Different types of critical behavior in conservatively coupled H\'enon maps

Different types of critical behavior in conservatively coupled Hénon maps

Dmitry V. Savin, Alexander P. Kuznetsov, Alexey V. Savin, and Ulrike Feudel

Phys. Rev. E 91, 062905 – Published 5 June 2015

Abstract

We study the dynamics of two conservatively coupled Hénon maps at different levels of dissipation. It is shown that the decrease of dissipation leads to changes in the structure of the parameter plane and the scenarios of transition to chaos compared to the case of infinitely strong dissipation. Particularly, the Feigenbaum line becomes divided into several fragments. Some of these fragments have critical points of different types, namely, of C and H type, as their terminal points. Also the mechanisms of formation of these Feigenbaum line ruptures are described.

1 More

Received 30 August 2014

DOI:https://doi.org/10.1103/PhysRevE.91.062905

Authors & Affiliations

Dmitry V. Savin^1,*, Alexander P. Kuznetsov^1,2, Alexey V. Savin¹, and Ulrike Feudel³

¹Department of Nonlinear Processes, Chernyshevsky Saratov State University, Astrakhanskaya Street 83, 410012, Saratov, Russia
²Kotel'nikov Institute of Radioengineering and Electronics of RAS, Saratov Branch, Zelenaya Street 38, 410019, Saratov, Russia
³Institute for Chemistry and Biology of the Marine Environment, Carl von Ossietzky University Oldenburg, Carl von Ossietzky Street 9-11, D-26111, Oldenburg, Germany

^*Corresponding author: savin.dmitry.v@gmail.com

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 91, Iss. 6 — June 2015

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Physical Review E

covering statistical, nonlinear, biological, and soft matter physics

Different types of critical behavior in conservatively coupled Hénon maps

Dmitry V. Savin, Alexander P. Kuznetsov, Alexey V. Savin, and Ulrike Feudel

Phys. Rev. E 91, 062905 – Published 5 June 2015

Abstract

Authors & Affiliations

Article Text (Subscription Required)

References (Subscription Required)

Issue

Access Options

Physical Review E

covering statistical, nonlinear, biological, and soft matter physics

Different types of critical behavior in conservatively coupled Hénon maps

Dmitry V. Savin, Alexander P. Kuznetsov, Alexey V. Savin, and Ulrike Feudel

Phys. Rev. E 91, 062905 – Published 5 June 2015

Abstract

Authors & Affiliations

Article Text (Subscription Required)

References (Subscription Required)

Issue

Access Options

Authorization Required

Other Options

Download & Share

Images

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Log In

Search

Article Lookup

Paste a citation or DOI

Enter a citation