Complex Chaotic Attractor via Fractal Transformation
Based on simplified Lorenz multiwing and Chua multiscroll chaotic systems, a rotation compound chaotic system is presented via transformation. Based on a binary fractal algorithm, a new ternary fractal algorithm is proposed. In the ternary fractal algorithm, the number of input sequences is extended...
Saved in:
| Published in: | Entropy (Basel, Switzerland) Vol. 21; no. 11; p. 1115 |
|---|---|
| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Basel
MDPI AG
14.11.2019
MDPI |
| Subjects: | |
| ISSN: | 1099-4300, 1099-4300 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | Based on simplified Lorenz multiwing and Chua multiscroll chaotic systems, a rotation compound chaotic system is presented via transformation. Based on a binary fractal algorithm, a new ternary fractal algorithm is proposed. In the ternary fractal algorithm, the number of input sequences is extended from 2 to 3, which means the chaotic attractor with fractal transformation can be presented in the three-dimensional space. Taking Lorenz system, rotation Lorenz system and compound chaotic system as the seed chaotic systems, the dynamics of the complex chaotic attractors with fractal transformation are analyzed by means of bifurcation diagram, complexity and power spectrum, and the results show that the chaotic sequences with fractal transformation have higher complexity. As the experimental verification, one kind of complex chaotic attractors is implemented by DSP, and the result is consistent with that of the simulation, which verifies the feasibility of digital circuit implement. |
|---|---|
| AbstractList | Based on simplified Lorenz multiwing and Chua multiscroll chaotic systems, a rotation compound chaotic system is presented via transformation. Based on a binary fractal algorithm, a new ternary fractal algorithm is proposed. In the ternary fractal algorithm, the number of input sequences is extended from 2 to 3, which means the chaotic attractor with fractal transformation can be presented in the three-dimensional space. Taking Lorenz system, rotation Lorenz system and compound chaotic system as the seed chaotic systems, the dynamics of the complex chaotic attractors with fractal transformation are analyzed by means of bifurcation diagram, complexity and power spectrum, and the results show that the chaotic sequences with fractal transformation have higher complexity. As the experimental verification, one kind of complex chaotic attractors is implemented by DSP, and the result is consistent with that of the simulation, which verifies the feasibility of digital circuit implement. |
| Author | Ai, Wei Dai, Shengqiu He, Shaobo Sun, Kehui |
| AuthorAffiliation | School of Physics and Electronics, Central South University, Changsha 410083, China; shengqiu@csu.edu.cn (S.D.); heshaobo_123@163.com (S.H.); aiwei123@csu.edu.cn (W.A.) |
| AuthorAffiliation_xml | – name: School of Physics and Electronics, Central South University, Changsha 410083, China; shengqiu@csu.edu.cn (S.D.); heshaobo_123@163.com (S.H.); aiwei123@csu.edu.cn (W.A.) |
| Author_xml | – sequence: 1 givenname: Shengqiu surname: Dai fullname: Dai, Shengqiu – sequence: 2 givenname: Kehui surname: Sun fullname: Sun, Kehui – sequence: 3 givenname: Shaobo orcidid: 0000-0001-5190-4841 surname: He fullname: He, Shaobo – sequence: 4 givenname: Wei surname: Ai fullname: Ai, Wei |
| BookMark | eNptkE1LAzEQhoNUsK0e_AcLnjys5ns3F6EsVoWCl3oO2TRrU3aTmk2L_nvTD4qKc5mBeeedh3cEBs47A8A1gneECHhvMNoXOwNDBIXIKYFw8GO-AKO-X0GICUZ8CGjlu3VrPrNqqXy0OpvEGJSOPmRbq7LpblZtNg_K9Y0PnYrWu0tw3qi2N1fHPgZv08d59ZzPXp9eqsks14QWMaeFopoRrEpWY4MwKXmDjaYa1ZxyvhBC1QiWhi0YaRIPUayBlNNSUcOEIWQMHg6-603dmYU2LrG1ch1sp8KX9MrK3xtnl_Ldb2XBEKUcJoObo0HwHxvTR7nym-ASs8SMlkTgEhZJdXtQ6eD7Ppjm9AFBuUtVnlJN2vs_Wm3jPpQEYNt_Lr4BNwF6Vg |
| CitedBy_id | crossref_primary_10_1016_j_physa_2024_129586 crossref_primary_10_1088_1402_4896_ab842e crossref_primary_10_1109_TCSII_2021_3082271 crossref_primary_10_3390_e25091261 crossref_primary_10_1016_j_physa_2023_128688 crossref_primary_10_1007_s11063_021_10568_w crossref_primary_10_1016_j_cjph_2024_04_003 crossref_primary_10_1142_S0218127425500166 crossref_primary_10_1007_s11128_024_04492_w crossref_primary_10_1109_TVLSI_2021_3106312 crossref_primary_10_1140_epjp_s13360_021_01503_y crossref_primary_10_3390_mi15030401 crossref_primary_10_1007_s11128_024_04328_7 crossref_primary_10_1140_epjs_s11734_022_00651_1 crossref_primary_10_1016_j_chaos_2023_114084 crossref_primary_10_1109_JIOT_2024_3506567 crossref_primary_10_1140_epjs_s11734_022_00615_5 crossref_primary_10_1007_s11071_021_07149_w crossref_primary_10_1088_1402_4896_ad9ef5 crossref_primary_10_1007_s11128_022_03823_z crossref_primary_10_1088_1402_4896_ad0c10 crossref_primary_10_1007_s11128_023_04110_1 |
| Cites_doi | 10.1142/S0218127415300025 10.1142/S0217979208039575 10.1103/PhysRevLett.88.174102 10.1007/s11071-012-0562-4 10.3390/e21090819 10.1016/j.chaos.2017.11.027 10.1140/epjp/i2017-11310-7 10.1016/j.ijleo.2016.10.085 10.1142/S0218127409023688 10.1142/S0218127414501314 10.1109/TCSII.2014.2345307 10.1016/j.proeng.2012.01.071 10.1142/S0218127407019809 10.1016/j.jfranklin.2013.04.018 10.1142/S0218127412501209 10.7498/aps.63.040503 10.1063/1.4958717 10.4028/www.scientific.net/AMM.716-717.1352 10.1119/1.13295 10.1063/1.4979039 10.1142/S0218127410025387 10.1142/S0129183118500493 10.1007/s12043-015-1118-1 10.1007/s11071-016-2852-8 10.1007/s11071-016-2861-7 10.1007/s11071-016-3094-5 10.3390/e17127882 10.1016/j.chaos.2010.12.005 10.1109/TCS.1984.1085459 10.1142/S0218127410027039 10.1016/0167-2789(85)90011-9 10.1142/S0218127414500485 10.1063/1.4923302 10.1007/s11071-014-1260-1 10.1103/PhysRevLett.117.091601 10.1142/S021812741530027X 10.1063/1.4958296 |
| ContentType | Journal Article |
| Copyright | 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. 2019 by the authors. 2019 |
| Copyright_xml | – notice: 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. – notice: 2019 by the authors. 2019 |
| DBID | AAYXX CITATION 7TB 8FD 8FE 8FG ABJCF ABUWG AFKRA AZQEC BENPR BGLVJ CCPQU DWQXO FR3 HCIFZ KR7 L6V M7S PHGZM PHGZT PIMPY PKEHL PQEST PQGLB PQQKQ PQUKI PRINS PTHSS 5PM |
| DOI | 10.3390/e21111115 |
| DatabaseName | CrossRef Mechanical & Transportation Engineering Abstracts Technology Research Database ProQuest SciTech Collection ProQuest Technology Collection Materials Science & Engineering Collection (subscription) ProQuest Central (Alumni) ProQuest Central UK/Ireland ProQuest Central Essentials ProQuest Central ProQuest Technology Collection ProQuest One Community College ProQuest Central Engineering Research Database SciTech Premium Collection Civil Engineering Abstracts ProQuest Engineering Collection Engineering Database (subscription) ProQuest Databases ProQuest One Academic (New) Publicly Available Content Database ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition ProQuest Central China Engineering Collection PubMed Central (Full Participant titles) |
| DatabaseTitle | CrossRef Publicly Available Content Database Technology Collection Technology Research Database ProQuest One Academic Middle East (New) Mechanical & Transportation Engineering Abstracts ProQuest Central Essentials ProQuest Central (Alumni Edition) SciTech Premium Collection ProQuest One Community College ProQuest Central China ProQuest Central ProQuest One Applied & Life Sciences ProQuest Engineering Collection ProQuest Central Korea ProQuest Central (New) Engineering Collection Civil Engineering Abstracts Engineering Database ProQuest One Academic Eastern Edition ProQuest Technology Collection ProQuest SciTech Collection ProQuest One Academic UKI Edition Materials Science & Engineering Collection Engineering Research Database ProQuest One Academic ProQuest One Academic (New) |
| DatabaseTitleList | CrossRef Publicly Available Content Database |
| Database_xml | – sequence: 1 dbid: PIMPY name: Publicly Available Content Database url: http://search.proquest.com/publiccontent sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| EISSN | 1099-4300 |
| ExternalDocumentID | PMC7514460 10_3390_e21111115 |
| GroupedDBID | 29G 2WC 5GY 5VS 8FE 8FG AADQD AAFWJ AAYXX ABDBF ABJCF ACIWK ACUHS ADBBV AEGXH AENEX AFFHD AFKRA AFPKN AFZYC ALMA_UNASSIGNED_HOLDINGS BCNDV BENPR BGLVJ CCPQU CITATION CS3 DU5 E3Z ESX F5P GROUPED_DOAJ GX1 HCIFZ HH5 IAO J9A KQ8 L6V M7S MODMG M~E OK1 OVT PGMZT PHGZM PHGZT PIMPY PQGLB PROAC PTHSS RNS RPM TR2 TUS XSB ~8M 7TB 8FD ABUWG AZQEC DWQXO FR3 KR7 PKEHL PQEST PQQKQ PQUKI PRINS 5PM |
| ID | FETCH-LOGICAL-c347t-47a4c532a85b2e12386f2ec4c1b6466d99ab108e5d53f2323a5f04648a4e59e33 |
| IEDL.DBID | BENPR |
| ISICitedReferencesCount | 25 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000502145000088&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1099-4300 |
| IngestDate | Tue Nov 04 02:04:03 EST 2025 Fri Jul 25 11:52:53 EDT 2025 Tue Nov 18 22:02:23 EST 2025 Sat Nov 29 07:15:13 EST 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 11 |
| Language | English |
| License | Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c347t-47a4c532a85b2e12386f2ec4c1b6466d99ab108e5d53f2323a5f04648a4e59e33 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0001-5190-4841 |
| OpenAccessLink | https://www.proquest.com/docview/2548392807?pq-origsite=%requestingapplication% |
| PQID | 2548392807 |
| PQPubID | 2032401 |
| ParticipantIDs | pubmedcentral_primary_oai_pubmedcentral_nih_gov_7514460 proquest_journals_2548392807 crossref_primary_10_3390_e21111115 crossref_citationtrail_10_3390_e21111115 |
| PublicationCentury | 2000 |
| PublicationDate | 20191114 |
| PublicationDateYYYYMMDD | 2019-11-14 |
| PublicationDate_xml | – month: 11 year: 2019 text: 20191114 day: 14 |
| PublicationDecade | 2010 |
| PublicationPlace | Basel |
| PublicationPlace_xml | – name: Basel |
| PublicationTitle | Entropy (Basel, Switzerland) |
| PublicationYear | 2019 |
| Publisher | MDPI AG MDPI |
| Publisher_xml | – name: MDPI AG – name: MDPI |
| References | Yu (ref_7) 2010; 20 Zhou (ref_10) 2016; 85 Ai (ref_35) 2015; 25 Wang (ref_20) 2017; 27 Sun (ref_34) 2009; 19 Zhang (ref_8) 2017; 132 Matsumoto (ref_37) 1984; 31 Ma (ref_25) 2014; 76 Bouallegue (ref_30) 2015; 25 Wang (ref_12) 2008; 22 Chen (ref_19) 2016; 26 Hong (ref_26) 2017; 87 Ai (ref_38) 2014; 63 (ref_23) 2013; 350 Chen (ref_16) 2016; 130 He (ref_32) 2015; 17 Li (ref_1) 2014; 24 Blake (ref_2) 2016; 117 Bouallegue (ref_29) 2011; 44 Zuo (ref_4) 2014; 61 Zhang (ref_9) 2016; 25 Yuan (ref_11) 2016; 26 Yadav (ref_5) 2017; 53 Gao (ref_33) 2014; 716 Bandt (ref_42) 2002; 88 Bao (ref_13) 2010; 20 ref_3 Wolf (ref_36) 1985; 16 Kengne (ref_15) 2018; 106 (ref_22) 2012; 70 Bouallegue (ref_31) 2015; 25 ref_27 (ref_21) 2016; 28 Lin (ref_40) 2016; 86 Guo (ref_28) 2016; 85 Yu (ref_14) 2007; 17 Ai (ref_6) 2018; 29 (ref_24) 2014; 233 Zhang (ref_39) 2012; 22 Sun (ref_41) 2013; 62 Shen (ref_17) 2014; 24 Liu (ref_18) 2012; 29 |
| References_xml | – volume: 53 start-page: 594 year: 2017 ident: ref_5 article-title: Stability analysis, chaos control of a fractional order chaotic chemical reactor system and its function projective synchronization with parametric uncertainties publication-title: Acta Phys. Sin. – volume: 25 start-page: 1530002 year: 2015 ident: ref_31 article-title: Gallery of chaotic attractors generated by fractal network publication-title: Int. J. Bifurcat. Chaos doi: 10.1142/S0218127415300025 – volume: 22 start-page: 2399 year: 2008 ident: ref_12 article-title: Generation of multi-scroll chaotic attractors via the saw-tooth function publication-title: Int. J. Mod. Phys. B doi: 10.1142/S0217979208039575 – volume: 88 start-page: 174102 year: 2002 ident: ref_42 article-title: Permutation entropy: A natural complexity measure for time series publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.88.174102 – volume: 70 start-page: 1633 year: 2012 ident: ref_22 article-title: Synchronization of PWL function-based 2D and 3D multi-scroll chaotic systems publication-title: Nonlinear Dyn. doi: 10.1007/s11071-012-0562-4 – volume: 62 start-page: 709 year: 2013 ident: ref_41 article-title: Complexity analysis of chaotic pseudo-random sequences based on spectral entropy algorithm publication-title: Acta Phys. Sin. – ident: ref_3 doi: 10.3390/e21090819 – volume: 106 start-page: 201 year: 2018 ident: ref_15 article-title: A plethora of coexisting strange attractors in a simple Jerk system with hyperbolic tangent nonlinearity publication-title: Chaos Soliton Fract. doi: 10.1016/j.chaos.2017.11.027 – volume: 132 start-page: 31 year: 2017 ident: ref_8 article-title: Solution and dynamics of a fractional-order 5-D hyperchaotic system with four wings publication-title: Eur. Phys. J. Plus doi: 10.1140/epjp/i2017-11310-7 – volume: 130 start-page: 594 year: 2016 ident: ref_16 article-title: Generation of grid multi-scroll chaotic attractors via hyperbolic tangent function series publication-title: Optik doi: 10.1016/j.ijleo.2016.10.085 – volume: 19 start-page: 1357 year: 2009 ident: ref_34 article-title: Dynamics of a simplified Lorenz system publication-title: Int. J. Bifurcat. Chaos doi: 10.1142/S0218127409023688 – volume: 24 start-page: 1450131 year: 2014 ident: ref_1 article-title: Multistability in the Lorenz system: A broken butterfly publication-title: Int. J. Bifurcat. Chaos doi: 10.1142/S0218127414501314 – volume: 61 start-page: 818 year: 2014 ident: ref_4 article-title: High-order grid multiscroll chaotic attractors generated by the second-generation current conveyor circuit publication-title: IEEE Trans. Circuits Syst. doi: 10.1109/TCSII.2014.2345307 – volume: 29 start-page: 957 year: 2012 ident: ref_18 article-title: Research on the multi-scroll chaos generation based on Jerk model publication-title: Procedia Eng. doi: 10.1016/j.proeng.2012.01.071 – volume: 17 start-page: 3951 year: 2007 ident: ref_14 article-title: Generation of nm-scroll attractors under a Chua-circuit framework publication-title: Int. J. Bifurcat. Chaos doi: 10.1142/S0218127407019809 – volume: 350 start-page: 2867 year: 2013 ident: ref_23 article-title: Preservation of a two-wing Lorenz-like attractor with stable equilibria publication-title: J. Frankl. Inst. doi: 10.1016/j.jfranklin.2013.04.018 – volume: 22 start-page: 367 year: 2012 ident: ref_39 article-title: Design and implementation of compound chaotic attractors publication-title: Int. J. Bifurcat. Chaos doi: 10.1142/S0218127412501209 – volume: 63 start-page: 40503 year: 2014 ident: ref_38 article-title: Compound attractors between different chaotic systems publication-title: Acta Phys. Sin. doi: 10.7498/aps.63.040503 – volume: 26 start-page: 084303 year: 2016 ident: ref_19 article-title: Design and implementation of grid multi-scroll fractional-order chaotic attractors publication-title: Chaos doi: 10.1063/1.4958717 – volume: 716 start-page: 1352 year: 2014 ident: ref_33 article-title: Realization of digital chaotic signal generation circuits publication-title: Appl. Mech. Mater. doi: 10.4028/www.scientific.net/AMM.716-717.1352 – ident: ref_27 doi: 10.1119/1.13295 – volume: 27 start-page: 33114 year: 2017 ident: ref_20 article-title: Multi-piecewise quadratic nonlinearity memristor and its 2n-scroll and 2n+1-scroll chaotic attractors system publication-title: Chaos doi: 10.1063/1.4979039 – volume: 20 start-page: 1002538 year: 2010 ident: ref_7 article-title: Design and implementation of multiwing butterfly chaotic attractors via Lorenz-type systems publication-title: Int. J. Bifurcat. Chaos doi: 10.1142/S0218127410025387 – volume: 29 start-page: 1850049 year: 2018 ident: ref_6 article-title: Design of multiwing-multiscroll grid compound chaotic system and its circuit implementation publication-title: Int. J. Mod. Phys. C doi: 10.1142/S0129183118500493 – volume: 86 start-page: 801 year: 2016 ident: ref_40 article-title: A novel four-wing non-equilibrium chaotic system and its circuit implementation publication-title: Pramana doi: 10.1007/s12043-015-1118-1 – volume: 85 start-page: 1 year: 2016 ident: ref_10 article-title: Generating hyperchaotic multi-wing attractor in a 4D memristive circuit publication-title: Nonlinear Dyn. doi: 10.1007/s11071-016-2852-8 – volume: 85 start-page: 1 year: 2016 ident: ref_28 article-title: A multi-wing spherical chaotic system using fractal process publication-title: Nonlinear Dyn. doi: 10.1007/s11071-016-2861-7 – volume: 87 start-page: 1015 year: 2017 ident: ref_26 article-title: A novel approach for generating multi-direction multi-double-scroll attractors publication-title: Nonlinear Dyn. doi: 10.1007/s11071-016-3094-5 – volume: 17 start-page: 8299 year: 2015 ident: ref_32 article-title: Complexity analysis and DSP implementation of the fractional-order Lorenz hyperchaotic system publication-title: Entropy doi: 10.3390/e17127882 – volume: 44 start-page: 79 year: 2011 ident: ref_29 article-title: Multi-scroll and multi-wing chaotic attractor generated with Julia process fractal publication-title: Chaos Soliton Fract. doi: 10.1016/j.chaos.2010.12.005 – volume: 31 start-page: 1055 year: 1984 ident: ref_37 article-title: A chaotic attractor from Chua’s circuit publication-title: IEEE Trans. Circuits Syst. doi: 10.1109/TCS.1984.1085459 – volume: 20 start-page: 2203 year: 2010 ident: ref_13 article-title: Multiscroll chaotic attractors from a modified colpitts oscillator model publication-title: Int. J. Bifurcat. Chaos doi: 10.1142/S0218127410027039 – volume: 28 start-page: 1750008 year: 2016 ident: ref_21 article-title: Generation of chaotic attractors without equilibria via piecewise linear systems publication-title: Int. J. Mod Phys. C – volume: 16 start-page: 285 year: 1985 ident: ref_36 article-title: Determining Lyapounov exponents from a time series publication-title: Physica D doi: 10.1016/0167-2789(85)90011-9 – volume: 24 start-page: 1450048 year: 2014 ident: ref_17 article-title: Design and circuit implementation of discrete-time chaotic systems with modulus of triangular wave functions publication-title: Int. J. Bifurcat. Chaos doi: 10.1142/S0218127414500485 – volume: 25 start-page: 83 year: 2016 ident: ref_9 article-title: A novel methodology for constructing a multi-wing chaotic and hyperchaotic system with a unified step function switching control publication-title: Chin. Phys. B – volume: 25 start-page: 073108 year: 2015 ident: ref_30 article-title: Chaotic attractors with separated scrolls publication-title: Chaos doi: 10.1063/1.4923302 – volume: 76 start-page: 1951 year: 2014 ident: ref_25 article-title: Selection of multi-scroll attractors in Jerk circuits and their verification using Pspice publication-title: Nonlinear Dyn. doi: 10.1007/s11071-014-1260-1 – volume: 117 start-page: 1465 year: 2016 ident: ref_2 article-title: Universal charge diffusion and the butterfly effect in holographic theories publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.117.091601 – volume: 25 start-page: 1530027 year: 2015 ident: ref_35 article-title: Design of grid multiscroll chaotic attractors via transformations publication-title: Int. J. Bifurcat. Chaos doi: 10.1142/S021812741530027X – volume: 233 start-page: 522 year: 2014 ident: ref_24 article-title: A family of hyperchaotic multi-scroll attractors in Rn publication-title: Appl. Math. Comput. – volume: 26 start-page: 073107 year: 2016 ident: ref_11 article-title: Extreme multistability in a memristor-based multi-scroll hyper-chaotic system publication-title: Chaos doi: 10.1063/1.4958296 |
| SSID | ssj0023216 |
| Score | 2.328633 |
| Snippet | Based on simplified Lorenz multiwing and Chua multiscroll chaotic systems, a rotation compound chaotic system is presented via transformation. Based on a... |
| SourceID | pubmedcentral proquest crossref |
| SourceType | Open Access Repository Aggregation Database Enrichment Source Index Database |
| StartPage | 1115 |
| SubjectTerms | Algorithms Chaos theory Complexity Design Digital electronics Digital signal processors Fractal analysis Fractal transforms Fractals Lorenz system Rotation Sequences Variables |
| Title | Complex Chaotic Attractor via Fractal Transformation |
| URI | https://www.proquest.com/docview/2548392807 https://pubmed.ncbi.nlm.nih.gov/PMC7514460 |
| Volume | 21 |
| WOSCitedRecordID | wos000502145000088&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVAON databaseName: DOAJ Directory of Open Access Journals customDbUrl: eissn: 1099-4300 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0023216 issn: 1099-4300 databaseCode: DOA dateStart: 20160101 isFulltext: true titleUrlDefault: https://www.doaj.org/ providerName: Directory of Open Access Journals – providerCode: PRVHPJ databaseName: ROAD: Directory of Open Access Scholarly Resources customDbUrl: eissn: 1099-4300 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0023216 issn: 1099-4300 databaseCode: M~E dateStart: 19990101 isFulltext: true titleUrlDefault: https://road.issn.org providerName: ISSN International Centre – providerCode: PRVPQU databaseName: Engineering Database (subscription) customDbUrl: eissn: 1099-4300 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0023216 issn: 1099-4300 databaseCode: M7S dateStart: 19990301 isFulltext: true titleUrlDefault: http://search.proquest.com providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: eissn: 1099-4300 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0023216 issn: 1099-4300 databaseCode: BENPR dateStart: 19990301 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVPQU databaseName: Publicly Available Content Database customDbUrl: eissn: 1099-4300 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0023216 issn: 1099-4300 databaseCode: PIMPY dateStart: 19990301 isFulltext: true titleUrlDefault: http://search.proquest.com/publiccontent providerName: ProQuest |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3NS8MwFA-6efDiBypO5yjiwUvZ0iRNcpI5NhR0FJ0wTyXNUjYY7dzq8OTfbtJl3QrixR5K4b2G8svHey95_T0AbuSIE4Wx52IaMRfHErlCiMiFVFKKUMSUzHv6ifb7bDjkgd1wW9i0yvWamC_Uo1SaPfKmDmSMLWctejf7cE3VKHO6akto7IKqYSrDFVC97_aDlyLkQh70V3xCSAf3TeXB_CJlK7RxLcuJkVuWpnf43288AgfWx3Taq0FxDHZUcgKwmflT9eV0xiLVAqedZfO82I6znAinZ571S4MtRzZNTsFbrzvoPLi2ZIIrEaaZRlxgSZAnGIk8pa0S82NPSSxh5GPfH3EuIthiiowIijU6SJDYHG4ygRXhCqEzUEnSRJ0DR8CYcMikRIpojUhQHzLBY0ojSRVlNXC7hjCUlk_clLWYhjquMGiHBdo1cF2ozlYkGr8p1deghnYeLcINojVAS31TNGT4scuSZDLOebIpMcFu6-Lvhi_BvnaCuPm_EOI6qGTzT3UF9uQymyzmDTugGnms3jCZoa_m_t3VkuDxOXj_AS4n3FM |
| linkProvider | ProQuest |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V3fS8MwED5EBX3xBypOpxZR8KW4NEmTPIiM6XBsDsEJe6tplrKBdLrVqf-Uf6NJ184VxDcf7FMh1xD6Hd_dJZc7gBPVE1QT4rmEhdwlkcKulDJ0EVOMYRxyrVKkW6zd5t2uuFuAz_wujE2rzDkxJereUNk98nMTyFhbzivs8vnFtV2j7Olq3kJjqhZN_fFmQrbxRePK4HvqefXrTu3GzboKuAoTlphFSaIo9iSnoacNcXM_8rQiCoU-8f2eEDJEFa5pj-LI-BtY0sie_3FJNBXaboAayl8ilv3TVMH7WYCHPeRPqxdhLCrn2kPpQ4s279uRLaZhztm1-vp_-yMbsJZ50E51qvKbsKDjLSCW1570u1Pry6EZcKpJMkpbCTmTgXTq9t181Jlz04fxNjz8yUJ3YDEexnoXHIkiKhBXCmtqJELJfMSliBgLFdOMl-AshyxQWbV027TjKTBRk0U3mKFbguOZ6PO0RMhPQuUcxCBjiXHwjWAJWEEXZhPZ6t_FkXjQT6uAM2pD-cre7xMfwcpN57YVtBrt5j6sGndP2JuUiJRhMRm96gNYVpNkMB4dpqrswONfa8oXU_ExLw |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V3dS8MwED-GivjiByrOzyIKvpQtTdIkDyLiHI6NMXCCbzXNUjYY7dzq17_mX2fStXMD8c0H-1TINYT8rr_cJZc7gDPVE1QT4rmEhdwlkcKulDJ0EVOMYRxyrTKkW6zd5o-PolOCz-IujA2rLDgxI-peouweecU4MnYt51VWifKwiE6tfjV6dm0FKXvSWpTTmKpIU3-8GfdtctmoGazPPa9-2725c_MKA67ChKVmgJIoij3JaehpQ-LcjzytiEKhT3y_J4QMUZVr2qM4MrYHljSyZ4FcEk2Ftpuhhv6XGTF2QhY2eD9z9rCH_GkmI4xFtaI9lD10cf37NmoXQzLn1rj6xn-enU1Yzy1r53r6K2xBScfbQCzfDfW7c9OXiWlwrtN0nJUYcl4H0qnbd_NRd858T-IdePiTge7CUpzEeg8ciSIqEFcKa2okQsl8xKWIGAsV04yX4aKAL1B5FnVbzGMYGG_KIh3MkC7D6Ux0NE0d8pPQYQFokLPHJPhGswxsQS9mHdms4Ist8aCfZQdn1Lr41f3fOz6BVaMgQavRbh7AmrEChb1gicghLKXjF30EK-o1HUzGx5lWO_D014ryBQhQOfU |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Complex+Chaotic+Attractor+via+Fractal+Transformation&rft.jtitle=Entropy+%28Basel%2C+Switzerland%29&rft.au=Dai%2C+Shengqiu&rft.au=Sun%2C+Kehui&rft.au=He%2C+Shaobo&rft.au=Ai%2C+Wei&rft.date=2019-11-14&rft.pub=MDPI&rft.eissn=1099-4300&rft.volume=21&rft.issue=11&rft_id=info:doi/10.3390%2Fe21111115&rft.externalDocID=PMC7514460 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1099-4300&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1099-4300&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1099-4300&client=summon |