An infinite 2-D lattice of strange attractors

An infinite 2-D lattice of strange attractors Periodic trigonometric functions are introduced in 2-D offset-boostable chaotic flows to generate an infinite 2-D lattice of strange attractors. These 2-D offset-boostable chaotic systems are constructed based on standard jerk flows and extended to more general systems by exhaustive computer searching. Two regimes of multistability with a lattice of strange attractors are explored where the infinitely many attractors come from a 2-D offset-boostable chaotic system in cascade or in an interactive mode. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nonlinear Dynamics Springer Journals

An infinite 2-D lattice of strange attractors

An infinite 2-D lattice of strange attractors

Nonlinear Dyn (2017) 89:2629–2639 DOI 10.1007/s11071-017-3612-0 ORIGINAL PAPER An infinite 2-D lattice of strange attractors Chunbiao Li · Julien Clinton Sprott · Yong Mei Received: 17 November 2016 / Accepted: 9 June 2017 / Published online: 24 June 2017 © Springer Science+Business Media B.V. 2017 Abstract Periodic trigonometric functions are intro- of the system cannot be guaranteed, since the system duced in 2-D offset-boostable chaotic flows to gener- may unpredictably visit its various solutions depend- ate an infinite 2-D lattice of strange attractors. These ing on the initial conditions. For this reason, multista- 2-D offset-boostable chaotic systems are constructed bility has recently been extensively studied, including based on standard jerk flows and extended to more gen- symmetric multistability [1–8], asymmetric multista- eral systems by exhaustive computer searching. Two bility [8–10], conditional symmetric multistability [11– regimes of multistability with a lattice of strange attrac- 13], delay or hysteresis-induced multistability [14–18], tors are explored where the infinitely many attractors driving-induced multistability [19], and extreme multi- come from a 2-D offset-boostable chaotic system in stability [20–23]. On the other hand, multistability may cascade or in an interactive mode. have applications to understanding memory [15,16], and it can enhance the performance of secure commu- Keywords Offset boosting · Multistability · nications when chaos is used to conceal information Infinitely many attractors since the initial conditions can provide an additional secret key. A multistable system can have multiple attractors, 1 Introduction even infinitely many attractors (a special case of which is known as extreme multistability [20–23]), or hidden Multistability in a dynamical system poses a threat in attractors [24–31] which cannot be found using initial...
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Publisher
Springer Netherlands
Copyright
Copyright © 2017 by Springer Science+Business Media B.V.
Subject
Engineering; Vibration, Dynamical Systems, Control; Classical Mechanics; Mechanical Engineering; Automotive Engineering
ISSN
0924-090X
eISSN
1573-269X
D.O.I.
10.1007/s11071-017-3612-0
Publisher site
See Article on Publisher Site

Abstract

Periodic trigonometric functions are introduced in 2-D offset-boostable chaotic flows to generate an infinite 2-D lattice of strange attractors. These 2-D offset-boostable chaotic systems are constructed based on standard jerk flows and extended to more general systems by exhaustive computer searching. Two regimes of multistability with a lattice of strange attractors are explored where the infinitely many attractors come from a 2-D offset-boostable chaotic system in cascade or in an interactive mode.

Journal

Nonlinear DynamicsSpringer Journals

Published: Jun 24, 2017

References

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