scholarly journals On time dependent multistep dynamic processes

1991 ◽  
Vol 43 (1) ◽  
pp. 51-61
Author(s):  
Ferenc Szidarovszky ◽  
Ioannis K. Argyros
Keyword(s):  
Topological Space ◽  
Discrete Time ◽  
Difference Equations ◽  
Time Scale ◽  
Time Dependent ◽  
Dynamic Processes ◽  
Monotone Convergence ◽  
Speed Of Convergence ◽  
Nonlinear Difference Equations ◽  
Ordered Topological Space

The discrete time scale Liapunov theory is extended to time dependent, higher order, nonlinear difference equations in a partially ordered topological space. The monotone convergence of the solution is examined and the speed of convergence is estimated.

scholarly journals Discrete dynamics of complex systems

1997 ◽  
Vol 1 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Hermann Haken
Keyword(s):  
Stability Analysis ◽  
Discrete Time ◽  
Difference Equations ◽  
Control Parameter ◽  
Multiplicative Noise ◽  
Critical Value ◽  
Discrete Dynamics ◽  
Nonlinear Difference Equations ◽  
Starting Point ◽  
The Stability

This article extends the slaving principle of synergetics to processes with discrete time steps. Starting point is a set of nonlinear difference equations which contain multiplicative noise and which refer to multidimensional state vectors. The system depends on a control parameter. When its value is changed beyond a critical value, an instability of the solution occurs. The stability analysis allows us to divide the system into stable and unstable modes. The original equations can be transformed to a set of difference equations for the unstable and stable modes. The extension of the slaving principle to the time-discrete case then states that all the stable modes can be explicitly expressed by the unstable modes or so-called order-parameters.

Investigation of the dynamics of the some class of neuronet represented by weeknonlinear difference systems

2019 ◽  
Vol 24 (1-2) ◽  
pp. 49-58
Author(s):  
Khusainov D.Y. ◽  
◽  
Shatyrko A.V. ◽  
Puzha B. ◽  
Novotna V. ◽  
...  
Keyword(s):  
Artificial Intelligence ◽  
Neural Networks ◽  
Difference Equations ◽  
Lyapunov Method ◽  
Transient Processes ◽  
Dynamic Processes ◽  
Direct Lyapunov Method ◽  
Nonlinear Difference Equations ◽  
Weakly Nonlinear ◽  
Difference Systems

The article is devoted to dynamic processes in the field of artificial intelligence, namely in the tasks of neurodynamics. The problems of stability of transient processes in neural networks, which dynamics can be described by systems of weakly nonlinear difference equations, are considered. Conditions are formulated in terms of the direct Lyapunov method.

scholarly journals Elliptic Solutions of Dynamical Lucas Sequences

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 183
Author(s):  
Michael J. Schlosser ◽  
Meesue Yoo
Keyword(s):  
Discrete Time ◽  
Time Dependent ◽  
Fibonacci Polynomials ◽  
Lucas Sequences ◽  
Elliptic Solutions

We study two types of dynamical extensions of Lucas sequences and give elliptic solutions for them. The first type concerns a level-dependent (or discrete time-dependent) version involving commuting variables. We show that a nice solution for this system is given by elliptic numbers. The second type involves a non-commutative version of Lucas sequences which defines the non-commutative (or abstract) Fibonacci polynomials introduced by Johann Cigler. If the non-commuting variables are specialized to be elliptic-commuting variables the abstract Fibonacci polynomials become non-commutative elliptic Fibonacci polynomials. Some properties we derive for these include their explicit expansion in terms of normalized monomials and a non-commutative elliptic Euler–Cassini identity.

scholarly journals Antisymmetry of the Stochastical Order on all Ordered Topological Spaces

2019 ◽  
Vol 7 (1) ◽  
pp. 250-252 ◽  
Author(s):  
Tobias Fritz
Keyword(s):  
Topological Space ◽  
General Result ◽  
Elementary Proof ◽  
Short Note ◽  
Stochastic Order ◽  
Topological Spaces ◽  
Probability Measures ◽  
Ordered Topological Space ◽  
Special Cases

Abstract In this short note, we prove that the stochastic order of Radon probability measures on any ordered topological space is antisymmetric. This has been known before in various special cases. We give a simple and elementary proof of the general result.

The solution of an infinite set of differential-difference equations occurring in polymerization and queueing problems

1963 ◽  
Vol 59 (1) ◽  
pp. 117-124 ◽  
Author(s):  
A. Wragg
Keyword(s):  
Difference Equations ◽  
Queueing Theory ◽  
Bessel Functions ◽  
Formal Solution ◽  
Monomer Concentration ◽  
Arrival Rate ◽  
Time Dependent ◽  
Type Integral ◽  
Dependent Parameter ◽  
Infinite Set

AbstractThe time-dependent solutions of an infinite set of differential-difference equations arising from queueing theory and models of ‘living’ polymer are expressed in terms of modified Bessel functions. Explicit solutions are available for constant values of a parameter describing the arrival rate or monomer concentration; for time-dependent parameter a formal solution is obtained in terms of a function which satisfies a Volterra type integral equation of the second kind. These results are used as the basis of a numerical method of solving the infinite set of differential equations when the time-dependent parameter itself satisfies a differential equation.

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