Coexisting Infinite Orbits in an Area-Preserving Lozi Map

Coexisting Infinite Orbits in an Area-Preserving Lozi Map

Extreme multistability with coexisting infinite orbits has been reported in many continuous memristor-based dynamical circuits and systems, but rarely in discrete dynamical systems. This paper reports the finding of initial values-related coexisting infinite orbits in an area-preserving Lozi map und...

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Main Authors: Houzhen Li, Kexin Li, Mo Chen, Bocheng Bao
Format: Article
Language:English
Published: MDPI AG 2020-10-01
Series:Entropy
Subjects:
discrete maps
coexisting orbits
initial values
complexity
hardware platform
Online Access:https://www.mdpi.com/1099-4300/22/10/1119
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spelling doaj-b1c807e3fd7a4eecb2dbb18e0de457912020-11-25T03:41:07ZengMDPI AGEntropy1099-43002020-10-01221119111910.3390/e22101119Coexisting Infinite Orbits in an Area-Preserving Lozi MapHouzhen Li0Kexin Li1Mo Chen2Bocheng Bao3School of Microelectronics and Control Engineering, Changzhou University, Changzhou 213164, ChinaSchool of Microelectronics and Control Engineering, Changzhou University, Changzhou 213164, ChinaSchool of Microelectronics and Control Engineering, Changzhou University, Changzhou 213164, ChinaSchool of Microelectronics and Control Engineering, Changzhou University, Changzhou 213164, ChinaExtreme multistability with coexisting infinite orbits has been reported in many continuous memristor-based dynamical circuits and systems, but rarely in discrete dynamical systems. This paper reports the finding of initial values-related coexisting infinite orbits in an area-preserving Lozi map under specific parameter settings. We use the bifurcation diagram and phase orbit diagram to disclose the coexisting infinite orbits that include period, quasi-period and chaos with different types and topologies, and we employ the spectral entropy and sample entropy to depict the initial values-related complexity. Finally, a microprocessor-based hardware platform is developed to acquire four sets of four-channel voltage sequences by switching the initial values. The results show that the area-preserving Lozi map displays coexisting infinite orbits with complicated complexity distributions, which heavily rely on its initial values.https://www.mdpi.com/1099-4300/22/10/1119discrete mapscoexisting orbitsinitial valuescomplexityhardware platform
collection DOAJ
language English
format Article
sources DOAJ
author Houzhen Li
Kexin Li
Mo Chen
Bocheng Bao
spellingShingle Houzhen Li
Kexin Li
Mo Chen
Bocheng Bao
Coexisting Infinite Orbits in an Area-Preserving Lozi Map
Entropy
discrete maps
coexisting orbits
initial values
complexity
hardware platform
author_facet Houzhen Li
Kexin Li
Mo Chen
Bocheng Bao
author_sort Houzhen Li
title Coexisting Infinite Orbits in an Area-Preserving Lozi Map
title_short Coexisting Infinite Orbits in an Area-Preserving Lozi Map
title_full Coexisting Infinite Orbits in an Area-Preserving Lozi Map
title_fullStr Coexisting Infinite Orbits in an Area-Preserving Lozi Map
title_full_unstemmed Coexisting Infinite Orbits in an Area-Preserving Lozi Map
title_sort coexisting infinite orbits in an area-preserving lozi map
publisher MDPI AG
series Entropy
issn 1099-4300
publishDate 2020-10-01
description Extreme multistability with coexisting infinite orbits has been reported in many continuous memristor-based dynamical circuits and systems, but rarely in discrete dynamical systems. This paper reports the finding of initial values-related coexisting infinite orbits in an area-preserving Lozi map under specific parameter settings. We use the bifurcation diagram and phase orbit diagram to disclose the coexisting infinite orbits that include period, quasi-period and chaos with different types and topologies, and we employ the spectral entropy and sample entropy to depict the initial values-related complexity. Finally, a microprocessor-based hardware platform is developed to acquire four sets of four-channel voltage sequences by switching the initial values. The results show that the area-preserving Lozi map displays coexisting infinite orbits with complicated complexity distributions, which heavily rely on its initial values.
topic discrete maps
coexisting orbits
initial values
complexity
hardware platform
url https://www.mdpi.com/1099-4300/22/10/1119
work_keys_str_mv AT houzhenli coexistinginfiniteorbitsinanareapreservinglozimap
AT kexinli coexistinginfiniteorbitsinanareapreservinglozimap
AT mochen coexistinginfiniteorbitsinanareapreservinglozimap
AT bochengbao coexistinginfiniteorbitsinanareapreservinglozimap
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