{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T07:05:53Z","timestamp":1777705553273,"version":"3.51.4"},"reference-count":31,"publisher":"SAGE Publications","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2022,1,25]]},"abstract":"<jats:p>This paper proposes a scheme to synchronize fractional order chaotic systems employing fractional PID controller. The parameters of FOPID are tuned using Swarm based optimization techniques, viz.: Whale optimization algorithm and Particle swarm optimization techniques. To assert the complete synchronization, master-slave method has been implemented. Chaotic systems are highly dependent upon initial conditions and parameter perturbations. Therefore, taking these properties into consideration, synchronization of two identical fractional order financial chaotic systems is performed with distinct initial conditions. To show the efficacy of the proposed method, analysis is performed for orders between 0 to 1, and also for sensitivity to initial conditions.<\/jats:p>","DOI":"10.3233\/jifs-189761","type":"journal-article","created":{"date-parts":[[2021,3,5]],"date-time":"2021-03-05T12:38:25Z","timestamp":1614947905000},"page":"929-942","source":"Crossref","is-referenced-by-count":4,"title":["Whale optimization based synchronization and control of two identical fractional order financial chaotic systems"],"prefix":"10.1177","volume":"42","author":[{"given":"Sangeeta","family":"Gupta","sequence":"first","affiliation":[{"name":"Division of Instrumentation and Control Engineering, Netaji Subhas Institute of Technology (NSIT), University of Delhi, Sec-3, Dwarka, New Delhi, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pragya","family":"Varshney","sequence":"additional","affiliation":[{"name":"Division of Instrumentation and Control Engineering, Netaji Subhas Institute of Technology (NSIT), University of Delhi, Sec-3, Dwarka, New Delhi, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Smriti","family":"Srivastava","sequence":"additional","affiliation":[{"name":"Division of Instrumentation and Control Engineering, Netaji Subhas Institute of Technology (NSIT), University of Delhi, Sec-3, Dwarka, New Delhi, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","reference":[{"issue":"8","key":"10.3233\/JIFS-189761_ref1","doi-asserted-by":"publisher","first-page":"485","DOI":"10.1109\/81.404062","article-title":"Chaos in a fractional order Chua\u2019s system","volume":"42","author":"Hartley","year":"1995","journal-title":"IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications"},{"issue":"8","key":"10.3233\/JIFS-189761_ref3","doi-asserted-by":"crossref","first-page":"821","DOI":"10.1103\/PhysRevLett.64.821","article-title":"Synchronization in chaotic systems","volume":"64","author":"Pecora","year":"1990","journal-title":"Physical review letters"},{"issue":"5","key":"10.3233\/JIFS-189761_ref4","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1016\/S0032-9592(98)00112-5","article-title":"Pseudo-second order model for sorption processes","volume":"34","author":"Ho","year":"1999","journal-title":"Process biochemistry"},{"issue":"1","key":"10.3233\/JIFS-189761_ref5","first-page":"963","article-title":"Stability results for fractional differential equations with applications to control processing, In Lille, France","volume":"2","author":"Matignon","year":"1996","journal-title":"Computational engineering in systems applications, Multiconference, IMACS, IEEE-SMC"},{"issue":"3-4","key":"10.3233\/JIFS-189761_ref6","doi-asserted-by":"crossref","first-page":"482","DOI":"10.1016\/S0378-4371(00)00387-3","article-title":"Fractional market dynamics","volume":"287","author":"Laskin","year":"2000","journal-title":"Physica A: Statistical Mechanics and its Applications"},{"key":"10.3233\/JIFS-189761_ref7","doi-asserted-by":"crossref","unstructured":"Azar A.T. and Vaidyanathan S. and Advances eds. , in chaos theory and intelligent control, Germany: Springer 337 (2016). doi: https:\/\/doi.org\/10.1007\/978-3-319-30340-6.","DOI":"10.1007\/978-3-319-30340-6"},{"issue":"12","key":"10.3233\/JIFS-189761_ref9","doi-asserted-by":"publisher","first-page":"1394","DOI":"10.1109\/TCSI.2001.972846","article-title":"Chaotic communications over radio channels","volume":"48","author":"Williams","year":"2001","journal-title":"IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications"},{"issue":"2","key":"10.3233\/JIFS-189761_ref10","first-page":"15","article-title":"Generalized Projective Synchronization of Fractional-order Hyperchaotic Lu and Hyperchaotic Cai System via Active Control","volume":"8","author":"Balochian","year":"2019","journal-title":"Majlesi Journal of Mechatronic Systems"},{"issue":"9","key":"10.3233\/JIFS-189761_ref11","doi-asserted-by":"publisher","first-page":"5774","DOI":"10.1109\/TIE.2016.2573239","article-title":"Design and implementation of adaptive terminal sliding-mode control on a steer-by-wire equipped road vehicle","volume":"63","author":"Wang","year":"2016","journal-title":"IEEE Transactions on Industrial Electronics"},{"issue":"4","key":"10.3233\/JIFS-189761_ref12","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1109\/TCSII.2016.2563758","article-title":"Disturbance-observer-based robust synchronization control for a class of fractional-order chaotic systems","volume":"64","author":"Chen","year":"2016","journal-title":"IEEE Transactions on Circuits and Systems II: Express Briefs"},{"key":"10.3233\/JIFS-189761_ref13","doi-asserted-by":"crossref","first-page":"1341","DOI":"10.1016\/j.neucom.2015.09.007","article-title":"Complete synchronization of delayed chaotic neural networks by intermittent control with two switches in a control period","volume":"173","author":"Li","year":"2016","journal-title":"Neurocomputing"},{"issue":"2","key":"10.3233\/JIFS-189761_ref14","first-page":"980","article-title":"Generalized synchronization of chaos in directionally coupled chaotic systems","volume":"E51","author":"Rulkov","year":"1995","journal-title":"Physical Review"},{"issue":"3","key":"10.3233\/JIFS-189761_ref15","doi-asserted-by":"crossref","first-page":"1522","DOI":"10.1016\/j.jfranklin.2018.10.024","article-title":"Lag projective synchronization of fractional-order delayed chaotic systems","volume":"356","author":"Zhang","year":"2019","journal-title":"Journal of the Franklin Institute"},{"key":"10.3233\/JIFS-189761_ref16","first-page":"129","article-title":"Hybrid projective synchronization of time-delayed fractional order chaotic systems","volume":"11","author":"Wang","year":"2014","journal-title":"Nonlinear Analysis: Hybrid Systems"},{"key":"10.3233\/JIFS-189761_ref17","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/j.physa.2005.01.021","article-title":"Chaos synchronization of the fractional L\u00fc system","volume":"353","author":"Deng","year":"2005","journal-title":"Physica A: Statistical Mechanics and its Applications"},{"key":"10.3233\/JIFS-189761_ref18","doi-asserted-by":"publisher","DOI":"10.1109\/JAS.2016.7510148"},{"issue":"22","key":"10.3233\/JIFS-189761_ref19","doi-asserted-by":"crossref","first-page":"10930","DOI":"10.1016\/j.ijleo.2016.08.105","article-title":"Synchronization and secure communication in time delayed semiconductor laser systems","volume":"127","author":"Hoang","year":"2016","journal-title":"Optik"},{"issue":"1","key":"10.3233\/JIFS-189761_ref20","doi-asserted-by":"publisher","first-page":"228","DOI":"10.1109\/JAS.2016.7510145","article-title":"Robust finite-time synchronization of non-identical fractional-order hyperchaotic systems and its application in secure communication","volume":"6","author":"Delavari","year":"2016","journal-title":"IEEE\/CAA Journal of Automatica Sinica"},{"key":"10.3233\/JIFS-189761_ref21","doi-asserted-by":"publisher","DOI":"10.1109\/CCDC.2017.7978284"},{"issue":"4","key":"10.3233\/JIFS-189761_ref22","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1109\/TCSII.2016.2563758","article-title":"Disturbance-observer-based robust synchronization control for a class of fractional-order chaotic systems","volume":"64","author":"Chen","year":"2016","journal-title":"IEEE Transactions on Circuits and Systems II: Express Briefs"},{"issue":"3","key":"10.3233\/JIFS-189761_ref23","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1080\/00107514.2017.1345844","article-title":"Synchronisation of chaos and its applications","volume":"58","author":"Eroglu","year":"2017","journal-title":"Contemporary Physics"},{"issue":"4","key":"10.3233\/JIFS-189761_ref24","doi-asserted-by":"crossref","first-page":"1251","DOI":"10.1093\/imamci\/dnx025","article-title":"Chaos synchronization and parameters estimation of chaotic Lur\u2019e systems with full unknown parameters via sampled-data control","volume":"35","author":"Gao","year":"2018","journal-title":"IMA Journal of Mathematical Control and Information"},{"key":"10.3233\/JIFS-189761_ref25","doi-asserted-by":"publisher","DOI":"10.1109\/CCAA.2017.8229962"},{"issue":"2","key":"10.3233\/JIFS-189761_ref26","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1109\/JAS.2016.7510127","article-title":"The switching fractional order chaotic system and its application to image encryption","volume":"4","author":"Hou","year":"2016","journal-title":"IEEE\/CAA Journal of Automatica Sinica"},{"key":"10.3233\/JIFS-189761_ref27","doi-asserted-by":"crossref","unstructured":"Huang Y. , Wang D. , Zhang J. and Guo F. , Controlling and synchronizing a fractional-order chaotic system using stability theory of a time-varying fractional-order system, in: PLoS ONE 13(3) e0194112, 2018. doi: https:\/\/doi.org\/10.1371\/journal.pone.0194112.","DOI":"10.1371\/journal.pone.0194112"},{"issue":"2","key":"10.3233\/JIFS-189761_ref28","doi-asserted-by":"crossref","first-page":"910","DOI":"10.1016\/j.chaos.2007.01.064","article-title":"PID control for chaotic synchronization using particle swarm optimization","volume":"39","author":"Chang","year":"2009","journal-title":"Chaos Solitons Fractals"},{"issue":"1","key":"10.3233\/JIFS-189761_ref29","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1515\/nleng-2017-0073","article-title":"Combination synchronization of fractional order n-chaotic systems using active backstepping design","volume":"8","author":"Yadav","year":"2019","journal-title":"Nonlinear Engineering"},{"issue":"5","key":"10.3233\/JIFS-189761_ref30","doi-asserted-by":"crossref","first-page":"1305","DOI":"10.1016\/j.chaos.2006.07.051","article-title":"Nonlinear dynamics and chaos in a fractional-order financial system","volume":"36","author":"Chen","year":"2008","journal-title":"Chaos, Solitons & Fractals"},{"issue":"3","key":"10.3233\/JIFS-189761_ref31","first-page":"1","article-title":"Fractional-order systems and fractional-order controllers","volume":"12","author":"Podlubny","year":"1994","journal-title":"Institute of Experimental Physics Slovak Academy of Sciences Kosice"},{"key":"10.3233\/JIFS-189761_ref32","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/j.advengsoft.2016.01.008","article-title":"The whale optimization algorithm","volume":"95","author":"Mirjalili","year":"2016","journal-title":"Advances in engineering software"},{"key":"10.3233\/JIFS-189761_ref33","doi-asserted-by":"publisher","first-page":"1942","DOI":"10.1109\/ICNN.1995.488968","article-title":"Particle swarm optimization","volume":"4","author":"Kennedy","year":"1995","journal-title":"Proceedings of ICNN\u201995 - International Conference on Neural Networks"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"link":[{"URL":"https:\/\/content.iospress.com\/download?id=10.3233\/JIFS-189761","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:44:13Z","timestamp":1777455853000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/full\/10.3233\/JIFS-189761"}},"subtitle":[],"editor":[{"given":"Hasmat","family":"Malik","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]},{"given":"Gopal","family":"Chaudhary","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]},{"given":"Smriti","family":"Srivastava","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2022,1,25]]},"references-count":31,"journal-issue":{"issue":"2"},"URL":"https:\/\/doi.org\/10.3233\/jifs-189761","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,1,25]]}}}