Anti-control of continuous-time dynamical systems

2012 ◽  
Vol 17 (6) ◽  
pp. 2617-2627 ◽  
Author(s):  
Simin Yu ◽  
Guanrong Chen
Keyword(s):  
Dynamical Systems ◽  
Continuous Time

scholarly journals Numerical detection of unstable periodic orbits in continuous-time dynamical systems with chaotic behaviors

2007 ◽  
Vol 14 (5) ◽  
pp. 615-620 ◽  
Author(s):  
Y. Saiki
Keyword(s):  
Dynamical Systems ◽  
Periodic Orbits ◽  
Infinite Number ◽  
Continuous Time ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Complex Phenomenon ◽  
Unstable Periodic Orbits ◽  
Newton Raphson ◽  
The Lorenz System

Abstract. An infinite number of unstable periodic orbits (UPOs) are embedded in a chaotic system which models some complex phenomenon. Several algorithms which extract UPOs numerically from continuous-time chaotic systems have been proposed. In this article the damped Newton-Raphson-Mees algorithm is reviewed, and some important techniques and remarks concerning the practical numerical computations are exemplified by employing the Lorenz system.

From Dispersion to Laminarity in Dynamical Systems

1994 ◽  
Vol 49 (12) ◽  
pp. 1241-1247 ◽  
Author(s):  
G. Zumofen ◽  
J. Klafter
Keyword(s):  
Random Walk ◽  
Dynamical Systems ◽  
Continuous Time ◽  
Chaotic Behavior ◽  
Continuous Time Random Walk ◽  
Standard Map ◽  
One Dimensional ◽  
Enhanced Diffusion

Abstract We study transport in dynamical systems characterized by intermittent chaotic behavior with coexistence of dispersive motion due to periods of localization, and of enhanced diffusion due to periods of laminar motion. This transport is discussed within the continuous-time random walk approach which applies to both dispersive and enhanced motions. We analyze the coexistence for the standard map and for a one-dimensional map.

Continuity of dynamical systems: The continuous-time case

1992 ◽  
Vol 5 (4) ◽  
pp. 391-400 ◽  
Author(s):  
J. W. Nieuwenhuis ◽  
J. C. Willems
Keyword(s):  
Dynamical Systems ◽  
Continuous Time

scholarly journals PAC Model Checking of Black-Box Continuous-Time Dynamical Systems

2020 ◽  
Vol 39 (11) ◽  
pp. 3944-3955 ◽  
Author(s):  
Bai Xue ◽  
Miaomiao Zhang ◽  
Arvind Easwaran ◽  
Qin Li
Keyword(s):  
Dynamical Systems ◽  
Model Checking ◽  
Continuous Time ◽  
Black Box ◽  
Pac Model

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.

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