GLOBALLY EXPONENTIAL HYPERCHAOS (LAG) SYNCHRONIZATION IN A FAMILY OF MODIFIED HYPERCHAOTIC RÖSSLER SYSTEMS

2007 ◽  
Vol 17 (05) ◽  
pp. 1759-1774 ◽  
Author(s):  
ZHENYA YAN ◽  
PEI YU
Keyword(s):  
Stability Criteria ◽  
Nonlinear Feedback Control ◽  
Nonlinear Feedback ◽  
Feedback Controllers ◽  
Lag Synchronization ◽  
Control Laws ◽  
New Family ◽  
The Family ◽  
Lyapunov Stability Criteria ◽  
Theoretical Results

In this paper, we consider a new family of modified hyperchaotic Rössler systems, recently studied by Nikolov and Clodong using proper nonlinear feedback controllers. Particular attention is given to (i) globally exponential lag synchronization (GELS) for τ > 0; and (ii) globally exponential synchronization (GES) for τ = 0. As a representative example, one system of the family of modified hyperchaotic Rössler systems is particularly studied, and Lyapunov stability criteria for the GELS and GES are derived via eight families of proper nonlinear feedback controllers. Moreover, we also present some nonlinear feedback control laws for other modified hyperchaotic Rössler systems. Numerical simulations are used to illustrate the theoretical results.

scholarly journals An approach to exact nonlinear feedback control design employing recursive approximations and the null space

2021 ◽  
Author(s):  
Parisa Khosravi ◽  
Robert H. Bishop
Keyword(s):  
Analytic Solution ◽  
Null Space ◽  
Nonlinear Partial Differential Equations ◽  
Approximate Solutions ◽  
Analytic Solutions ◽  
Nonlinear Feedback Control ◽  
Nonlinear Feedback ◽  
Feedback Controllers ◽  
Linearization Methods ◽  
Approximate Linearization

AbstractA strategy to design exact nonlinear feedback controllers based on a recursive application of approximate linearization methods is examined. The computations are algebraic and computationally simpler than solving the set of coupled nonlinear partial differential equations thereby facilitating practical symbolic computer computations enabling discernment of evolving patterns in the approximate solutions as the order of approximation increases. Utilizing the null space that appears at each step in the computations as part of the computations, a family of analytic solutions can be generated asymptotically. There are possibilities for optimizing the performance by judiciously choice of analytic solution that emerge from the selective use of the null space.

scholarly journals An Efficient Family of Traub-Steffensen-Type Methods for Solving Systems of Nonlinear Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Janak Raj Sharma ◽  
Puneet Gupta
Keyword(s):  
Nonlinear Equations ◽  
Systems Of Nonlinear Equations ◽  
Numerical Tests ◽  
New Family ◽  
Several Variables ◽  
Derivative Free ◽  
The Family ◽  
Large Systems ◽  
Steffensen Method ◽  
Theoretical Results

Based on Traub-Steffensen method, we present a derivative free three-step family of sixth-order methods for solving systems of nonlinear equations. The local convergence order of the family is determined using first-order divided difference operator for functions of several variables and direct computation by Taylor's expansion. Computational efficiency is discussed, and a comparison between the efficiencies of the proposed techniques with the existing ones is made. Numerical tests are performed to compare the methods of the proposed family with the existing methods and to confirm the theoretical results. It is shown that the new family is especially efficient in solving large systems.

STUDY OF GLOBALLY EXPONENTIAL SYNCHRONIZATION FOR THE FAMILY OF RÖSSLER SYSTEMS

2006 ◽  
Vol 16 (08) ◽  
pp. 2395-2406 ◽  
Author(s):  
XIAOXIN LIAO ◽  
PEI YU
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Functions ◽  
Chaos Control ◽  
Chaotic Systems ◽  
Exponential Synchronization ◽  
Nonlinear Feedback ◽  
Feedback Controls ◽  
The Family ◽  
Control And Synchronization ◽  
Theoretical Results

This paper considers the globally exponential synchronization (GES) of the family of Rössler chaotic systems. One pair of the six transmitter-receiver systems is specifically studied, and algebraic criterion for the GES is obtained via proper nonlinear feedback controls. Based on the study of the systems' structures, appropriate Lyapunov functions are constructed for error systems. The method presented in this paper provides a convenient tool in the practical use of chaos control and synchronization. Numerical simulations are provided to demonstrate the theoretical results.

Three new species, two new genera, and new family Biphragmosagittidae (Сhaetognatha) from Southwest Pacific Ocean

2011 ◽  
Vol 20 (1) ◽  
pp. 161-173
Author(s):  
A.P. Kassatkina
Keyword(s):  
New Species ◽  
Type Species ◽  
Morphological Characters ◽  
The Body ◽  
New Order ◽  
New Genera ◽  
New Family ◽  
The Family ◽  
Three New Species

Resuming published and own data, a revision of classification of Chaetognatha is presented. The family Sagittidae Claus & Grobben, 1905 is given a rank of subclass, Sagittiones, characterised, in particular, by the presence of two pairs of sac-like gelatinous structures or two pairs of fins. Besides the order Aphragmophora Tokioka, 1965, it contains the new order Biphragmosagittiformes ord. nov., which is a unique group of Chaetognatha with an unusual combination of morphological characters: the transverse muscles present in both the trunk and the tail sections of the body; the seminal vesicles simple, without internal complex compartments; the presence of two pairs of lateral fins. The only family assigned to the new order, Biphragmosagittidae fam. nov., contains two genera. Diagnoses of the two new genera, Biphragmosagitta gen. nov. (type species B. tarasovi sp. nov. and B. angusticephala sp. nov.) and Biphragmofastigata gen. nov. (type species B. fastigata sp. nov.), detailed descriptions and pictures of the three new species are presented.

Correcting a 135-year error: Limulidae Leach, 1819 (Chelicerata, Xiphosura) is the proper authority, not Limulidae Zittel, 1885

2021 ◽  
pp. 1-2
Author(s):  
Philip M. Novack-Gottshall ◽  
Roy E. Plotnick
Keyword(s):  
Horseshoe Crab ◽  
Marine Species ◽  
Limulus Polyphemus ◽  
Junior Synonym ◽  
Living Fossil ◽  
New Family ◽  
The Family ◽  
The World ◽  
Modern Genus

The horseshoe crab Limulus polyphemus (Linnaeus, 1758) is a famous species, renowned as a ‘living fossil’ (Owen, 1873; Barthel, 1974; Kin and Błażejowski, 2014) for its apparently little-changed morphology for many millions of years. The genus Limulus Müller, 1785 was used by Leach (1819, p. 536) as the basis of a new family Limulidae and synonymized it with Polyphemus Lamarck, 1801 (Lamarck's proposed but later unaccepted replacement for Limulus, as discussed by Van der Hoeven, 1838, p. 8) and Xyphotheca Gronovius, 1764 (later changed to Xiphosura Gronovius, 1764, another junior synonym of Limulus). He also included the valid modern genus Tachypleus Leach, 1819 in the family. The primary authority of Leach (1819) is widely recognized in the neontological literature (e.g., Dunlop et al., 2012; Smith et al., 2017). It is also the authority recognized in the World Register of Marine Species (WoRMS Editorial Board, 2021).

Sign in / Sign up

Export Citation Format

Share Document