Embedding of topological dynamical systems into symbolic dynamical systems: A necessary and sufficient condition

2006 ◽  
Vol 57 (3) ◽  
pp. 457-461 ◽  
Author(s):  
Yangeng Wang ◽  
Guo Wei
Keyword(s):  
Dynamical Systems ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Topological Dynamical Systems ◽  
Necessary And Sufficient

scholarly journals Controllability of Nonlinear Fractional Dynamical Systems with a Mittag–Leffler Kernel

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2139
Author(s):  
Jiale Sheng ◽  
Wei Jiang ◽  
Denghao Pang ◽  
Sen Wang
Keyword(s):  
Fixed Point ◽  
Dynamical Systems ◽  
Fixed Point Theorem ◽  
Laplace Transform ◽  
Point Theorem ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

This paper is concerned with controllability of nonlinear fractional dynamical systems with a Mittag–Leffler kernel. First, the solution of fractional dynamical systems with a Mittag–Leffler kernel is given by Laplace transform. In addition, one necessary and sufficient condition for controllability of linear fractional dynamical systems with Mittag–Leffler kernel is established. On this basis, we obtain one sufficient condition to guarantee controllability of nonlinear fractional dynamical systems with a Mittag–Leffler kernel by fixed point theorem. Finally, an example is given to illustrate the applicability of our results.

scholarly journals A LIMIT THEOREM FOR OCCUPATION MEASURES OF LÉVY PROCESSES IN COMPACT GROUPS

2012 ◽  
Vol 13 (01) ◽  
pp. 1250008
Author(s):  
ARNO BERGER ◽  
STEVEN N. EVANS
Keyword(s):  
Limit Theorem ◽  
Dynamical Systems ◽  
Compact Group ◽  
Short Proof ◽  
Compact Groups ◽  
Sufficient Condition ◽  
Occupation Measure ◽  
Necessary And Sufficient Condition ◽  
Occupation Measures ◽  
Necessary And Sufficient

A short proof utilizing dynamical systems techniques is given of a necessary and sufficient condition for the normalized occupation measure of a Lévy process in a metrizable compact group to be asymptotically uniform with probability one.

scholarly journals Finite-Time Set Reachability of Probabilistic Boolean Multiplex Control Networks

2022 ◽  
Vol 12 (2) ◽  
pp. 883
Author(s):  
Yuxin Cui ◽  
Shu Li ◽  
Yunxiao Shan ◽  
Fengqiu Liu
Keyword(s):  
Dynamical Systems ◽  
Finite Time ◽  
The State ◽  
Reconstruction Technique ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Control Networks ◽  
State Transfer ◽  
Necessary And Sufficient

This study focuses on the finite-time set reachability of probabilistic Boolean multiplex control networks (PBMCNs). Firstly, based on the state transfer graph (STG) reconstruction technique, the PBMCNs are extended to random logic dynamical systems. Then, a necessary and sufficient condition for the finite-time set reachability of PBMCNs is obtained. Finally, the obtained results are effectively illustrated by an example.

scholarly journals Controllability of generalised dynamical systems with constrained control

1988 ◽  
Vol 30 (1) ◽  
pp. 69-78
Author(s):  
Chen Zhaolin ◽  
Hong Huimin ◽  
Zhang Jifeng
Keyword(s):  
Dynamical Systems ◽  
Control Function ◽  
The State ◽  
Sufficient Condition ◽  
Constrained Control ◽  
Sense Of Control ◽  
Necessary And Sufficient Condition ◽  
Impulsive Behaviour ◽  
Necessary And Sufficient

AbstractThe state controllability for generalised dynamical systems with constrained control is discussed in this paper. The main results of the paper are the following:(1) a necessary and sufficient condition of the state controllability in the sense of control energy or amplitude constrained for generalised dynamical systems is obtained;(2) a control function u(t) is constructed such thata) u(t) satisfies constrained energy or amplitude condition,b) the state driven by u(t) moves from an arbitrary x(0−) = x0 to x(T(x0)) = 0,c) the trajectory driven by u(t) has no impulsive behaviour within (0, T(x0)].

scholarly journals Stability of Fuzzy Dynamical Systems via Lyapunov Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Abdelati El Allaoui ◽  
Said Melliani ◽  
Lalla Saadia Chadli
Keyword(s):  
Dynamical Systems ◽  
Initial Value Problems ◽  
Lyapunov Functions ◽  
Equilibrium Points ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Initial Value ◽  
Necessary And Sufficient ◽  
Fuzzy Dynamical Systems

The purpose of this paper is to introduce the concept of fuzzy Lyapunov functions to study the notion of stability of equilibrium points for fuzzy dynamical systems associated with fuzzy initial value problems, through the principle of Zadeh. Our contribution consists in a qualitative characterization of stability by a study of the trajectories of fuzzy dynamical systems, using auxiliary functions, and they will be called fuzzy Lyapunov functions. And, among the main results that have been proven is that the existence of fuzzy Lyapunov functions is a necessary and sufficient condition for stability. Some examples are given to illustrate the obtained results.

scholarly journals Existence of Ψ-bounded solutions for sylvester matrix dynamical systems on time scales

Filomat ◽  
2018 ◽  
Vol 32 (12) ◽  
pp. 4209-4219 ◽  
Author(s):  
Appa Rao ◽  
K.A.S.N.V. Prasad
Keyword(s):  
Dynamical Systems ◽  
Time Scales ◽  
Bounded Solution ◽  
Discrete Systems ◽  
Sufficient Condition ◽  
Bounded Solutions ◽  
Necessary And Sufficient Condition ◽  
Sylvester Matrix ◽  
Necessary And Sufficient ◽  
Existence Criteria

In this paper, we study the existence criteria for ?-bounded solutions of Sylvester matrix dynamical systems on time scales. The advantage of studying this system is it unifies continuous and discrete systems. First, we prove a necessary and sufficient condition for the existence of atleast one ?-bounded solution for Sylvester matrix dynamical systems on time scales, for every Lebesgue ?-deltaintegrable function F, on time scale T+. Further, we obtain a result relating to asymptotic behavior of ?-bounded solutions of this equation. The results are illustrated with suitable examples.

STABILIZING HIGHER PERIODIC ORBITS

1994 ◽  
Vol 04 (02) ◽  
pp. 457-460 ◽  
Author(s):  
M. PASKOTA ◽  
A.I. MEES ◽  
K.L. TEO
Keyword(s):  
Dynamical Systems ◽  
Periodic Orbits ◽  
State Feedback ◽  
State Feedback Control ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Chaotic Dynamical Systems ◽  
Linear State ◽  
Necessary And Sufficient ◽  
Bounded Perturbations

In this paper, we consider stabilization of chaotic dynamical systems onto higher periodic orbits. We give a necessary and sufficient condition for using local linear state feedback control for this purpose. The control is achieved using small, bounded perturbations, and the method proposed is shown to be effective even in the presence of relatively small random dynamical noise.

Sign in / Sign up

Export Citation Format

Share Document