On the stochastic stability of some two-dimensional dynamical systems

2010 ◽  
Vol 46 (6) ◽  
pp. 901-905
Author(s):  
M. M. Shumafov
Keyword(s):  
Dynamical Systems ◽  
Stochastic Stability ◽  
Two Dimensional

Integrable two-dimensional dynamical systems and the characteristic Lie algebras

2007 ◽  
Vol 5 ◽  
pp. 195-200
Author(s):  
A.V. Zhiber ◽  
O.S. Kostrigina
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Second Order ◽  
System Of Equations ◽  
Two Dimensional ◽  
Finite Dimensional ◽  
Dimensional Dynamical System

In the paper it is shown that the two-dimensional dynamical system of equations is Darboux integrable if and only if its characteristic Lie algebra is finite-dimensional. The class of systems having a full set of fist and second order integrals is described.

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 Conditional Lie-Bäcklund Symmetries and Differential Constraints of Radially Symmetric Nonlinear Convection-Diffusion Equations with Source

Entropy ◽  
2020 ◽  
Vol 22 (8) ◽  
pp. 873
Author(s):  
Lina Ji ◽  
Rui Wang
Keyword(s):  
Dynamical Systems ◽  
Diffusion Equations ◽  
Two Dimensional ◽  
Nonlinear Convection ◽  
Differential Constraint ◽  
Invariant Surface ◽  
Differential Constraints ◽  
Convection Diffusion ◽  
Constraint Method ◽  
Symmetry Method

A conditional Lie-Bäcklund symmetry method and differential constraint method are developed to study the radially symmetric nonlinear convection-diffusion equations with source. The equations and the admitted conditional Lie-Bäcklund symmetries (differential constraints) are identified. As a consequence, symmetry reductions to two-dimensional dynamical systems of the resulting equations are derived due to the compatibility of the original equation and the additional differential constraint corresponding to the invariant surface equation of the admitted conditional Lie-Bäcklund symmetry.

scholarly journals The stability theorems for discrete dynamical systems on two-dimensional manifolds

1983 ◽  
Vol 90 ◽  
pp. 1-55 ◽  
Author(s):  
Atsuro Sannami
Keyword(s):  
Dynamical Systems ◽  
Smooth Manifold ◽  
Riemannian Metric ◽  
Discrete Dynamical Systems ◽  
Two Dimensional ◽  
Stability Theorems ◽  
The Stability

One of the basic problems in the theory of dynamical systems is the characterization of stable systems.Let M be a closed (i.e. compact without boundary) connected smooth manifold with a smooth Riemannian metric and Diffr (M) (r ≥ 1) denote the space of Cr diffeomorphisms on M with the uniform Cr topology.

ON SUPERSYMMETRIC NONLINEAR σ MODELS AND CLASSICAL DYNAMICAL SYSTEMS

1996 ◽  
Vol 11 (06) ◽  
pp. 1101-1115
Author(s):  
ANTTI J. NIEMI ◽  
KAUPO PALO
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Partition Function ◽  
Integrable Systems ◽  
Morse Theory ◽  
General Class ◽  
Loop Space ◽  
Two Dimensional ◽  
Hamiltonian Flow ◽  
Classical Dynamical System

We construct a two-dimensional nonlinear σ model that describes the Hamiltonian flow in the loop space of a classical dynamical system. This model is obtained by equivariantizing the standard N=1 supersymmetric nonlinear σ model by the Hamiltonian flow. We use localization methods to evaluate the corresponding partition function for a general class of integrable systems, and find relations that can be viewed as generalizations of standard relations in classical Morse theory.

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