Discrete dynamical systems on graphs and Boolean functions

2004 ◽  
Vol 66 (6) ◽  
pp. 487-497 ◽  
Author(s):  
Chris L Barrett ◽  
William Y.C Chen ◽  
Michelle J Zheng
Keyword(s):  
Dynamical Systems ◽  
Boolean Functions ◽  
Discrete Dynamical Systems

scholarly journals On the Lyapunov Exponent of Monotone Boolean Networks †

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 1035
Author(s):  
Ilya Shmulevich
Keyword(s):  
Lyapunov Exponent ◽  
Dynamical Systems ◽  
Boolean Functions ◽  
Boolean Network ◽  
Discrete Dynamical Systems ◽  
Boolean Networks ◽  
Asymptotic Formulas ◽  
Small Perturbations ◽  
Monotone Boolean Functions ◽  
Almost All

Boolean networks are discrete dynamical systems comprised of coupled Boolean functions. An important parameter that characterizes such systems is the Lyapunov exponent, which measures the state stability of the system to small perturbations. We consider networks comprised of monotone Boolean functions and derive asymptotic formulas for the Lyapunov exponent of almost all monotone Boolean networks. The formulas are different depending on whether the number of variables of the constituent Boolean functions, or equivalently, the connectivity of the Boolean network, is even or odd.

scholarly journals Parallel discrete dynamical systems on maxterm and minterm Boolean functions

2012 ◽  
Vol 55 (3-4) ◽  
pp. 666-671 ◽  
Author(s):  
J.A. Aledo ◽  
S. Martínez ◽  
F.L. Pelayo ◽  
Jose C. Valverde
Keyword(s):  
Dynamical Systems ◽  
Boolean Functions ◽  
Discrete Dynamical Systems

scholarly journals Hidden Attractors in Discrete Dynamical Systems

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 616
Author(s):  
Marek Berezowski ◽  
Marcin Lawnik
Keyword(s):  
Dynamical Systems ◽  
Chaos Theory ◽  
Scientific Literature ◽  
Discrete Systems ◽  
Discrete Dynamical Systems ◽  
Continuous Systems ◽  
Hidden Attractors ◽  
Negative Effects ◽  
Chemical Reactors ◽  
Points Of View

Research using chaos theory allows for a better understanding of many phenomena modeled by means of dynamical systems. The appearance of chaos in a given process can lead to very negative effects, e.g., in the construction of bridges or in systems based on chemical reactors. This problem is important, especially when in a given dynamic process there are so-called hidden attractors. In the scientific literature, we can find many works that deal with this issue from both the theoretical and practical points of view. The vast majority of these works concern multidimensional continuous systems. Our work shows these attractors in discrete systems. They can occur in Newton’s recursion and in numerical integration.

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.

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