Distributed Stabilized Region Regulator for Discrete-Time Dynamics

2019 ◽  
pp. 109-125
Author(s):  
Hongjing Liang ◽  
Huaguang Zhang
Keyword(s):  
Discrete Time ◽  
Time Dynamics

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.

CHAOS OF DYNAMICAL SYSTEMS ON GENERAL TIME DOMAINS

2009 ◽  
Vol 19 (11) ◽  
pp. 3829-3832
Author(s):  
ABRAHAM BOYARSKY ◽  
PAWEŁ GÓRA
Keyword(s):  
Dynamical Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
Chaotic Map ◽  
Discrete Time System ◽  
Combined System ◽  
Time Intervals ◽  
Time Dynamics ◽  
Time Component ◽  
Time Domains

We consider dynamical systems on time domains that alternate between continuous time intervals and discrete time intervals. The dynamics on the continuous portions may represent species growth when there is population overlap and are governed by differential or partial differential equations. The dynamics across the discrete time intervals are governed by a chaotic map and may represent population growth which is seasonal. We study the long term dynamics of this combined system. We study various conditions on the continuous time dynamics and discrete time dynamics that produce chaos and alternatively nonchaos for the combined system. When the discrete system alone is chaotic we provide a condition on the continuous dynamical component such that the combined system behaves chaotically. We also provide a condition that ensures that if the discrete time system has an absolutely continuous invariant measure so will the combined system. An example based on the logistic continuous time and logistic discrete time component is worked out.

Effective discrete-time dynamics in Monte Carlo simulations

1986 ◽  
Vol 33 (7) ◽  
pp. 4734-4738 ◽  
Author(s):  
H. A. Ceccatto
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Discrete Time ◽  
Time Dynamics

scholarly journals Robust Exponential Stabilization of Uncertain Impulsive Bilinear Time-Delay Systems with Saturating Actuators

2010 ◽  
Vol 2010 ◽  
pp. 1-6 ◽  
Author(s):  
Yang Shujie ◽  
Shi Bao ◽  
Zhang Qiang ◽  
Pan Tetie
Keyword(s):  
Time Delay ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Exponential Stabilization ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Time Dynamics ◽  
Saturating Actuators ◽  
Robust Exponential Stabilization

This paper investigates the problem of robust exponential stabilization for uncertain impulsive bilinear time-delay systems with saturating actuators. By using the Lyapunov function and Razumikhin-type techniques, two classes of impulsive systems are considered: the systems with unstable discrete-time dynamics and the ones with stable discrete-time dynamics. Sufficient conditions for robust stabilization are obtained in terms of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness of the theoretical results.

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