AN EXTENDED ŠIL'NIKOV HOMOCLINIC THEOREM AND ITS APPLICATIONS
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Publication:3394431
DOI10.1142/S0218127409023779zbMath1168.34329MaRDI QIDQ3394431
Baoying Chen, Tianshou Zhou, Guan-Rong Chen
Publication date: 31 August 2009
Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)
Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Complex behavior and chaotic systems of ordinary differential equations (34C28) Almost and pseudo-almost periodic solutions to ordinary differential equations (34C27)
Related Items (13)
The related extension and application of the Ši'lnikov theorem ⋮ Elementary quadratic chaotic flows with a single non-hyperbolic equilibrium ⋮ A novel search method of chaotic autonomous quadratic dynamical systems without equilibrium points ⋮ New types of 3-D systems of quadratic differential equations with chaotic dynamics based on Ricker discrete population model ⋮ Implicit one-dimensional discrete maps and their connection with existence problem of chaotic dynamics in 3-D systems of differential equations ⋮ Study on the Geometrical Properties and Existence of Orbit Homoclinic to a Saddle Point in n-Dimensional Autonomous Vector Field with Polynomials ⋮ Reduction Method for Search of Chaotic Attractors in Generic Autonomous Quadratic Dynamical Systems ⋮ General Method of Construction of Implicit Discrete Maps Generating Chaos in 3D Quadratic Systems of Differential Equations ⋮ Chaotic dynamics in quadratic systems with singular linear part ⋮ ŠIL'NIKOV HOMOCLINIC ORBITS IN TWO CLASSES OF 3D AUTONOMOUS NONLINEAR SYSTEMS ⋮ Some new insights into a known Chen-like system ⋮ GENERATING CHAOS IN 3D SYSTEMS OF QUADRATIC DIFFERENTIAL EQUATIONS WITH 1D EXPONENTIAL MAPS ⋮ Chaotic systems with any number and various types of equilibria
Cites Work
- Preturbulence: A regime observed in a fluid flow model of Lorenz
- Snap-back repellers imply chaos in \(\mathbb{R}^n\)
- Analytic approximation of the homoclinic orbits of the Lorenz system at \(\sigma=10\), \(b=8/3\) and \(\rho=13. 926\dots\)
- The complicated trajectory behaviors in the Lorenz equation
- Constructing a new chaotic system based on the Šilnikov criterion
- Ši'lnikov chaos in the generalized Lorenz canonical form of dynamical systems
- Complex Dynamical Behaviors of the Chaotic Chen's System
- CLASSIFICATION OF CHAOS IN 3-D AUTONOMOUS QUADRATIC SYSTEMS-I: BASIC FRAMEWORK AND METHODS
- A SIMPLE SMOOTH CHAOTIC SYSTEM WITH A 3-LAYER ATTRACTOR
- CHEN'S ATTRACTOR EXISTS
- Introduction to Applied Nonlinear Dynamical Systems and Chaos
- 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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