Trying to Characterize Robust and Generic Dynamics

2009 ◽  
pp. 549-563 ◽  
Author(s):  
Enrique R. Pujals
Keyword(s):  
Generic Dynamics

SURVEY Towards a global view of dynamical systems, for the C1-topology

2011 ◽  
Vol 31 (4) ◽  
pp. 959-993 ◽  
Author(s):  
C. BONATTI
Keyword(s):  
Dynamical Systems ◽  
Compact Manifold ◽  
Global Structure ◽  
Point Of View ◽  
List Type ◽  
Global View ◽  
Local Phenomenon ◽  
Generic Dynamics

AbstractThis paper suggests a program for getting a global view of the dynamics of diffeomorphisms, from the point of view of the C1-topology. More precisely, given any compact manifold M, one splits Diff1(M) into disjoint C1-open regions whose union is C1-dense, and conjectures state that each of these open sets and their complements is characterized by the presence of: •either a robust local phenomenon;•or a global structure forbidding this local phenomenon. Other conjectures state that some of these regions are empty. This set of conjectures draws a global view of the dynamics, putting in evidence the coherence of the numerous recent results on C1-generic dynamics.

Equivariant Hopf-Pitchfork Bifurcation of Symmetric Coupled Neural Network with Delay

2016 ◽  
Vol 26 (12) ◽  
pp. 1650205 ◽  
Author(s):  
Baodong Zheng ◽  
Haidong Yin ◽  
Chunrui Zhang
Keyword(s):  
Neural Network ◽  
Pitchfork Bifurcation ◽  
Stable Fixed Point ◽  
System Of Differential Equations ◽  
Codimension Two ◽  
Rich Variety ◽  
Mode Interactions ◽  
Generic Dynamics ◽  
Pitchfork Bifurcations ◽  
Two Parameter

This paper is concerned with how the symmetry and singularity of a system of differential equations affect generic dynamics and bifurcations. By computation of Hopf-pitchfork point in a two-parameter nonlinear problem satisfying a [Formula: see text]-symmetry condition, the mode interactions in two-parameter bifurcations with a single zero and two pairs of imaginary roots are considered. The codimension two normal form with equivariant Hopf-pitchfork bifurcations are given. Through analyzing the unfolding structure, local classification in the neighborhood of equivariant Hopf-pitchfork bifurcations point for the [Formula: see text]-symmetric is undertaken. A rich variety of dynamical and bifurcation behaviors is pointed out. Beyond a stable fixed point or a pair of stable fixed points, some interesting phenomena are also found, such as the coexistence of two periodic solutions which are verified both theoretically and numerically.

scholarly journals Generic dynamics and monotone complete $C\sp \ast$-algebras

1986 ◽  
Vol 295 (2) ◽  
pp. 795-795
Author(s):  
Dennis Sullivan ◽  
B. Weiss ◽  
J. D. Maitland Wright
Keyword(s):  
Generic Dynamics

THE INTERPLAY OF UNCORRELATED NOISE AND SMALL WORLD EFFECT ON PATTERN FORMATION IN TWO-DIMENSIONAL COUPLED MAP LATTICES

2012 ◽  
Vol 26 (31) ◽  
pp. 1250130 ◽  
Author(s):  
DAOGUANG WANG ◽  
XIAOSHA KANG ◽  
HUAPING LÜ
Keyword(s):  
Pattern Formation ◽  
Coupling Strength ◽  
Gaussian Noise ◽  
Nearest Neighbor ◽  
Spiral Wave ◽  
Small World ◽  
Coupled Map Lattices ◽  
Two Dimensional ◽  
Excitable Systems ◽  
Generic Dynamics

By using a neuron-like map model to denote the generic dynamics of excitable systems, Gaussian-noise-induced pattern formation in the two-dimensional coupled map lattices with nearest-neighbor coupling and shortcut links has been studied. Given the appropriate initial values and parameter regions, with all nodes concerned, the functions of δ(n), χ and ℜ are introduced to analyze the evolution of pattern formation. It is found that there exists a critical εc beyond which the stable rotating spiral wave will appear. After introducing the Gaussian noise for the homogeneous ε region, different spatiotemporal stable patterns will be achieved. Additionally, the importance of the parameter I on the coupling strength C is discussed.

scholarly journals Generic Dynamics of 4-Dimensional C 2 Hamiltonian Systems

2008 ◽  
Vol 281 (3) ◽  
pp. 597-619 ◽  
Author(s):  
Mário Bessa ◽  
João Lopes Dias
Keyword(s):  
Hamiltonian Systems ◽  
Generic Dynamics

scholarly journals The locking-decoding frontier for generic dynamics

2013 ◽  
Vol 469 (2159) ◽  
pp. 20130289 ◽  
Author(s):  
Frédéric Dupuis ◽  
Jan Florjanczyk ◽  
Patrick Hayden ◽  
Debbie Leung
Keyword(s):  
Mutual Information ◽  
Quantum Key Distribution ◽  
Black Hole Physics ◽  
Quantum Systems ◽  
Classical Information ◽  
Accessible Information ◽  
Generic Dynamics ◽  
Quantum Mutual Information ◽  
Logarithmic Number ◽  
Quantum Key Distribution Protocol

It is known that the maximum classical mutual information, which can be achieved between measurements on pairs of quantum systems, can drastically underestimate the quantum mutual information between them. In this article, we quantify this distinction between classical and quantum information by demonstrating that after removing a logarithmic-sized quantum system from one half of a pair of perfectly correlated bitstrings, even the most sensitive pair of measurements might yield only outcomes essentially independent of each other. This effect is a form of information locking but the definition we use is strictly stronger than those used previously. Moreover, we find that this property is generic, in the sense that it occurs when removing a random subsystem. As such, the effect might be relevant to statistical mechanics or black hole physics. While previous works had always assumed a uniform message, we assume only a min-entropy bound and also explore the effect of entanglement. We find that classical information is strongly locked almost until it can be completely decoded. Finally, we exhibit a quantum key distribution protocol that is ‘secure’ in the sense of accessible information but in which leakage of even a logarithmic number of bits compromises the secrecy of all others.

Simulation of generic dynamics flight equations of a parafoil/payload system

2012 ◽  
Author(s):  
Christelle Cumer ◽  
Clement Toussaint ◽  
Thierry Le Moing ◽  
Eric Poquillon ◽  
Yves Coquet
Keyword(s):  
Generic Dynamics
Sign in / Sign up

Export Citation Format

Share Document