scholarly journals Topological chaos, braiding and bifurcation of almost-cyclic sets

2012 ◽  
Vol 22 (4) ◽  
pp. 043135 ◽  
Author(s):  
Piyush Grover ◽  
Shane D. Ross ◽  
Mark A. Stremler ◽  
Pankaj Kumar
Keyword(s):  
Topological Chaos ◽  
Cyclic Sets

scholarly journals Topological Chaos and Periodic Braiding of Almost-Cyclic Sets

2011 ◽  
Vol 106 (11) ◽  
Author(s):  
Mark A. Stremler ◽  
Shane D. Ross ◽  
Piyush Grover ◽  
Pankaj Kumar
Keyword(s):  
Topological Chaos ◽  
Cyclic Sets

scholarly journals COMPLETELY REDUCIBLE SETS

2013 ◽  
Vol 23 (04) ◽  
pp. 915-941 ◽  
Author(s):  
DOMINIQUE PERRIN
Keyword(s):  
Closure Properties ◽  
Linear Representations ◽  
Complete Reducibility ◽  
The Family ◽  
Syntactic Representation ◽  
Completely Reducible ◽  
Rational Sets ◽  
Cyclic Sets

We study the family of rational sets of words, called completely reducible and which are such that the syntactic representation of their characteristic series is completely reducible. This family contains, by a result of Reutenauer, the submonoids generated by bifix codes and, by a result of Berstel and Reutenauer, the cyclic sets. We study the closure properties of this family. We prove a result on linear representations of monoids which gives a generalization of the result concerning the complete reducibility of the submonoid generated by a bifix code to sets called birecurrent. We also give a new proof of the result concerning cyclic sets.

TOPOLOGICAL CHAOS FOR BIRTH-AND-DEATH-TYPE MODELS WITH PROLIFERATION

2002 ◽  
Vol 12 (06) ◽  
pp. 755-775 ◽  
Author(s):  
JACEK BANASIAK ◽  
MIROSŁAW LACHOWICZ
Keyword(s):  
Death Process ◽  
Antineoplastic Drugs ◽  
Birth And Death Process ◽  
Neoplastic Cells ◽  
Cellular Resistance ◽  
Infinite Systems ◽  
Topological Chaos ◽  
Linear Odes ◽  
Different Levels

In this paper we consider a class of infinite systems of linear ODEs. Each system corresponds to a process characterized by two components: the conservative one (birth-and-death process) and the proliferative one. A system of this type can describe the population of neoplastic cells divided into subpopulations characterized by different levels of cellular resistance to antineoplastic drugs. Under suitable assumptions on the "birth" (amplification) coefficients, the "death" (deamplification) coefficients and the averages of the life-spans we prove that this class of models is topologically chaotic.

scholarly journals The double-morse well and topological chaos

1988 ◽  
Vol 145 (4) ◽  
pp. 299-304 ◽  
Author(s):  
Michael Berblinger ◽  
Christoph Schlier
Keyword(s):  
Topological Chaos

On cyclic sets of operators

2018 ◽  
Vol 68 (3) ◽  
pp. 521-529
Author(s):  
Mohamed Amouch ◽  
Otmane Benchiheb
Keyword(s):  
Cyclic Sets

scholarly journals Investigating topological chaos by elementary cellular automata dynamics

2000 ◽  
Vol 244 (1-2) ◽  
pp. 219-241 ◽  
Author(s):  
Gianpiero Cattaneo ◽  
Michele Finelli ◽  
Luciano Margara
Keyword(s):  
Cellular Automata ◽  
Elementary Cellular Automata ◽  
Topological Chaos

scholarly journals Topological chaos in a three-dimensional spherical fluid vortex

2017 ◽  
Vol 117 (6) ◽  
pp. 60005 ◽  
Author(s):  
Spencer A. Smith ◽  
Joshua Arenson ◽  
Eric Roberts ◽  
Suzanne Sindi ◽  
Kevin A. Mitchell
Keyword(s):  
Three Dimensional ◽  
Topological Chaos ◽  
Spherical Fluid
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