A new method for finding cycles by semilinear control

Dmitriy Dmitrishin; Goran Lesaja; Ivan Skrinnik; Alex Stokolos

doi:10.1016/j.physleta.2019.03.013

A new method for finding cycles by semilinear control

Dmitriy Dmitrishin, Goran Lesaja, Ivan Skrinnik, Alex Stokolos

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

In the paper two new results that prove typically real and local univalent properties of certain class of rational functions in the unit disc D are presented. They provide a theoretical justification of a new method for finding periodic solutions of the discrete vector dynamical systems. The main goal of the paper is to propose and investigate the two-delays generalization of the scheme introduced by Ö. Morgül. The analysis shows that the coefficients in the proposed method can be chosen in a way that improves the admissible range of parameters. The method is elementary and easy to implement. Furthermore, numerical experiments with several well known maps show effectiveness of the control scheme.

Original language	English
Pages (from-to)	1871-1878
Number of pages	8
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	383
Issue number	16
DOIs	https://doi.org/10.1016/j.physleta.2019.03.013
State	Published - Jun 6 2019

Scopus Subject Areas

General Physics and Astronomy

Keywords

Chaos control
Discrete vector dynamical systems
Periodic solutions
Stability

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10.1016/j.physleta.2019.03.013

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title = "A new method for finding cycles by semilinear control",

abstract = "In the paper two new results that prove typically real and local univalent properties of certain class of rational functions in the unit disc D are presented. They provide a theoretical justification of a new method for finding periodic solutions of the discrete vector dynamical systems. The main goal of the paper is to propose and investigate the two-delays generalization of the scheme introduced by {\"O}. Morg{\"u}l. The analysis shows that the coefficients in the proposed method can be chosen in a way that improves the admissible range of parameters. The method is elementary and easy to implement. Furthermore, numerical experiments with several well known maps show effectiveness of the control scheme.",

keywords = "Chaos control, Discrete vector dynamical systems, Periodic solutions, Stability",

author = "Dmitriy Dmitrishin and Goran Lesaja and Ivan Skrinnik and Alex Stokolos",

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year = "2019",

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T1 - A new method for finding cycles by semilinear control

AU - Dmitrishin, Dmitriy

AU - Lesaja, Goran

AU - Skrinnik, Ivan

AU - Stokolos, Alex

PY - 2019/6/6

Y1 - 2019/6/6

N2 - In the paper two new results that prove typically real and local univalent properties of certain class of rational functions in the unit disc D are presented. They provide a theoretical justification of a new method for finding periodic solutions of the discrete vector dynamical systems. The main goal of the paper is to propose and investigate the two-delays generalization of the scheme introduced by Ö. Morgül. The analysis shows that the coefficients in the proposed method can be chosen in a way that improves the admissible range of parameters. The method is elementary and easy to implement. Furthermore, numerical experiments with several well known maps show effectiveness of the control scheme.

AB - In the paper two new results that prove typically real and local univalent properties of certain class of rational functions in the unit disc D are presented. They provide a theoretical justification of a new method for finding periodic solutions of the discrete vector dynamical systems. The main goal of the paper is to propose and investigate the two-delays generalization of the scheme introduced by Ö. Morgül. The analysis shows that the coefficients in the proposed method can be chosen in a way that improves the admissible range of parameters. The method is elementary and easy to implement. Furthermore, numerical experiments with several well known maps show effectiveness of the control scheme.

KW - Chaos control

KW - Discrete vector dynamical systems

KW - Periodic solutions

KW - Stability

UR - https://www.scopus.com/pages/publications/85063272916

U2 - 10.1016/j.physleta.2019.03.013

DO - 10.1016/j.physleta.2019.03.013

M3 - Article

AN - SCOPUS:85063272916

SN - 0375-9601

VL - 383

SP - 1871

EP - 1878

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 16

ER -

A new method for finding cycles by semilinear control

Abstract

Scopus Subject Areas

Keywords

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