scholarly journals Local bifurcations of continuous dynamical systems under higher order conditions

2010 ◽  
Vol 23 (3) ◽  
pp. 230-234 ◽  
Author(s):  
F. Balibrea ◽  
A. Martinez ◽  
Jose C. Valverde
Keyword(s):  
Dynamical Systems ◽  
Higher Order ◽  
Order Conditions ◽  
Local Bifurcations

HIGHER ORDER CELLULAR AUTOMATA

2005 ◽  
Vol 08 (02n03) ◽  
pp. 169-192 ◽  
Author(s):  
NILS A. BAAS ◽  
TORBJØRN HELVIK
Keyword(s):  
Dynamical Systems ◽  
Cellular Automata ◽  
Level Structure ◽  
Higher Order ◽  
New Concepts ◽  
Multi Level

We introduce a class of dynamical systems called Higher Order Cellular Automata (HOCA). These are based on ordinary CA, but have a hierarchical, or multi-level, structure and/or dynamics. We present a detailed formalism for HOCA and illustrate the concepts through four examples. Throughout the article we emphasize the principles and ideas behind the construction of HOCA, such that these easily can be applied to other types of dynamical systems. The article also presents new concepts and ideas for describing and studying hierarchial dynamics in general.

scholarly journals Stratifications of equivariant varieties

1977 ◽  
Vol 16 (2) ◽  
pp. 279-295 ◽  
Author(s):  
M.J. Field
Keyword(s):  
Lie Group ◽  
General Position ◽  
Higher Order ◽  
Order Conditions ◽  
Compact Lie Group ◽  
Algebraic Varieties ◽  
Equivariant Maps

Let G be a compact Lie group and V and W be linear G spaces. A study is made of the canonical stratification of some algebraic varieties that arise naturally in the theory of C∞ equivariant maps from V to W. The main corollary of our results is the equivalence of Bierstone's concept of “equivariant general position” with our own of “G transversal”. The paper concludes with a description of Bierstone's higher order conditions for equivariant maps in the framework of equisingularity sequences.

scholarly journals Distributed Higher Order Consensus Protocols in Multiagent Dynamical Systems

2011 ◽  
Vol 58 (8) ◽  
pp. 1924-1932 ◽  
Author(s):  
Wenwu Yu ◽  
Guanrong Chen ◽  
Wei Ren ◽  
Jürgen Kurths ◽  
Wei Xing Zheng
Keyword(s):  
Dynamical Systems ◽  
Higher Order
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