scholarly journals Dimensional Characteristics of Diffusion Chaos

2015 ◽  
Vol 20 (1) ◽  
pp. 30-51 ◽  
Author(s):  
S. D. Glyzin
Keyword(s):  
Dynamical System ◽  
Diffusion Coefficient ◽  
Lyapunov Dimension ◽  
Diffusion Chaos

The phenomenon of multimode diffusion chaos is considered. For a number of examples it is shown that the Lyapunov dimension of the attractor of a distributed dynamical system increases as the diffusion coefficient tends to 0.

scholarly journals Data-Rate Constrained Observers of Nonlinear Systems

Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 282 ◽  
Author(s):  
Quentin Voortman ◽  
Alexander Pogromsky ◽  
Alexey Matveev ◽  
Henk Nijmeijer
Keyword(s):  
Dynamical System ◽  
Communication Channel ◽  
Lorenz System ◽  
Upper Bounds ◽  
Data Rate ◽  
The State ◽  
Box Dimension ◽  
Lyapunov Dimension ◽  
Remote Location ◽  
The Lorenz System

In this paper, the design of a data-rate constrained observer for a dynamical system is presented. This observer is designed to function both in discrete time and continuous time. The system is connected to a remote location via a communication channel which can transmit limited amounts of data per unit of time. The objective of the observer is to provide estimates of the state at the remote location through messages that are sent via the channel. The observer is designed such that it is robust toward losses in the communication channel. Upper bounds on the required communication rate to implement the observer are provided in terms of the upper box dimension of the state space and an upper bound on the largest singular value of the system’s Jacobian. Results that provide an analytical bound on the required minimum communication rate are then presented. These bounds are obtained by using the Lyapunov dimension of the dynamical system rather than the upper box dimension in the rate. The observer is tested through simulations for the Lozi map and the Lorenz system. For the Lozi map, the Lyapunov dimension is computed. For both systems, the theoretical bounds on the communication rate are compared to the simulated rates.

Brief-Measurements of Vapor Diffusion Coefficient

1954 ◽  
Vol 46 (11) ◽  
pp. 47-49 ◽  
Author(s):  
C.Y. Lee ◽  
C.R. Wilke
Keyword(s):  
Diffusion Coefficient ◽  
Vapor Diffusion
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