scholarly journals Studying discrete dynamical systems through differential equations

2008 ◽  
Vol 244 (3) ◽  
pp. 630-648 ◽  
Author(s):  
Anna Cima ◽  
Armengol Gasull ◽  
Víctor Mañosa
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Discrete Dynamical Systems

scholarly journals Sur le retard à la bifurcation

2008 ◽  
Vol Volume 9, 2007 Conference in... ◽  
Author(s):  
Augustin Fruchard ◽  
Reinhard Schäfke
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Discrete Dynamical Systems ◽  
International Audience ◽  
Bifurcation Delay

International audience We give a non-exhaustive overview of the problem of bifurcation delay from its appearance in France at the end of the 80ies to the most recent contributions. We present the bifurcation delay for differential equations as well as for discrete dynamical systems. Nous donnons un aperçu non exhaustif du problème du retard à la bifurcation, depuis son apparition en France à la fin des années 1980 jusqu’aux contributions les plus récentes. Le problème et les résultats sont présentés d’une part pour les équations différentielles et d’autre part pour les systèmes dynamiques discrets

Discrete dynamical systems and bifurcation for periodic differential equations

1988 ◽  
Vol 12 (9) ◽  
pp. 881-893
Author(s):  
S.R. Bernfeld ◽  
L. Salvadori ◽  
F. Visentin
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Discrete Dynamical Systems

ON THE DYNAMICS OF SOME NUMERICAL METHODS

2000 ◽  
Vol 11 (07) ◽  
pp. 1481-1487 ◽  
Author(s):  
E. AHMED ◽  
A. S. HEGAZI
Keyword(s):  
Partial Differential Equations ◽  
Dynamical Systems ◽  
Numerical Methods ◽  
Differential Equations ◽  
Reaction Diffusion ◽  
Discrete Dynamical Systems ◽  
Point Of View ◽  
Partial Differential ◽  
Dynamical Behaviors ◽  
Telegraph Equations

From numerical methods point of view of dynamical systems, we have determined dynamical behaviors of the corresponding systems (i.e., chaotic, stable, bifurcations possibility, etc.). New versions of numerical methods are derived and we have compared the dynamical behaviors of the continuous dynamical systems with their corresponding discrete dynamical systems. An application of partial differential equations is given for reaction-diffusion and telegraph equations.

Application of Polynomial Filtering Algorithms to Nonlinear Discrete Dynamical Systems in Navigation Data Processing

2020 ◽  
Author(s):  
Oleg A. Stepanov ◽  
Vladimir A. Vasiliev ◽  
Mihail V. Basin ◽  
Viktor A. Tupysev ◽  
Yulia A. Litvinenko
Keyword(s):  
Dynamical Systems ◽  
Data Processing ◽  
Discrete Dynamical Systems ◽  
Filtering Algorithms ◽  
Navigation Data ◽  
Polynomial Filtering

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.

scholarly journals Failure Detection in Linear Discrete Dynamical Systems and its Detectionability

1987 ◽  
Vol 20 (5) ◽  
pp. 75-80 ◽  
Author(s):  
S. Tanaka ◽  
T. Okita ◽  
P.C. Müller
Keyword(s):  
Dynamical Systems ◽  
Failure Detection ◽  
Discrete Dynamical Systems
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