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Dynamic analysis of the dual Lorenz system

Faculty of Computer Sciences, Goce Delc̆ev, University Stip, Republic of North Macedonia

E-mail Address: biljana.zlatanovska@ugd.edu.mk

Corresponding author.

and

Faculty of Electrical Engineering and Information Technologies, Ss Cyril and Methodius, University, Skopje, Republic of North Macedonia

E-mail Address: borom@feit.ukim.edu.mk

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https://doi.org/10.1142/S1793557120501715Cited by:5 (Source: Crossref)

Abstract

The dual Lorenz system as an autonomous system of three differential equations is obtained by using the Lorenz system of differential equations in the paper [B. M. Piperevski, For one system of differential equations taken as dual of the Lorenz system, Bull. Math.40(1) (2014) 37–44]. In this paper, we will do a comparison of the dual Lorenz system with the Lorenz system for different values of parameters. The dynamic analysis of its behavior will be done. The basic properties of the dual Lorenz system are analyzed by means of the symmetry of the system, dissipativity of the system, the Lyapunov function, the behavior of the system in the neighborhood of fixed points, etc. By using mathematical software Mathematica, we will give a graphical visualization of the dual Lorenz system for some values of parameters via examples.

Communicated by J. Koppitz

Keywords:

AMSC: 34A34, 37C10, 37C37

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