scholarly journals Constructing complete chaotic maps with reciprocal structures

2005 ◽  
Vol 2005 (3) ◽  
pp. 357-372 ◽  
Author(s):  
Weihong Huang
Keyword(s):  
Numerical Simulations ◽  
Chaotic Maps ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Reciprocal Structures ◽  
Functional Forms ◽  
Necessary And Sufficient

A class of unimodal complete chaotic mapsf={fL,fR}with reciprocal functional forms(fR=1/fL)are examined. The necessary and sufficient conditions are provided to construct such maps. The theoretical conclusions are then verified by numerical simulations.

scholarly journals Constructing chaotic transformations with closed functional forms

2006 ◽  
Vol 2006 ◽  
pp. 1-16 ◽  
Author(s):  
Weihong Huang
Keyword(s):  
Computer Simulations ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Functional Forms ◽  
Necessary And Sufficient

The properties of complete chaotic unimodal transformations with closed functional forms are examined and the necessary and sufficient conditions are provided to construct such transformations. Theoretical findings are verified with computer simulations.

scholarly journals Simultaneity of Synchronization and Antisynchronization in a Class of Chaotic Systems

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Zhi Liu ◽  
Rongwei Guo ◽  
Yi Qi ◽  
Cuimei Jiang
Keyword(s):  
Numerical Simulations ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Synchronization Phenomenon ◽  
All Solutions ◽  
Necessary And Sufficient ◽  
Theoretical Results

In this paper, a new synchronization phenomenon, that is, the simultaneity of synchronization and antisynchronization, is investigated for a class of chaotic systems. First, for a given chaotic system, necessary and sufficient conditions for the simultaneity of synchronization and antisynchronization are proved. Then, based on these conditions, all solutions of such synchronization phenomenon for a given chaotic system are derived. After that, physical controllers that are not only simple but also implementable are designed to realize the simultaneity of synchronization and antisynchronization in the above system. Finally, illustrative examples based on numerical simulations are used to verify the validity and effectiveness of the above theoretical results.

Chaotic Synchronization of a Controlled, Noised, Gyroscope System With an Expected Gyroscope System

2011 ◽  
Author(s):  
Fuhong Min ◽  
Albert C. J. Luo
Keyword(s):  
Dynamical Systems ◽  
Numerical Simulations ◽  
Sufficient Conditions ◽  
Chaotic Synchronization ◽  
Necessary And Sufficient Conditions ◽  
Gyroscope System ◽  
Necessary And Sufficient

In this paper, chaotic synchronization of a controlled, noised gyroscope system with an expected gyroscope system is investigated. From the theory of discontinuous dynamical systems, the necessary and sufficient conditions of such synchronization are presented. Numerical simulations for non-synchronization, partial and full chaotic synchronizations of two gyroscope systems are carried out.

scholarly journals Static Consensus in Passifiable Linear Networks

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
Ibragim A. Junussov
Keyword(s):  
Numerical Simulations ◽  
Output Feedback ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Linear Networks ◽  
Necessary And Sufficient

Sufficient conditions of consensus (synchronization) in networks described by digraphs and consisting of identical deterministic SIMO systems are derived. Identical and nonidentical control gains (positive arc weights) are considered. Connection between admissible digraphs and nonsmooth hypersurfaces (sufficient gain boundary) is established. Necessary and sufficient conditions for static consensus by output feedback in networks consisting of certain class of double integrators are rediscovered. Scalability for circle digraph in terms of gain magnitudes is studied. Examples and results of numerical simulations are presented.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

Nonlinear boundary-value problems for degenerate differential-algebraic systems

2020 ◽  
Vol 17 (3) ◽  
pp. 313-324
Author(s):  
Sergii Chuiko ◽  
Ol'ga Nesmelova
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Algebraic System ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Weakly Nonlinear ◽  
Differential Algebraic System ◽  
Linear Differential ◽  
Necessary And Sufficient

The study of the differential-algebraic boundary value problems, traditional for the Kiev school of nonlinear oscillations, founded by academicians M.M. Krylov, M.M. Bogolyubov, Yu.A. Mitropolsky and A.M. Samoilenko. It was founded in the 19th century in the works of G. Kirchhoff and K. Weierstrass and developed in the 20th century by M.M. Luzin, F.R. Gantmacher, A.M. Tikhonov, A. Rutkas, Yu.D. Shlapac, S.L. Campbell, L.R. Petzold, Yu.E. Boyarintsev, V.F. Chistyakov, A.M. Samoilenko, O.A. Boichuk, V.P. Yacovets, C.W. Gear and others. In the works of S.L. Campbell, L.R. Petzold, Yu.E. Boyarintsev, V.F. Chistyakov, A.M. Samoilenko and V.P. Yakovets were obtained sufficient conditions for the reducibility of the linear differential-algebraic system to the central canonical form and the structure of the general solution of the degenerate linear system was obtained. Assuming that the conditions for the reducibility of the linear differential-algebraic system to the central canonical form were satisfied, O.A.~Boichuk obtained the necessary and sufficient conditions for the solvability of the linear Noetherian differential-algebraic boundary value problem and constructed a generalized Green operator of this problem. Based on this, later O.A. Boichuk and O.O. Pokutnyi obtained the necessary and sufficient conditions for the solvability of the weakly nonlinear differential algebraic boundary value problem, the linear part of which is a Noetherian differential algebraic boundary value problem. Thus, out of the scope of the research, the cases of dependence of the desired solution on an arbitrary continuous function were left, which are typical for the linear differential-algebraic system. Our article is devoted to the study of just such a case. The article uses the original necessary and sufficient conditions for the solvability of the linear Noetherian differential-algebraic boundary value problem and the construction of the generalized Green operator of this problem, constructed by S.M. Chuiko. Based on this, necessary and sufficient conditions for the solvability of the weakly nonlinear differential-algebraic boundary value problem were obtained. A typical feature of the obtained necessary and sufficient conditions for the solvability of the linear and weakly nonlinear differential-algebraic boundary-value problem is its dependence on the means of fixing of the arbitrary continuous function. An improved classification and a convergent iterative scheme for finding approximations to the solutions of weakly nonlinear differential algebraic boundary value problems was constructed in the article.

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