Dynamic Behavior of the Fractional-Order Ananthakrishna Model for Repeated Yielding Article Swipe
Hongyi Zhu
,
Li‐Ping Yu
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.3390/fractalfract9070425
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.3390/fractalfract9070425
This paper introduces and analyzes a novel fractional-order Ananthakrishna model. The stability of its equilibrium points is first investigated using fractional-order stability criteria, particularly in regions where the corresponding integer-order model exhibits instability. A linear finite difference scheme is then developed, incorporating an accelerated L1 method for the fractional derivative. This enables a detailed exploration of the model’s dynamic behavior in both the time domain and phase plane. Numerical simulations, including Lyapunov exponents, bifurcation diagrams, phase and time diagrams, demonstrate that the fractional model exhibits stable and periodic behaviors across various fractional orders. Notably, as the fractional order approaches a critical threshold, the time required to reach stability increases significantly, highlighting complex stability-transition dynamics. The computational efficiency of the proposed scheme is also validated, showing linear CPU time scaling with respect to the number of time steps, compared to the nearly quadratic growth of the classical L1 and Grünwald-Letnikow schemes, making it more suitable for long-term simulations of complex fractional-order models. Finally, four types of stress-time curves are simulated based on the fractional Ananthakrishna model, corresponding to both stable and unstable domains, effectively capturing and interpreting experimentally observed repeated yielding phenomena.
Related Topics
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.3390/fractalfract9070425
- OA Status
- gold
- References
- 42
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4411787179
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W4411787179Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.3390/fractalfract9070425Digital Object Identifier
- Title
-
Dynamic Behavior of the Fractional-Order Ananthakrishna Model for Repeated YieldingWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2025Year of publication
- Publication date
-
2025-06-28Full publication date if available
- Authors
-
Hongyi Zhu, Li‐Ping YuList of authors in order
- Landing page
-
https://doi.org/10.3390/fractalfract9070425Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
goldOpen access status per OpenAlex
- OA URL
-
https://doi.org/10.3390/fractalfract9070425Direct OA link when available
- Concepts
-
Order (exchange), Mathematics, Psychology, Econometrics, Economics, FinanceTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
0Total citation count in OpenAlex
- References (count)
-
42Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
Full payload
| id | https://openalex.org/W4411787179 |
|---|---|
| doi | https://doi.org/10.3390/fractalfract9070425 |
| ids.doi | https://doi.org/10.3390/fractalfract9070425 |
| ids.openalex | https://openalex.org/W4411787179 |
| fwci | 0.0 |
| type | article |
| title | Dynamic Behavior of the Fractional-Order Ananthakrishna Model for Repeated Yielding |
| awards[0].id | https://openalex.org/G76118270 |
| awards[0].funder_id | https://openalex.org/F4320321001 |
| awards[0].display_name | |
| awards[0].funder_award_id | 12001238 |
| awards[0].funder_display_name | National Natural Science Foundation of China |
| awards[1].id | https://openalex.org/G3678425248 |
| awards[1].funder_id | https://openalex.org/F4320323845 |
| awards[1].display_name | |
| awards[1].funder_award_id | 232300420346 |
| awards[1].funder_display_name | Natural Science Foundation of Henan Province |
| biblio.issue | 7 |
| biblio.volume | 9 |
| biblio.last_page | 425 |
| biblio.first_page | 425 |
| topics[0].id | https://openalex.org/T10288 |
| topics[0].field.id | https://openalex.org/fields/26 |
| topics[0].field.display_name | Mathematics |
| topics[0].score | 0.9969000220298767 |
| topics[0].domain.id | https://openalex.org/domains/3 |
| topics[0].domain.display_name | Physical Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/2611 |
| topics[0].subfield.display_name | Modeling and Simulation |
| topics[0].display_name | Fractional Differential Equations Solutions |
| funders[0].id | https://openalex.org/F4320321001 |
| funders[0].ror | https://ror.org/01h0zpd94 |
| funders[0].display_name | National Natural Science Foundation of China |
| funders[1].id | https://openalex.org/F4320323845 |
| funders[1].ror | |
| funders[1].display_name | Natural Science Foundation of Henan Province |
| is_xpac | False |
| apc_list.value | 1600 |
| apc_list.currency | CHF |
| apc_list.value_usd | 1732 |
| apc_paid.value | 1600 |
| apc_paid.currency | CHF |
| apc_paid.value_usd | 1732 |
| concepts[0].id | https://openalex.org/C182306322 |
| concepts[0].level | 2 |
| concepts[0].score | 0.6119310855865479 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q1779371 |
| concepts[0].display_name | Order (exchange) |
| concepts[1].id | https://openalex.org/C33923547 |
| concepts[1].level | 0 |
| concepts[1].score | 0.38587310910224915 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q395 |
| concepts[1].display_name | Mathematics |
| concepts[2].id | https://openalex.org/C15744967 |
| concepts[2].level | 0 |
| concepts[2].score | 0.36139845848083496 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q9418 |
| concepts[2].display_name | Psychology |
| concepts[3].id | https://openalex.org/C149782125 |
| concepts[3].level | 1 |
| concepts[3].score | 0.32256245613098145 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q160039 |
| concepts[3].display_name | Econometrics |
| concepts[4].id | https://openalex.org/C162324750 |
| concepts[4].level | 0 |
| concepts[4].score | 0.23667782545089722 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q8134 |
| concepts[4].display_name | Economics |
| concepts[5].id | https://openalex.org/C10138342 |
| concepts[5].level | 1 |
| concepts[5].score | 0.0 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q43015 |
| concepts[5].display_name | Finance |
| keywords[0].id | https://openalex.org/keywords/order |
| keywords[0].score | 0.6119310855865479 |
| keywords[0].display_name | Order (exchange) |
| keywords[1].id | https://openalex.org/keywords/mathematics |
| keywords[1].score | 0.38587310910224915 |
| keywords[1].display_name | Mathematics |
| keywords[2].id | https://openalex.org/keywords/psychology |
| keywords[2].score | 0.36139845848083496 |
| keywords[2].display_name | Psychology |
| keywords[3].id | https://openalex.org/keywords/econometrics |
| keywords[3].score | 0.32256245613098145 |
| keywords[3].display_name | Econometrics |
| keywords[4].id | https://openalex.org/keywords/economics |
| keywords[4].score | 0.23667782545089722 |
| keywords[4].display_name | Economics |
| language | en |
| locations[0].id | doi:10.3390/fractalfract9070425 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S4210227020 |
| locations[0].source.issn | 2504-3110 |
| locations[0].source.type | journal |
| locations[0].source.is_oa | True |
| locations[0].source.issn_l | 2504-3110 |
| locations[0].source.is_core | True |
| locations[0].source.is_in_doaj | True |
| locations[0].source.display_name | Fractal and Fractional |
| locations[0].source.host_organization | https://openalex.org/P4310310987 |
| locations[0].source.host_organization_name | Multidisciplinary Digital Publishing Institute |
| locations[0].source.host_organization_lineage | https://openalex.org/P4310310987 |
| locations[0].source.host_organization_lineage_names | Multidisciplinary Digital Publishing Institute |
| locations[0].license | cc-by |
| locations[0].pdf_url | |
| locations[0].version | publishedVersion |
| locations[0].raw_type | journal-article |
| locations[0].license_id | https://openalex.org/licenses/cc-by |
| locations[0].is_accepted | True |
| locations[0].is_published | True |
| locations[0].raw_source_name | Fractal and Fractional |
| locations[0].landing_page_url | https://doi.org/10.3390/fractalfract9070425 |
| locations[1].id | pmh:oai:doaj.org/article:a35fa61bee044f299bb991abad42badc |
| locations[1].is_oa | False |
| locations[1].source.id | https://openalex.org/S4306401280 |
| locations[1].source.issn | |
| locations[1].source.type | repository |
| locations[1].source.is_oa | False |
| locations[1].source.issn_l | |
| locations[1].source.is_core | False |
| locations[1].source.is_in_doaj | False |
| locations[1].source.display_name | DOAJ (DOAJ: Directory of Open Access Journals) |
| locations[1].source.host_organization | |
| locations[1].source.host_organization_name | |
| locations[1].license | |
| locations[1].pdf_url | |
| locations[1].version | submittedVersion |
| locations[1].raw_type | article |
| locations[1].license_id | |
| locations[1].is_accepted | False |
| locations[1].is_published | False |
| locations[1].raw_source_name | Fractal and Fractional, Vol 9, Iss 7, p 425 (2025) |
| locations[1].landing_page_url | https://doaj.org/article/a35fa61bee044f299bb991abad42badc |
| indexed_in | crossref, doaj |
| authorships[0].author.id | https://openalex.org/A5014699698 |
| authorships[0].author.orcid | https://orcid.org/0009-0001-7858-4996 |
| authorships[0].author.display_name | Hongyi Zhu |
| authorships[0].countries | CN |
| authorships[0].affiliations[0].institution_ids | https://openalex.org/I159948400 |
| authorships[0].affiliations[0].raw_affiliation_string | School of Intelligent Systems Science and Engineering, Jinan University, Zhuhai 519000, China |
| authorships[0].institutions[0].id | https://openalex.org/I159948400 |
| authorships[0].institutions[0].ror | https://ror.org/02xe5ns62 |
| authorships[0].institutions[0].type | education |
| authorships[0].institutions[0].lineage | https://openalex.org/I159948400 |
| authorships[0].institutions[0].country_code | CN |
| authorships[0].institutions[0].display_name | Jinan University |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Hongyi Zhu |
| authorships[0].is_corresponding | False |
| authorships[0].raw_affiliation_strings | School of Intelligent Systems Science and Engineering, Jinan University, Zhuhai 519000, China |
| authorships[1].author.id | https://openalex.org/A5101552651 |
| authorships[1].author.orcid | https://orcid.org/0000-0002-5073-8957 |
| authorships[1].author.display_name | Li‐Ping Yu |
| authorships[1].countries | CN |
| authorships[1].affiliations[0].institution_ids | https://openalex.org/I36152291 |
| authorships[1].affiliations[0].raw_affiliation_string | School of Artificial Intelligence and Big Data, Henan University of Technology, Zhengzhou 450001, China |
| authorships[1].institutions[0].id | https://openalex.org/I36152291 |
| authorships[1].institutions[0].ror | https://ror.org/05sbgwt55 |
| authorships[1].institutions[0].type | education |
| authorships[1].institutions[0].lineage | https://openalex.org/I36152291 |
| authorships[1].institutions[0].country_code | CN |
| authorships[1].institutions[0].display_name | Henan University of Technology |
| authorships[1].author_position | last |
| authorships[1].raw_author_name | Liping Yu |
| authorships[1].is_corresponding | False |
| authorships[1].raw_affiliation_strings | School of Artificial Intelligence and Big Data, Henan University of Technology, Zhengzhou 450001, China |
| has_content.pdf | False |
| has_content.grobid_xml | False |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://doi.org/10.3390/fractalfract9070425 |
| open_access.oa_status | gold |
| open_access.any_repository_has_fulltext | False |
| created_date | 2025-10-10T00:00:00 |
| display_name | Dynamic Behavior of the Fractional-Order Ananthakrishna Model for Repeated Yielding |
| has_fulltext | False |
| is_retracted | False |
| updated_date | 2025-11-06T03:46:38.306776 |
| primary_topic.id | https://openalex.org/T10288 |
| primary_topic.field.id | https://openalex.org/fields/26 |
| primary_topic.field.display_name | Mathematics |
| primary_topic.score | 0.9969000220298767 |
| primary_topic.domain.id | https://openalex.org/domains/3 |
| primary_topic.domain.display_name | Physical Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/2611 |
| primary_topic.subfield.display_name | Modeling and Simulation |
| primary_topic.display_name | Fractional Differential Equations Solutions |
| related_works | https://openalex.org/W2748952813, https://openalex.org/W4391375266, https://openalex.org/W1979597421, https://openalex.org/W2007980826, https://openalex.org/W2061531152, https://openalex.org/W3002753104, https://openalex.org/W2077600819, https://openalex.org/W2142036596, https://openalex.org/W2072657027, https://openalex.org/W2962838298 |
| cited_by_count | 0 |
| locations_count | 2 |
| best_oa_location.id | doi:10.3390/fractalfract9070425 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S4210227020 |
| best_oa_location.source.issn | 2504-3110 |
| best_oa_location.source.type | journal |
| best_oa_location.source.is_oa | True |
| best_oa_location.source.issn_l | 2504-3110 |
| best_oa_location.source.is_core | True |
| best_oa_location.source.is_in_doaj | True |
| best_oa_location.source.display_name | Fractal and Fractional |
| best_oa_location.source.host_organization | https://openalex.org/P4310310987 |
| best_oa_location.source.host_organization_name | Multidisciplinary Digital Publishing Institute |
| best_oa_location.source.host_organization_lineage | https://openalex.org/P4310310987 |
| best_oa_location.source.host_organization_lineage_names | Multidisciplinary Digital Publishing Institute |
| best_oa_location.license | cc-by |
| best_oa_location.pdf_url | |
| best_oa_location.version | publishedVersion |
| best_oa_location.raw_type | journal-article |
| best_oa_location.license_id | https://openalex.org/licenses/cc-by |
| best_oa_location.is_accepted | True |
| best_oa_location.is_published | True |
| best_oa_location.raw_source_name | Fractal and Fractional |
| best_oa_location.landing_page_url | https://doi.org/10.3390/fractalfract9070425 |
| primary_location.id | doi:10.3390/fractalfract9070425 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S4210227020 |
| primary_location.source.issn | 2504-3110 |
| primary_location.source.type | journal |
| primary_location.source.is_oa | True |
| primary_location.source.issn_l | 2504-3110 |
| primary_location.source.is_core | True |
| primary_location.source.is_in_doaj | True |
| primary_location.source.display_name | Fractal and Fractional |
| primary_location.source.host_organization | https://openalex.org/P4310310987 |
| primary_location.source.host_organization_name | Multidisciplinary Digital Publishing Institute |
| primary_location.source.host_organization_lineage | https://openalex.org/P4310310987 |
| primary_location.source.host_organization_lineage_names | Multidisciplinary Digital Publishing Institute |
| primary_location.license | cc-by |
| primary_location.pdf_url | |
| primary_location.version | publishedVersion |
| primary_location.raw_type | journal-article |
| primary_location.license_id | https://openalex.org/licenses/cc-by |
| primary_location.is_accepted | True |
| primary_location.is_published | True |
| primary_location.raw_source_name | Fractal and Fractional |
| primary_location.landing_page_url | https://doi.org/10.3390/fractalfract9070425 |
| publication_date | 2025-06-28 |
| publication_year | 2025 |
| referenced_works | https://openalex.org/W1972366002, https://openalex.org/W3022749001, https://openalex.org/W2016755336, https://openalex.org/W3002076527, https://openalex.org/W3154663709, https://openalex.org/W3007784796, https://openalex.org/W2731197913, https://openalex.org/W6782311182, https://openalex.org/W2489930379, https://openalex.org/W2784220585, https://openalex.org/W2976875602, https://openalex.org/W4313889737, https://openalex.org/W4391264761, https://openalex.org/W4394800136, https://openalex.org/W4399142575, https://openalex.org/W4307021529, https://openalex.org/W3213652266, https://openalex.org/W1969312973, https://openalex.org/W2165076033, https://openalex.org/W4205318556, https://openalex.org/W1975922398, https://openalex.org/W2062266804, https://openalex.org/W2065232540, https://openalex.org/W2511264644, https://openalex.org/W2757644851, https://openalex.org/W2589697132, https://openalex.org/W4391848701, https://openalex.org/W2581912600, https://openalex.org/W2593135059, https://openalex.org/W2963309992, https://openalex.org/W2550897446, https://openalex.org/W4405514497, https://openalex.org/W4392654682, https://openalex.org/W2991946954, https://openalex.org/W2741724023, https://openalex.org/W2595719915, https://openalex.org/W2036442409, https://openalex.org/W56786142, https://openalex.org/W2152254020, https://openalex.org/W2887320096, https://openalex.org/W2781303610, https://openalex.org/W3080404639 |
| referenced_works_count | 42 |
| abstract_inverted_index.A | 33 |
| abstract_inverted_index.a | 5, 52, 99 |
| abstract_inverted_index.L1 | 44, 146 |
| abstract_inverted_index.an | 42 |
| abstract_inverted_index.as | 94 |
| abstract_inverted_index.in | 24, 60 |
| abstract_inverted_index.is | 16, 38, 121 |
| abstract_inverted_index.it | 151 |
| abstract_inverted_index.of | 12, 55, 117, 134, 143, 157, 164 |
| abstract_inverted_index.on | 170 |
| abstract_inverted_index.to | 105, 131, 138, 176 |
| abstract_inverted_index.CPU | 126 |
| abstract_inverted_index.The | 10, 114 |
| abstract_inverted_index.and | 3, 65, 76, 86, 147, 179, 184 |
| abstract_inverted_index.are | 167 |
| abstract_inverted_index.for | 46, 154 |
| abstract_inverted_index.its | 13 |
| abstract_inverted_index.the | 27, 47, 56, 62, 81, 95, 102, 118, 132, 139, 144, 171 |
| abstract_inverted_index.This | 0, 50 |
| abstract_inverted_index.also | 122 |
| abstract_inverted_index.both | 61, 177 |
| abstract_inverted_index.four | 162 |
| abstract_inverted_index.more | 152 |
| abstract_inverted_index.that | 80 |
| abstract_inverted_index.then | 39 |
| abstract_inverted_index.time | 63, 77, 103, 127, 135 |
| abstract_inverted_index.with | 129 |
| abstract_inverted_index.based | 169 |
| abstract_inverted_index.first | 17 |
| abstract_inverted_index.model | 30, 83 |
| abstract_inverted_index.novel | 6 |
| abstract_inverted_index.order | 97 |
| abstract_inverted_index.paper | 1 |
| abstract_inverted_index.phase | 66, 75 |
| abstract_inverted_index.reach | 106 |
| abstract_inverted_index.types | 163 |
| abstract_inverted_index.using | 19 |
| abstract_inverted_index.where | 26 |
| abstract_inverted_index.across | 89 |
| abstract_inverted_index.curves | 166 |
| abstract_inverted_index.domain | 64 |
| abstract_inverted_index.finite | 35 |
| abstract_inverted_index.growth | 142 |
| abstract_inverted_index.linear | 34, 125 |
| abstract_inverted_index.making | 150 |
| abstract_inverted_index.method | 45 |
| abstract_inverted_index.model, | 174 |
| abstract_inverted_index.model. | 9 |
| abstract_inverted_index.nearly | 140 |
| abstract_inverted_index.number | 133 |
| abstract_inverted_index.plane. | 67 |
| abstract_inverted_index.points | 15 |
| abstract_inverted_index.scheme | 37, 120 |
| abstract_inverted_index.stable | 85, 178 |
| abstract_inverted_index.steps, | 136 |
| abstract_inverted_index.complex | 111, 158 |
| abstract_inverted_index.dynamic | 58 |
| abstract_inverted_index.enables | 51 |
| abstract_inverted_index.models. | 160 |
| abstract_inverted_index.orders. | 92 |
| abstract_inverted_index.regions | 25 |
| abstract_inverted_index.respect | 130 |
| abstract_inverted_index.scaling | 128 |
| abstract_inverted_index.showing | 124 |
| abstract_inverted_index.various | 90 |
| abstract_inverted_index.Finally, | 161 |
| abstract_inverted_index.Lyapunov | 71 |
| abstract_inverted_index.Notably, | 93 |
| abstract_inverted_index.analyzes | 4 |
| abstract_inverted_index.behavior | 59 |
| abstract_inverted_index.compared | 137 |
| abstract_inverted_index.critical | 100 |
| abstract_inverted_index.detailed | 53 |
| abstract_inverted_index.domains, | 181 |
| abstract_inverted_index.exhibits | 31, 84 |
| abstract_inverted_index.observed | 187 |
| abstract_inverted_index.periodic | 87 |
| abstract_inverted_index.proposed | 119 |
| abstract_inverted_index.repeated | 188 |
| abstract_inverted_index.required | 104 |
| abstract_inverted_index.schemes, | 149 |
| abstract_inverted_index.suitable | 153 |
| abstract_inverted_index.unstable | 180 |
| abstract_inverted_index.yielding | 189 |
| abstract_inverted_index.Numerical | 68 |
| abstract_inverted_index.behaviors | 88 |
| abstract_inverted_index.capturing | 183 |
| abstract_inverted_index.classical | 145 |
| abstract_inverted_index.criteria, | 22 |
| abstract_inverted_index.diagrams, | 74, 78 |
| abstract_inverted_index.dynamics. | 113 |
| abstract_inverted_index.including | 70 |
| abstract_inverted_index.increases | 108 |
| abstract_inverted_index.long-term | 155 |
| abstract_inverted_index.model’s | 57 |
| abstract_inverted_index.quadratic | 141 |
| abstract_inverted_index.simulated | 168 |
| abstract_inverted_index.stability | 11, 21, 107 |
| abstract_inverted_index.approaches | 98 |
| abstract_inverted_index.developed, | 40 |
| abstract_inverted_index.difference | 36 |
| abstract_inverted_index.efficiency | 116 |
| abstract_inverted_index.exponents, | 72 |
| abstract_inverted_index.fractional | 48, 82, 91, 96, 172 |
| abstract_inverted_index.introduces | 2 |
| abstract_inverted_index.phenomena. | 190 |
| abstract_inverted_index.threshold, | 101 |
| abstract_inverted_index.validated, | 123 |
| abstract_inverted_index.accelerated | 43 |
| abstract_inverted_index.bifurcation | 73 |
| abstract_inverted_index.demonstrate | 79 |
| abstract_inverted_index.derivative. | 49 |
| abstract_inverted_index.effectively | 182 |
| abstract_inverted_index.equilibrium | 14 |
| abstract_inverted_index.exploration | 54 |
| abstract_inverted_index.simulations | 156 |
| abstract_inverted_index.stress-time | 165 |
| abstract_inverted_index.highlighting | 110 |
| abstract_inverted_index.instability. | 32 |
| abstract_inverted_index.interpreting | 185 |
| abstract_inverted_index.investigated | 18 |
| abstract_inverted_index.particularly | 23 |
| abstract_inverted_index.simulations, | 69 |
| abstract_inverted_index.computational | 115 |
| abstract_inverted_index.corresponding | 28, 175 |
| abstract_inverted_index.incorporating | 41 |
| abstract_inverted_index.integer-order | 29 |
| abstract_inverted_index.Ananthakrishna | 8, 173 |
| abstract_inverted_index.experimentally | 186 |
| abstract_inverted_index.significantly, | 109 |
| abstract_inverted_index.fractional-order | 7, 20, 159 |
| abstract_inverted_index.Grünwald-Letnikow | 148 |
| abstract_inverted_index.stability-transition | 112 |
| cited_by_percentile_year | |
| countries_distinct_count | 1 |
| institutions_distinct_count | 2 |
| citation_normalized_percentile.value | 0.29267458 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |