Algorithm for solving of two-level hierarchical minimax program control problem in discrete-time dynamical system with incomplete information

2016 ◽  
Author(s):  
A. F. Shorikov
Keyword(s):  
Dynamical System ◽  
Control Problem ◽  
Incomplete Information ◽  
Discrete Time ◽  
Program Control ◽  
Discrete Time Dynamical System

Ocean ecosystem discrete time dynamics generated by ℓ-Volterra operators

2019 ◽  
Vol 12 (02) ◽  
pp. 1950015 ◽  
Author(s):  
U. A. Rozikov ◽  
S. K. Shoyimardonov
Keyword(s):  
Dynamical System ◽  
Fixed Points ◽  
Discrete Time ◽  
Volterra Operator ◽  
Saddle Points ◽  
Time Dynamics ◽  
Discrete Time Dynamical System ◽  
Starting Point ◽  
Ocean Ecosystem ◽  
Initial Starting

We consider a discrete-time dynamical system generated by a nonlinear operator (with four real parameters [Formula: see text]) of ocean ecosystem. We find conditions on the parameters under which the operator is reduced to a [Formula: see text]-Volterra quadratic stochastic operator mapping two-dimensional simplex to itself. We show that if [Formula: see text], then (under some conditions on [Formula: see text]) this [Formula: see text]-Volterra operator may have up to three or a countable set of fixed points; if [Formula: see text], then the operator has up to three fixed points. Depending on the parameters, the fixed points may be attracting, repelling or saddle points. The limit behaviors of trajectories of the dynamical system are studied. It is shown that independently on values of parameters and on initial (starting) point, all trajectories converge. Thus, the operator (dynamical system) is regular. We give some biological interpretations of our results.

Feedback Anticontrol of Discrete Chaos

1998 ◽  
Vol 08 (07) ◽  
pp. 1585-1590 ◽  
Author(s):  
Guanrong Chen ◽  
Dejian Lai
Keyword(s):  
Dynamical System ◽  
Discrete Time ◽  
State Feedback ◽  
Design Method ◽  
Control Design ◽  
Rigorous Approach ◽  
Discrete Time Dynamical System ◽  
Discrete Chaos ◽  
Simple Feedback ◽  
Discrete Time Dynamical Systems

In this paper, a simple feedback control design method earlier proposed by us for discrete-time dynamical systems is proved to be a mathematically rigorous approach for anticontrol of chaos, in the sense that any given discrete-time dynamical system can be made chaotic by the designed state-feedback controller along with the mod-operations.

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