scholarly journals Studying discrete dynamical systems through differential equations

2008 ◽  
Vol 244 (3) ◽  
pp. 630-648 ◽  
Author(s):  
Anna Cima ◽  
Armengol Gasull ◽  
Víctor Mañosa

2008 ◽  
Vol Volume 9, 2007 Conference in... ◽  
Author(s):  
Augustin Fruchard ◽  
Reinhard Schäfke

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



1988 ◽  
Vol 12 (9) ◽  
pp. 881-893
Author(s):  
S.R. Bernfeld ◽  
L. Salvadori ◽  
F. Visentin


2000 ◽  
Vol 11 (07) ◽  
pp. 1481-1487 ◽  
Author(s):  
E. AHMED ◽  
A. S. HEGAZI

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.





Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 616
Author(s):  
Marek Berezowski ◽  
Marcin Lawnik

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.



1993 ◽  
Vol 03 (02) ◽  
pp. 293-321 ◽  
Author(s):  
JÜRGEN WEITKÄMPER

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.



1987 ◽  
Vol 20 (5) ◽  
pp. 75-80 ◽  
Author(s):  
S. Tanaka ◽  
T. Okita ◽  
P.C. Müller


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