A new conservative chaotic dynamical system with lemniscate equilibrium, its circuit model and FPGA implementation

We report on the tendency of chaotic systems to be controlled onto their unstable periodic orbits in such a way that these orbits are stabilized. The resulting orbits are known as cupolets and collectively provide a rich source of qualitative information on the associated chaotic dynamical system. We show that pairs of interacting cupolets may be induced into a state of mutually sustained stabilization that requires no external intervention in order to be maintained and is thus considered bound or entangled. A number of properties of this sort of entanglement are discussed. For instance, should the interaction be disturbed, then the chaotic entanglement would be broken. Based on certain properties of chaotic systems and on examples which we present, there is further potential for chaotic entanglement to be naturally occurring. A discussion of this and of the implications of chaotic entanglement in future research investigations is also presented.

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TREATMENT OF THE ERROR DUE TO UNRESOLVED SCALES IN SEQUENTIAL DATA ASSIMILATION

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127411030775 ◽

2011 ◽

Vol 21 (12) ◽

pp. 3619-3626 ◽

Cited By ~ 7

Author(s):

ALBERTO CARRASSI ◽

STÉPHANE VANNITSEM

Keyword(s):

Dynamical System ◽

Kalman Filter ◽

Data Assimilation ◽

Large Scale ◽

Model Error ◽

Environmental Modeling ◽

Sequential Data ◽

Chaotic Dynamical System ◽

Error Covariance ◽

Sequential Data Assimilation

In this paper, a method to account for model error due to unresolved scales in sequential data assimilation, is proposed. An equation for the model error covariance required in the extended Kalman filter update is derived along with an approximation suitable for application with large scale dynamics typical in environmental modeling. This approach is tested in the context of a low order chaotic dynamical system. The results show that the filter skill is significantly improved by implementing the proposed scheme for the treatment of the unresolved scales.

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Active synchronization between two different chaotic dynamical system

10.1063/1.4915686 ◽

2015 ◽

Author(s):

M. Maheri ◽

N. Md Arifin ◽

F. Ismail

Keyword(s):

Dynamical System ◽

Chaotic Dynamical System

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Some Chaos Notions on Dendrites

Symmetry ◽

10.3390/sym11101309 ◽

2019 ◽

Vol 11 (10) ◽

pp. 1309

Author(s):

Asmaa Fadel ◽

Syahida Che Dzul-Kifli

Keyword(s):

Dynamical System ◽

Chaotic Dynamical System ◽

Devaney Chaos

Transitivity is a key element in a chaotic dynamical system. In this paper, we present some relations between transitivity, stronger and alternative notions of it on compact and dendrite spaces. The relation between Auslander and Yorke chaos and Devaney chaos on dendrites is also discussed. Moreover, we prove that Devaney chaos implies strong dense periodicity on dendrites while the converse is not true.

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Stabilization of Rössler chaotic dynamical system using fuzzy logic control algorithm

International Journal of General Systems ◽

10.1080/03081079.2014.893299 ◽

2014 ◽

Vol 43 (5) ◽

pp. 413-433 ◽

Cited By ~ 30

Author(s):

Radu-Emil Precup ◽

Marius-Lucian Tomescu ◽

Claudia-Adina Dragos

Keyword(s):

Dynamical System ◽

Fuzzy Logic ◽

Fuzzy Logic Control ◽

Control Algorithm ◽

Chaotic Dynamical System ◽

Logic Control

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Smale spaces via inverse limits

Ergodic Theory and Dynamical Systems ◽

10.1017/etds.2013.19 ◽

2013 ◽

Vol 34 (6) ◽

pp. 2066-2092 ◽

Cited By ~ 6

Author(s):

SUSANA WIELER

Keyword(s):

Dynamical System ◽

Inverse Limits ◽

Canonical Coordinates ◽

Chaotic Dynamical System ◽

Smale Space ◽

Smale Spaces ◽

Special Case ◽

Basic Sets

AbstractA Smale space is a chaotic dynamical system with canonical coordinates of contracting and expanding directions. The basic sets for Smale’s Axiom $A$ systems are a key class of examples. We consider the special case of irreducible Smale spaces with zero-dimensional contracting directions, and characterize these as stationary inverse limits satisfying certain conditions.

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