Results 31 to 40 of about 2,258 (187)
Symbolic Encoding of Periodic Orbits and Chaos in the Rucklidge System
Complexity, Volume 2021, Issue 1, 2021., 2021 To describe and analyze the unstable periodic orbits of the Rucklidge system, a so‐called symbolic encoding method is introduced, which has been proven to be an efficient tool to explore the topological properties concealed in these periodic orbits. In this work, the unstable periodic orbits up to a certain topological length in the Rucklidge system ...
Chengwei Dong +4 more
wiley +1 more source
Oscillatory long-wave Marangoni convection in a layer of a binary liquid: Hexagonal patterns [PDF]
, 2011 We consider a long-wave oscillatory Marangoni convection in a layer of a binary liquid in the presence of the Soret effect. A weakly nonlinear analysis is carried out on a hexagonal lattice.
Nepomnyashchy, A. A. +2 more
core +1 more source
FPGA Realization of Spherical Chaotic System with Application in Image Transmission
Mathematical Problems in Engineering, Volume 2021, Issue 1, 2021., 2021 This paper considers a three‐dimensional nonlinear dynamical system capable of generating spherical attractors. The main activity is the realization of a spherical chaotic attractor on Intel and Xilinx FPGA boards, with a focus on implementation of a secure communication system.
Jose Cruz Nuñez-Perez +5 more
wiley +1 more source
Homoclinic crossing in open systems: Chaos in periodically perturbed monopole plus quadrupolelike potentials [PDF]
, 2002 The Melnikov method is applied to periodically perturbed open systems modeled by an inverse--square--law attraction center plus a quadrupolelike term. A compactification approach that regularizes periodic orbits at infinity is introduced.
A. E. Motter +30 more
core +2 more sources
Transport in Transitory Dynamical Systems [PDF]
, 2010 We introduce the concept of a "transitory" dynamical system---one whose time-dependence is confined to a compact interval---and show how to quantify transport between two-dimensional Lagrangian coherent structures for the Hamiltonian case.
B. A. Mosovsky, J. D. Meiss, Kaper T. J.
core +1 more source
Global bifurcations close to symmetry [PDF]
, 2016 Heteroclinic cycles involving two saddle-foci, where the saddle-foci share both invariant manifolds, occur persistently in some symmetric differential equations on the 3-dimensional sphere.
Labouriau, Isabel S. +1 more
core +2 more sources
Journal of Engineering, 2015 Based on the heteroclinic Shil’nikov theorem and switching control, a kind of multipiecewise linear chaotic system is constructed in this paper. Firstly, two fundamental linear systems are constructed via linearization of a chaotic system at its two ...
Chunyan Han, Fang Yuan, Xiaoyuan Wang
doaj +1 more source
Large amplitude oscillations for a class of symmetric polynomial differential systems in R³
Anais da Academia Brasileira de Ciências, 2007 In this paper we study a class of symmetric polynomial differential systems in R³, which has a set of parallel invariant straight lines, forming degenerate heteroclinic cycles, which have their two singular endpoints at infinity.
Jaume Llibre, Marcelo Messias
doaj +1 more source
Spiralling dynamics near heteroclinic networks [PDF]
, 2013 There are few explicit examples in the literature of vector fields exhibiting complex dynamics that may be proved analytically. We construct explicitly a {two parameter family of vector fields} on the three-dimensional sphere $\EU^3$, whose flow has a ...
Address Of Alex +7 more
core +1 more source
Interaction of two systems with saddle-node bifurcations on invariant circles. I. Foundations and the mutualistic case [PDF]
, 2013 The saddle-node bifurcation on an invariant circle (SNIC) is one of the codimension-one routes to creation or destruction of a periodic orbit in a continuous-time dynamical system.
Baesens, Claude, MacKay, Robert S.
core +2 more sources