Evolutionary Approaches to the Identification of Dynamic Processes in the Form of Differential Equations and Their Systems

Evolutionary approaches are widely applied in solving various types of problems. The paper considers the application of EvolODE and EvolODES approaches to the identification of dynamic systems. EvolODE helps to obtain a model in the form of an ordinary differential equation without restrictions on t...

Full description

Saved in:
Bibliographic Details
Published in:Algorithms Vol. 15; no. 10; p. 351
Main Authors: Karaseva, Tatiana, Semenkin, Eugene
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.10.2022
Subjects:
Algorithms
Analysis
Differential equations
Dynamical systems
evolutionary algorithms
Evolutionary computation
Genetic algorithms
genetic programming algorithm
Identification
identification of dynamic systems
Inverse problems
Mathematical models
Mutation
ordinary differential equation
ordinary differential equation system
Population
ISSN:1999-4893, 1999-4893
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract Evolutionary approaches are widely applied in solving various types of problems. The paper considers the application of EvolODE and EvolODES approaches to the identification of dynamic systems. EvolODE helps to obtain a model in the form of an ordinary differential equation without restrictions on the type of the equation. EvolODES searches for a model in the form of an ordinary differential equation system. The algorithmic basis of these approaches is a modified genetic programming algorithm for finding the structure of ordinary differential equations and differential evolution to optimize the values of numerical constants used in the equation. Testing for these approaches on problems in the form of ordinary differential equations and their systems was conducted. The influence of noise present in the data and the sample size on the model error was considered for each of the approaches. The symbolic accuracy of the resulting equations was studied. The proposed approaches make it possible to obtain models in symbolic form. They will provide opportunities for further interpretation and application.
AbstractList Evolutionary approaches are widely applied in solving various types of problems. The paper considers the application of EvolODE and EvolODES approaches to the identification of dynamic systems. EvolODE helps to obtain a model in the form of an ordinary differential equation without restrictions on the type of the equation. EvolODES searches for a model in the form of an ordinary differential equation system. The algorithmic basis of these approaches is a modified genetic programming algorithm for finding the structure of ordinary differential equations and differential evolution to optimize the values of numerical constants used in the equation. Testing for these approaches on problems in the form of ordinary differential equations and their systems was conducted. The influence of noise present in the data and the sample size on the model error was considered for each of the approaches. The symbolic accuracy of the resulting equations was studied. The proposed approaches make it possible to obtain models in symbolic form. They will provide opportunities for further interpretation and application.
Audience Academic
Author Semenkin, Eugene
Karaseva, Tatiana
Author_xml – sequence: 1
  givenname: Tatiana
  orcidid: 0000-0002-6880-7092
  surname: Karaseva
  fullname: Karaseva, Tatiana
– sequence: 2
  givenname: Eugene
  orcidid: 0000-0002-3776-5707
  surname: Semenkin
  fullname: Semenkin, Eugene
BookMark eNpNkUFrGzEQhZeSQJM0h_wDQU89ONGsJGt1NKnTGgItNDmLkXYUy9grR1oXnF9f2S4hCCQxfO8x8-ayORvSQE1zA_xWCMPvEBRwLhR8ai7AGDORnRFnH_6fm8tSVpxPlZnCRfM2_5vWuzGmAfOezbbbnNAvqbAxsXFJbNHTMMYQPR4YlgL7vh9wEz37nZOnUioahyP6kPLmCMQQKB9kuGbz191RWRgOPXtaUszsz76MtClfmvOA60LX_9-r5vlh_nT_c_L468fifvY48ULpsd7GYUDgpHvlpHaKWg8EdUynybuWu87IKQ8A0KLjoEJHuiPsW-1QenHVLE6-fcKV3ea4qaPahNEeCym_WMxj9GuyIDXU7KreCKnl1BnvnPfkhNMBPVWvryevmtPrjspoV2mXh9q-bXXbSeDQykrdnqgXrKZxCGnM6OvpqSZXFxZirc-0VCAFV10VfDsJfE6lZArvbQK3h73a972Kf66al8E
Cites_doi 10.1007/978-3-540-69432-8_3
10.5565/PUBLMAT_41197_09
10.1016/j.ins.2008.07.029
10.3390/a14050130
10.1088/1757-899X/734/1/012093
10.1103/PhysRevResearch.4.023174
10.1023/A:1008202821328
10.1016/j.automatica.2021.109600
10.1109/InfoTech52438.2021.9548643
10.1109/IPDPSW.2013.96
10.3390/systems3040348
10.3390/math8091526
10.1088/1361-665X/ab9149
10.1007/978-3-030-31362-3_33
10.1088/1757-899X/1047/1/012076
10.1016/j.ijtst.2018.10.002
10.5220/0008495302520258
10.1109/91.868943
10.1007/978-3-662-44303-3_3
10.1016/j.swevo.2016.01.004
10.1023/A:1010013106294
ContentType Journal Article
Copyright COPYRIGHT 2022 MDPI AG
2022 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 (https://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.
Copyright_xml – notice: COPYRIGHT 2022 MDPI AG
– notice: 2022 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 (https://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.
DBID AAYXX
CITATION
3V.
7SC
7TB
7XB
8AL
8FD
8FE
8FG
8FK
ABJCF
ABUWG
AFKRA
ARAPS
AZQEC
BENPR
BGLVJ
CCPQU
DWQXO
FR3
GNUQQ
HCIFZ
JQ2
K7-
KR7
L6V
L7M
L~C
L~D
M0N
M7S
P62
PHGZM
PHGZT
PIMPY
PKEHL
PQEST
PQGLB
PQQKQ
PQUKI
PRINS
PTHSS
Q9U
DOA
DOI 10.3390/a15100351
DatabaseName CrossRef
ProQuest Central (Corporate)
Computer and Information Systems Abstracts
Mechanical & Transportation Engineering Abstracts
ProQuest Central (purchase pre-March 2016)
Computing Database (Alumni Edition)
Technology Research Database
ProQuest SciTech Collection
ProQuest Technology Collection
ProQuest Central (Alumni) (purchase pre-March 2016)
Materials Science & Engineering Collection
ProQuest Central (Alumni)
ProQuest Central UK/Ireland
Advanced Technologies & Computer Science Collection
ProQuest Central Essentials
ProQuest Central
ProQuest Technology Collection
ProQuest One Community College
ProQuest Central Korea
Engineering Research Database
ProQuest Central Student
SciTech Premium Collection
ProQuest Computer Science Collection
Computer Science Database
Civil Engineering Abstracts
ProQuest Engineering Collection
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts – Academic
Computer and Information Systems Abstracts Professional
Computing Database
Engineering Database
ProQuest Advanced Technologies & Aerospace Collection
ProQuest Central Premium
ProQuest One Academic
Publicly Available Content Database
ProQuest One Academic Middle East (New)
ProQuest One Academic Eastern Edition (DO NOT USE)
ProQuest One Applied & Life Sciences
ProQuest One Academic (retired)
ProQuest One Academic UKI Edition
ProQuest Central China
Engineering Collection
ProQuest Central Basic
DOAJ Open Access Full Text
DatabaseTitle CrossRef
Publicly Available Content Database
Computer Science Database
ProQuest Central Student
Technology Collection
Technology Research Database
Computer and Information Systems Abstracts – Academic
ProQuest One Academic Middle East (New)
Mechanical & Transportation Engineering Abstracts
ProQuest Advanced Technologies & Aerospace Collection
ProQuest Central Essentials
ProQuest Computer Science Collection
Computer and Information Systems Abstracts
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)
Advanced Technologies Database with Aerospace
Engineering Collection
Advanced Technologies & Aerospace Collection
Civil Engineering Abstracts
ProQuest Computing
Engineering Database
ProQuest Central Basic
ProQuest Computing (Alumni Edition)
ProQuest One Academic Eastern Edition
ProQuest Technology Collection
ProQuest SciTech Collection
Computer and Information Systems Abstracts Professional
ProQuest One Academic UKI Edition
Materials Science & Engineering Collection
Engineering Research Database
ProQuest One Academic
ProQuest One Academic (New)
ProQuest Central (Alumni)
DatabaseTitleList Publicly Available Content Database

CrossRef
Database_xml – sequence: 1
  dbid: DOA
  name: DOAJ Directory of Open Access Journals
  url: https://www.doaj.org/
  sourceTypes: Open Website
– sequence: 2
  dbid: PIMPY
  name: Publicly Available Content Database
  url: http://search.proquest.com/publiccontent
  sourceTypes: Aggregation Database
DeliveryMethod fulltext_linktorsrc
Discipline Computer Science
EISSN 1999-4893
ExternalDocumentID oai_doaj_org_article_14713518e7934746b9cbbcceb3b7face
A745143058
10_3390_a15100351
GroupedDBID 23M
2WC
5VS
8FE
8FG
AADQD
AAFWJ
AAYXX
ABDBF
ABJCF
ABUWG
ACUHS
ADBBV
AFFHD
AFKRA
AFPKN
AFZYC
ALMA_UNASSIGNED_HOLDINGS
AMVHM
ARAPS
AZQEC
BCNDV
BENPR
BGLVJ
BPHCQ
CCPQU
CITATION
DWQXO
E3Z
ESX
GNUQQ
GROUPED_DOAJ
HCIFZ
IAO
ICD
ITC
J9A
K6V
K7-
KQ8
L6V
M7S
MODMG
M~E
OK1
OVT
P2P
PHGZM
PHGZT
PIMPY
PQGLB
PQQKQ
PROAC
PTHSS
TR2
TUS
3V.
7SC
7TB
7XB
8AL
8FD
8FK
FR3
JQ2
KR7
L7M
L~C
L~D
M0N
P62
PKEHL
PQEST
PQUKI
PRINS
Q9U
ID FETCH-LOGICAL-c357t-c39bafa10e7d5b47b5e2c1e1100b7ecb20b89460f1112ab015f8e78ead27ba4c3
IEDL.DBID DOA
ISICitedReferencesCount 0
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000872037600001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 1999-4893
IngestDate Fri Oct 03 12:40:59 EDT 2025
Fri Jul 25 11:47:44 EDT 2025
Tue Nov 04 17:55:59 EST 2025
Sat Nov 29 07:14:20 EST 2025
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 10
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c357t-c39bafa10e7d5b47b5e2c1e1100b7ecb20b89460f1112ab015f8e78ead27ba4c3
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ORCID 0000-0002-6880-7092
0000-0002-3776-5707
OpenAccessLink https://doaj.org/article/14713518e7934746b9cbbcceb3b7face
PQID 2728410124
PQPubID 2032439
ParticipantIDs doaj_primary_oai_doaj_org_article_14713518e7934746b9cbbcceb3b7face
proquest_journals_2728410124
gale_infotracacademiconefile_A745143058
crossref_primary_10_3390_a15100351
PublicationCentury 2000
PublicationDate 2022-10-01
PublicationDateYYYYMMDD 2022-10-01
PublicationDate_xml – month: 10
  year: 2022
  text: 2022-10-01
  day: 01
PublicationDecade 2020
PublicationPlace Basel
PublicationPlace_xml – name: Basel
PublicationTitle Algorithms
PublicationYear 2022
Publisher MDPI AG
Publisher_xml – name: MDPI AG
References Cao (ref_7) 2000; 1
Merta (ref_18) 2019; 1047
Chen (ref_6) 2022; 4
Iba (ref_12) 2008; 178
ref_13
Karaseva (ref_19) 2020; 734
ref_10
Medvedev (ref_14) 2017; 10
Gaucel (ref_11) 2014; 8599
Nesmachnow (ref_1) 2019; 8
Parmar (ref_5) 2007; 1
Beyer (ref_24) 2007; 54
Ballesteros (ref_16) 2021; 129
Karaseva (ref_21) 2021; 1047
Storn (ref_23) 1997; 11
Das (ref_20) 2016; 27
ref_25
Bagheri (ref_3) 2020; 29
Lee (ref_17) 2000; 8
ref_22
Sholokhova (ref_15) 2017; 4
ref_2
ref_26
Ryzhikov (ref_9) 2014; 1
Cottineau (ref_8) 2015; 3
Gasull (ref_27) 1997; 41
ref_4
References_xml – volume: 54
  start-page: 47
  year: 2007
  ident: ref_24
  article-title: Self-Adaptation in Evolutionary Algorithms
  publication-title: Parameter Setting Evol. Algorithm
  doi: 10.1007/978-3-540-69432-8_3
– volume: 41
  start-page: 149
  year: 1997
  ident: ref_27
  article-title: Limit cycles in the Holling-Tanner model
  publication-title: Publ. Mat.
  doi: 10.5565/PUBLMAT_41197_09
– volume: 178
  start-page: 4453
  year: 2008
  ident: ref_12
  article-title: Inference of differential equation models by genetic programming
  publication-title: Inf. Sci.
  doi: 10.1016/j.ins.2008.07.029
– ident: ref_26
– ident: ref_22
  doi: 10.3390/a14050130
– volume: 734
  start-page: 12093
  year: 2020
  ident: ref_19
  article-title: Automatic differential equations identification by self-configuring genetic programming algorithm
  publication-title: IOP Conf. Ser. Mater. Sci. Eng.
  doi: 10.1088/1757-899X/734/1/012093
– volume: 4
  start-page: 023174
  year: 2022
  ident: ref_6
  article-title: Symbolic genetic algorithm for discovering open-form partial differential equations (SGA-PDE)
  publication-title: Phys. Rev. Res.
  doi: 10.1103/PhysRevResearch.4.023174
– volume: 11
  start-page: 341
  year: 1997
  ident: ref_23
  article-title: Differential Evolution—A Simple and Efficient Heuristic for global Optimization over Continuous Spaces
  publication-title: J. Glob. Optim.
  doi: 10.1023/A:1008202821328
– volume: 129
  start-page: 109600
  year: 2021
  ident: ref_16
  article-title: Non-parametric identification of homogeneous dynamical systems
  publication-title: Automatica
  doi: 10.1016/j.automatica.2021.109600
– ident: ref_25
  doi: 10.1109/InfoTech52438.2021.9548643
– ident: ref_2
  doi: 10.1109/IPDPSW.2013.96
– volume: 3
  start-page: 348
  year: 2015
  ident: ref_8
  article-title: A Modular Modelling Framework for Hypotheses Testing in the Simulation of Urbanisation
  publication-title: Systems
  doi: 10.3390/systems3040348
– ident: ref_4
  doi: 10.3390/math8091526
– volume: 4
  start-page: 23
  year: 2017
  ident: ref_15
  article-title: Modeling of dynamic systems based on polynomial neural networks
  publication-title: Model. Optim. Inf. Technol.
– volume: 29
  start-page: 105004
  year: 2020
  ident: ref_3
  article-title: Application of artificial intelligence and evolutionary algorithms in simulation-based optimal design of a piezoelectric energy harvester
  publication-title: Smart Mater. Struct.
  doi: 10.1088/1361-665X/ab9149
– volume: 1
  start-page: 66
  year: 2014
  ident: ref_9
  article-title: Automatic linear differential equation identification in analytical form
  publication-title: Vestnik SibSAU Aerosp. Tehnol. Control Syst.
– volume: 1047
  start-page: 339
  year: 2019
  ident: ref_18
  article-title: Lifetime adaptation in genetic programming for the symbolic regression
  publication-title: Adv. Intell. Syst. Comput.
  doi: 10.1007/978-3-030-31362-3_33
– volume: 1047
  start-page: 12076
  year: 2021
  ident: ref_21
  article-title: Hybrid approach to the dynamic systems identification based on the self-configuring genetic programming algorithm and the differential evolution method
  publication-title: IOP Conf. Ser. Mater. Sci. Eng.
  doi: 10.1088/1757-899X/1047/1/012076
– volume: 8
  start-page: 53
  year: 2019
  ident: ref_1
  article-title: Traffic lights synchronization for Bus Rapid Transit using a parallel evolutionary algorithm
  publication-title: Int. J. Transp. Sci. Technol.
  doi: 10.1016/j.ijtst.2018.10.002
– ident: ref_10
  doi: 10.5220/0008495302520258
– volume: 1
  start-page: 26
  year: 2007
  ident: ref_5
  article-title: Order reduction of linear dynamic systems using stability equation method and GA
  publication-title: Int. J. Comput. Inf. Eng.
– ident: ref_13
– volume: 10
  start-page: 124
  year: 2017
  ident: ref_14
  article-title: On Nonparametric Modelling of Multidimensional Noninertial Systems with Delay
  publication-title: Bull. South Ural State Univ. Ser. Math. Model. Program. Comput. Softw.
– volume: 8
  start-page: 349
  year: 2000
  ident: ref_17
  article-title: Identification and Control of Dynamic Systems Using Recurrent Fuzzy Neural Networks
  publication-title: IEEE Trans. Fuzzy Syst.
  doi: 10.1109/91.868943
– volume: 8599
  start-page: 25
  year: 2014
  ident: ref_11
  article-title: Learning Dynamical Systems Using Standard Symbolic Regression
  publication-title: Lect. Notes Comput. Sci.
  doi: 10.1007/978-3-662-44303-3_3
– volume: 27
  start-page: 1
  year: 2016
  ident: ref_20
  article-title: Recent Advances in Differential Evolution—An Updated Survey
  publication-title: Swarm Evol. Comput.
  doi: 10.1016/j.swevo.2016.01.004
– volume: 1
  start-page: 309
  year: 2000
  ident: ref_7
  article-title: Evolutionary modeling of systems of ordinary differential equations with genetic programming
  publication-title: Genet. Program. Evol. Mach.
  doi: 10.1023/A:1010013106294
SSID ssj0065961
Score 2.2536733
Snippet Evolutionary approaches are widely applied in solving various types of problems. The paper considers the application of EvolODE and EvolODES approaches to the...
SourceID doaj
proquest
gale
crossref
SourceType Open Website
Aggregation Database
Index Database
StartPage 351
SubjectTerms Algorithms
Analysis
Differential equations
Dynamical systems
evolutionary algorithms
Evolutionary computation
Genetic algorithms
genetic programming algorithm
Identification
identification of dynamic systems
Inverse problems
Mathematical models
Mutation
ordinary differential equation
ordinary differential equation system
Population
SummonAdditionalLinks – databaseName: Engineering Database
  dbid: M7S
  link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LS8QwEB58Hbz4FldXCSJ4Kttn0p5k1V08iAiusLeSpKksSLvbVkF_vZM0XfGgF3vooZ2WwMx8mUky3wBceDJjOXczh3uY6eAMLZ1YcnQ8lOZURoFkplD4nj08xNNp8mgX3Gp7rLLDRAPUWSn1GvnAZwikmowqvJovHN01Su-u2hYaq7CuWRI8c3TvqUNiGiXUa9mEAkztBxwlzM7ZjznIUPX_Bshmlhlv_3d8O7Bl40sybA1iF1ZUsQfbXe8GYl15Hz5H79boePVBhpZZXNWkKQnGhKQt4M3tih4pc3Lb9q4ntrQARWeFER1j2GsEbK8VxIxXMlq0HOI14UVGJno7glh29AN4Ho8mN3eO7cPgyCBiDd4TwXPuuYplkQiZiJQvPaXJ5gRTUviuiJOQujnips8FBhh5rFiMNuozwUMZHMJaURbqCEjkZsJLIkU5dUOG39Es9zjDi4ocf9WD804z6byl20gxTdHqS5fq68G11tlSQDNkmwdl9ZJah8OUxjQfxIEkQchCKhIphJRKBAKNU6oeXGqNp9qPm4pLbssRcJyaESsdslDHkm4U96DfaTy1Dl6n3-o-_vv1CWz6umLCnP_rw1pTvalT2JDvzayuzoy9fgEv7Pe_
  priority: 102
  providerName: ProQuest
Title Evolutionary Approaches to the Identification of Dynamic Processes in the Form of Differential Equations and Their Systems
URI https://www.proquest.com/docview/2728410124
https://doaj.org/article/14713518e7934746b9cbbcceb3b7face
Volume 15
WOSCitedRecordID wos000872037600001&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: 1999-4893
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0065961
  issn: 1999-4893
  databaseCode: DOA
  dateStart: 20080101
  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: 1999-4893
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0065961
  issn: 1999-4893
  databaseCode: M~E
  dateStart: 20080101
  isFulltext: true
  titleUrlDefault: https://road.issn.org
  providerName: ISSN International Centre
– providerCode: PRVPQU
  databaseName: Computer Science Database
  customDbUrl:
  eissn: 1999-4893
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0065961
  issn: 1999-4893
  databaseCode: K7-
  dateStart: 20080301
  isFulltext: true
  titleUrlDefault: http://search.proquest.com/compscijour
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Engineering Database
  customDbUrl:
  eissn: 1999-4893
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0065961
  issn: 1999-4893
  databaseCode: M7S
  dateStart: 20080301
  isFulltext: true
  titleUrlDefault: http://search.proquest.com
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: ProQuest Central Database Suite (ProQuest)
  customDbUrl:
  eissn: 1999-4893
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0065961
  issn: 1999-4893
  databaseCode: BENPR
  dateStart: 20080301
  isFulltext: true
  titleUrlDefault: https://www.proquest.com/central
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Publicly Available Content Database
  customDbUrl:
  eissn: 1999-4893
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0065961
  issn: 1999-4893
  databaseCode: PIMPY
  dateStart: 20080301
  isFulltext: true
  titleUrlDefault: http://search.proquest.com/publiccontent
  providerName: ProQuest
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LT9wwEB4h4MClUB5qKF1ZqBKniCTr2MlxoVm1KqyiAhKcLNtxpJVQtt1NV2oP_e2MH0HtAXFpDj4kk8Sah2cm8XwD8DHVDW9l0sQyxUwHPbSOCy3R8JBaMp2PNXeFwld8Nivu78v6r1Zfdk-Yhwf2jDtPqWsiVxhUJMopU6VWSmvMARW-RBu7-ia8HJIpvwazvGSpxxEaY1J_LtGvuX9m_3gfB9L_0lLs_Mt0D96EwJBM_ITewobp9mF3aLpAgg0ewO9qHbRFLn-RSYAENyvSLwgGc8RX3rbhUxxZtOSTbzpPQk0Aks47RzrFeNURhCYpaOyPpPrhwb9XRHYNubX_EUiANT-Eu2l1e_k5Dg0UYj3OeY9jqWQr08TwJleUq9xkOjUWJU5xo1WWqKKkLGlxwcukwsigRT4XqFwZV5Lq8RFsdovOvAOSJ41Ky9wwyRLK8T7WtKnkeDDV4qMiOB0YK757nAyB-YXlvnjmfgQXluXPBBba2p1AgYsgcPGawCM4swIT1gD7pdQy1BHgPC2UlZhwaoPAJC8iOBlkKoJlrkTG0SFbUDN6_D9m8x52MlsQ4bb3ncBmv_xpPsC2Xvfz1XIEWxfVrP42csqJ41cej-zu0hs7_qnwev3lun54AuUe8O4
linkProvider Directory of Open Access Journals
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Nb9QwEB2VggQXSoGKhRasqohT1Hw4dnJAaGl31Wq3Kw6L1JuxHadaqSRtEoqWH8VvZOw4RRzg1gM55JBMrMh588aOPW8ADiJd8FKGRSAjnOlghNZBpiU6HlpLptNEc5coPOeLRXZ-nn_agJ9DLozdVjlwoiPqotb2H_lhzJFIrRgV_XB1HdiqUXZ1dSih0cNiZtbfccrWvj89xu_7No6nk-XRSeCrCgQ6SXmH51zJUkah4UWqKFepiXVkrHSa4karOFRZTllYIgvEUmG4LDPDM-zxmCtJdYLt3oP7NMm49asZDwbmZ2nOol69KEny8FBiNHUrdX_EPFca4G8BwEW16db_1h9P4LEfP5NxD_ht2DDVU9gaalMQT1XP4MfkxjuVbNZk7JXTTUu6muCYl_QJyqX_Y0nqkhyvK_l1pYlPnUDTVeVMpzisdwa-lgxy4iWZXPca6S2RVUGWdrmFePX35_D5TnpgBzarujIvgKRhoaI8NUyykHJ8jhVlJDkeTJXY1Aj2BySIq15OROA0zMJF3MJlBB8tRm4NrAK4u1A3F8ITCk7ZXHFFfJE8oZwylWultDYqUeh82ozgnUWYsDzVNVJLn26B72kVv8SYUztWDtNsBLsDwoQnsFb8htfLf99-Aw9PlmdzMT9dzF7Bo9hmh7i9jruw2TXfzB480Dfdqm1eO18h8OWuwfgLAUNV7g
linkToPdf http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Nb9QwEB2VLUJcKF8VCwUsBOIUbeIkdnKo0MLuilXLag9FKqdgOzZaCZI2CUXLT-PXdew4RRzg1gM55JCdRJH3zZtx7HkD8DJSJTciLAMR4UwHI7QKMiXQ8dBaMJXGirtC4WO-WmWnp_l6B34NtTB2W-XAiY6oy1rZb-QTypFIrRhVMjF-W8R6tnhzdh7YDlJ2pXVop9FD5Ehvf-D0rT1czvC_fkXpYn7y7n3gOwwEKk55h-dcCiOiUPMylQmXqaYq0lZGTXKtJA1llicsNMgIVEgMnSbTPMPRp1yKRMX43Buwiyl5Qkewu15-WH8a4gBLcxb1WkZxnIcTgbHVrdv9EQFdo4C_hQMX4xZ7__Po3IU7PrMm094V7sGOru7D3tC1gngSewA_5xfe3USzJVOvqa5b0tUEs2HSly4b_y2T1IbMtpX4tlHEF1Wg6aZypgtM-J2B7zKDbPmVzM979fSWiKokJ3Yhhnhd-Ifw8VpGYB9GVV3pR0DSsJRRnmomWJhwvI-VJhIcDyYNPmoMLwZUFGe90EiBEzQLneIKOmN4a_FyZWC1wd2FuvlSeKrByZxru4gvkscITCZzJaVSWsYS3VLpMby2aCssg3WNUMIXYuB7Wi2wYsoTm0WHaTaGgwFthae2tvgNtcf__vk53EIMFsfL1dETuE1t2YjbBHkAo675rp_CTXXRbdrmmXccAp-vG42XkK1gbw
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=Evolutionary+Approaches+to+the+Identification+of+Dynamic+Processes+in+the+Form+of+Differential+Equations+and+Their+Systems&rft.jtitle=Algorithms&rft.au=Tatiana+Karaseva&rft.au=Eugene+Semenkin&rft.date=2022-10-01&rft.pub=MDPI+AG&rft.eissn=1999-4893&rft.volume=15&rft.issue=10&rft.spage=351&rft_id=info:doi/10.3390%2Fa15100351&rft.externalDBID=DOA&rft.externalDocID=oai_doaj_org_article_14713518e7934746b9cbbcceb3b7face
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1999-4893&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1999-4893&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1999-4893&client=summon