[图书][B] Robust chaos and its applications
E Zeraoulia - 2012 - books.google.com
Robust chaos is defined by the absence of periodic windows and coexisting attractors in
some neighborhoods in the parameter space of a dynamical system. This unique book …
some neighborhoods in the parameter space of a dynamical system. This unique book …
Chaotic dynamics of three-dimensional H\'enon maps that originate from a homoclinic bifurcation
We study bifurcations of a three-dimensional diffeomorphism, $ g_0 $, that has a quadratic
homoclinic tangency to a saddle-focus fixed point with multipliers $(\lambda …
homoclinic tangency to a saddle-focus fixed point with multipliers $(\lambda …
[HTML][HTML] The three-dimensional generalized Hénon map: Bifurcations and attractors
AE Hampton, JD Meiss - Chaos: An Interdisciplinary Journal of …, 2022 - pubs.aip.org
We study dynamics of a generic quadratic diffeomorphism, a 3D generalization of the planar
Hénon map. Focusing on the dissipative, orientation preserving case, we give a …
Hénon map. Focusing on the dissipative, orientation preserving case, we give a …
Classification of three-dimensional quadratic diffeomorphisms with constant Jacobian
Z Elhadj, JC Sprott - Frontiers of Physics in China, 2009 - Springer
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Phys. China, 2009, 4(1): 111–121 DOI 10.1007/s11467-009-0005-y REVIEW ARTICLE …
Phys. China, 2009, 4(1): 111–121 DOI 10.1007/s11467-009-0005-y REVIEW ARTICLE …
High-order parameterization of stable/unstable manifolds for long periodic orbits of maps
JL Gonzalez, JD Mireles James - SIAM Journal on Applied Dynamical Systems, 2017 - SIAM
This paper develops seminumerical methods for computing high-order polynomial
approximations of stable/unstable manifolds attached to long periodic orbits in discrete time …
approximations of stable/unstable manifolds attached to long periodic orbits in discrete time …
[图书][B] 2-D quadratic maps and 3-D ODE systems: A Rigorous Approach
E Zeraoulia, JC Sprott - 2010 - books.google.com
This book is based on research on the rigorous proof of chaos and bifurcations in 2-D
quadratic maps, especially the invertible case such as the H non map, and in 3-D ODE's …
quadratic maps, especially the invertible case such as the H non map, and in 3-D ODE's …
Anti-integrability for three-dimensional quadratic maps
AE Hampton, JD Meiss - SIAM Journal on Applied Dynamical Systems, 2022 - SIAM
We study the dynamics of the three-dimensional quadratic diffeomorphism using a concept
first introduced 30 years ago for the Frenkel--Kontorova model of condensed matter physics …
first introduced 30 years ago for the Frenkel--Kontorova model of condensed matter physics …
Resonant tori, transport barriers, and chaos in a vector field with a Neimark–Sacker bifurcation
E Fleurantin, JDM James - … in Nonlinear Science and Numerical Simulation, 2020 - Elsevier
We make a detailed numerical study of a three dimensional dissipative vector field derived
from the normal form for a cusp-Hopf bifurcation. The vector field exhibits a Neimark–Sacker …
from the normal form for a cusp-Hopf bifurcation. The vector field exhibits a Neimark–Sacker …
Connecting Anti-integrability to Attractors for Three-Dimensional Quadratic Diffeomorphisms
AE Hampton, JD Meiss - SIAM Journal on Applied Dynamical Systems, 2024 - SIAM
We previously showed that three-dimensional quadratic diffeomorphisms have anti-
integrable (AI) limits that correspond to a quadratic correspondence, a pair of one …
integrable (AI) limits that correspond to a quadratic correspondence, a pair of one …
Heteroclinic primary intersections and codimension one Melnikov method for volume-preserving maps
We study families of volume preserving diffeomorphisms in R 3 that have a pair of hyperbolic
fixed points with intersecting codimension one stable and unstable manifolds. Our goal is to …
fixed points with intersecting codimension one stable and unstable manifolds. Our goal is to …