Simulation of a Cellular Automaton with Markov Chains: Applications in Self-Organized Dynamical Systems

2019 ◽  
Author(s):  
George I. Lambrou ◽  
Penelope Ioannidou ◽  
Paschalis Bizopoulos ◽  
Petros Toumpaniaris ◽  
Stavros Kepentzis ◽  
...  
Keyword(s):  
Dynamical Systems ◽  
Markov Chains ◽  
Cellular Automaton ◽  
Self Organized

A STUDY OF BIFURCATIONS IN A CIRCULAR REAL CELLULAR AUTOMATON

1993 ◽  
Vol 03 (02) ◽  
pp. 293-321 ◽  
Author(s):  
JÜRGEN WEITKÄMPER
Keyword(s):  
Hopf Bifurcation ◽  
Dynamical Systems ◽  
Cellular Automata ◽  
Cellular Automaton ◽  
Parallel Computers ◽  
Discrete Dynamical Systems ◽  
Two Dimensional ◽  
Bifurcation Structure ◽  
Logistic Mapping ◽  
Henon Mapping

Real cellular automata (RCA) are time-discrete dynamical systems on ℝN. Like cellular automata they can be obtained from discretizing partial differential equations. Due to their structure RCA are ideally suited to implementation on parallel computers with a large number of processors. In a way similar to the Hénon mapping, the system we consider here embeds the logistic mapping in a system on ℝN, N>1. But in contrast to the Hénon system an RCA in general is not invertible. We present some results about the bifurcation structure of such systems, mostly restricting ourselves, due to the complexity of the problem, to the two-dimensional case. Among others we observe cascades of cusp bifurcations forming generalized crossroad areas and crossroad areas with the flip curves replaced by Hopf bifurcation curves.

scholarly journals Self-Organized Criticality and Standard Model Parameters

2020 ◽  
Author(s):  
Ervin Goldfain
Keyword(s):  
Dynamical Systems ◽  
Standard Model ◽  
Metastable States ◽  
Model Parameters ◽  
Complex Behavior ◽  
Mixing Angles ◽  
Universal Scaling ◽  
Self Organized ◽  
Self Organized Criticality

As paradigm of complex behavior, Self-organized Criticality (SOC) reflects the ability of nonequilibrium dynamical systems to self-adjust into metastable states that are scale independent. The goal of this report is to tentatively show that the hierarchy of Standard Model masses and mixing angles follows from the universal scaling attributes of SOC.

scholarly journals Self-organized stochastic tipping in slow-fast dynamical systems

2013 ◽  
Vol 1 (2) ◽  
pp. 129-147 ◽  
Author(s):  
Mathias Linkerhand ◽  
Claudius Gros
Keyword(s):  
Dynamical Systems ◽  
Self Organized
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