Discrete Maps Generating Chaos in 3D Quadratic Systems of Differential Equations ⋮ The existence of homoclinic orbits in the Lorenz system via the undetermined coefficient method ⋮ A discussion on the coexistence of heteroclinic orbit and saddle foci for third-order systems ⋮ Existence of Chaos in the Chen System with Linear Time-Delay Feedback ⋮ QUADRATIC VECTOR FIELDS EQUIVARIANT UNDER THE D₂ SYMMETRY GROUP ⋮ GENERATING CHAOS IN 3D SYSTEMS OF QUADRATIC DIFFERENTIAL EQUATIONS WITH 1D EXPONENTIAL MAPS

Cites Work

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• Global bifurcations and chaos. Analytical methods
• Ši'lnikov chaos in the generalized Lorenz canonical form of dynamical systems
• CHEN'S ATTRACTOR EXISTS
• CAN A THREE-DIMENSIONAL SMOOTH AUTONOMOUS QUADRATIC CHAOTIC SYSTEM GENERATE A SINGLE FOUR-SCROLL ATTRACTOR?
• A NEW CHAOTIC SYSTEM AND ITS GENERATION
• Shil'nikov's theorem-a tutorial
• A CONTRIBUTION TO THE PROBLEM OF THE STRUCTURE OF AN EXTENDED NEIGHBORHOOD OF A ROUGH EQUILIBRIUM STATE OF SADDLE-FOCUS TYPE

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