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Homoclinic Bifurcations and Chaos in the Fishing Principle for the Lorenz-like Systems

G. A. Leonov

Faculty of Mathematics and Mechanics, St. Petersburg State University, Peterhof, St. Petersburg, Russia

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R. N. Mokaev

Faculty of Mathematics and Mechanics, St. Petersburg State University, Peterhof, St. Petersburg, Russia

Faculty of Information Technology, University of Jyväskylä, Jyväskylä, Finland

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N. V. Kuznetsov

http://orcid.org/0000-0002-6474-9657

Faculty of Mathematics and Mechanics, St. Petersburg State University, Peterhof, St. Petersburg, Russia

Faculty of Information Technology, University of Jyväskylä, Jyväskylä, Finland

Institute for Problems in Mechanical, Engineering RAS, Russia

E-mail Address: nkuznetsov239@gmail.com

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T. N. Mokaev

Faculty of Mathematics and Mechanics, St. Petersburg State University, Peterhof, St. Petersburg, Russia

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https://doi.org/10.1142/S0218127420501242Cited by:5 (Source: Crossref)

Abstract

In this article using an analytical method called Fishing principle we obtain the region of parameters, where the existence of a homoclinic orbit to a zero saddle equilibrium in the Lorenz-like system is proved. For a qualitative description of the different types of homoclinic bifurcations, a numerical analysis of the obtained region of parameters is organized, which leads to the discovery of new bifurcation scenarios.

Keywords:

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