{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T19:22:30Z","timestamp":1772133750648,"version":"3.50.1"},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2023,7,4]],"date-time":"2023-07-04T00:00:00Z","timestamp":1688428800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,7,4]],"date-time":"2023-07-04T00:00:00Z","timestamp":1688428800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Supercomput"],"published-print":{"date-parts":[[2024,1]]},"DOI":"10.1007\/s11227-023-05502-x","type":"journal-article","created":{"date-parts":[[2023,7,10]],"date-time":"2023-07-10T13:05:00Z","timestamp":1688994300000},"page":"835-864","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Stability and agent dynamics of artificial electric field algorithm"],"prefix":"10.1007","volume":"80","author":[{"given":"Dikshit","family":"Chauhan","sequence":"first","affiliation":[]},{"given":"Anupam","family":"Yadav","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,7,4]]},"reference":[{"key":"5502_CR1","doi-asserted-by":"crossref","unstructured":"Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of ICNN\u201995-International Conference on Neural Networks, vol 4, IEEE, pp 1942\u20131948","DOI":"10.1109\/ICNN.1995.488968"},{"key":"5502_CR2","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1016\/j.swevo.2018.02.018","volume":"41","author":"E Rashedi","year":"2018","unstructured":"Rashedi E, Rashedi E, Nezamabadi-pour H (2018) A comprehensive survey on gravitational search algorithm. Swarm Evolut Comput 41:141\u2013158","journal-title":"Swarm Evolut Comput"},{"key":"5502_CR3","doi-asserted-by":"publisher","first-page":"106469","DOI":"10.1016\/j.engappai.2023.106469","volume":"123","author":"D Chauhan","year":"2023","unstructured":"Chauhan D, Yadav A (2023) Optimizing the parameters of hybrid active power filters through a comprehensive and dynamic multi-swarm gravitational search algorithm. Eng Appl Artif Intell 123:106469","journal-title":"Eng Appl Artif Intell"},{"issue":"1","key":"5502_CR4","doi-asserted-by":"publisher","first-page":"687","DOI":"10.1016\/j.asoc.2007.05.007","volume":"8","author":"D Karaboga","year":"2008","unstructured":"Karaboga D, Basturk B (2008) On the performance of artificial bee colony (ABC) algorithm. Appl Soft Comput 8(1):687\u2013697","journal-title":"Appl Soft Comput"},{"issue":"4","key":"5502_CR5","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1109\/MCI.2006.329691","volume":"1","author":"M Dorigo","year":"2006","unstructured":"Dorigo M, Birattari M, Stutzle T (2006) Ant colony optimization. IEEE Comput Intell Mag 1(4):28\u201339","journal-title":"IEEE Comput Intell Mag"},{"key":"5502_CR6","doi-asserted-by":"crossref","unstructured":"Mirjalili S (2019) Genetic algorithm. In: Evolutionary algorithms and neural networks, Springer, Berlin, pp 43\u201355","DOI":"10.1007\/978-3-319-93025-1_4"},{"issue":"2","key":"5502_CR7","doi-asserted-by":"publisher","first-page":"60","DOI":"10.1177\/003754970107600201","volume":"76","author":"ZW Geem","year":"2001","unstructured":"Geem ZW, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. simulation 76(2):60\u201368","journal-title":"simulation"},{"key":"5502_CR8","doi-asserted-by":"crossref","unstructured":"Tayarani NMH, Akbarzadeh TMR (2008) Magnetic optimization algorithms a new synthesis. In: 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence), IEEE, pp 2659\u20132664","DOI":"10.1109\/CEC.2008.4631155"},{"issue":"2","key":"5502_CR9","doi-asserted-by":"publisher","first-page":"398","DOI":"10.1109\/TEVC.2008.927706","volume":"13","author":"A Qin","year":"2008","unstructured":"Qin A, Huang VL, Suganthan PN (2008) Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans Evol Comput 13(2):398\u2013417","journal-title":"IEEE Trans Evol Comput"},{"issue":"1","key":"5502_CR10","doi-asserted-by":"publisher","first-page":"58","DOI":"10.1109\/4235.985692","volume":"6","author":"M Clerc","year":"2002","unstructured":"Clerc M, Kennedy J (2002) The particle swarm-explosion, stability, and convergence in a multidimensional complex space. IEEE Trans Evol Comput 6(1):58\u201373","journal-title":"IEEE Trans Evol Comput"},{"issue":"6","key":"5502_CR11","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1016\/S0020-0190(02)00447-7","volume":"85","author":"IC Trelea","year":"2003","unstructured":"Trelea IC (2003) The particle swarm optimization algorithm: convergence analysis and parameter selection. Inf Process Lett 85(6):317\u2013325","journal-title":"Inf Process Lett"},{"issue":"8","key":"5502_CR12","doi-asserted-by":"publisher","first-page":"937","DOI":"10.1016\/j.ins.2005.02.003","volume":"176","author":"F van den Bergh","year":"2006","unstructured":"van den Bergh F, Engelbrecht AP (2006) A study of particle swarm optimization particle trajectories. Inf Sci 176(8):937\u2013971","journal-title":"Inf Sci"},{"issue":"6","key":"5502_CR13","doi-asserted-by":"publisher","first-page":"117","DOI":"10.14257\/ijgdc.2013.6.6.10","volume":"6","author":"DP Tian","year":"2013","unstructured":"Tian DP (2013) A review of convergence analysis of particle swarm optimization. Int J Grid Distrib Comput 6(6):117\u2013128","journal-title":"Int J Grid Distrib Comput"},{"issue":"5","key":"5502_CR14","doi-asserted-by":"publisher","first-page":"814","DOI":"10.1109\/TEVC.2015.2508101","volume":"20","author":"MR Bonyadi","year":"2015","unstructured":"Bonyadi MR, Michalewicz Z (2015) Stability analysis of the particle swarm optimization without stagnation assumption. IEEE Trans Evol Comput 20(5):814\u2013819","journal-title":"IEEE Trans Evol Comput"},{"issue":"1","key":"5502_CR15","doi-asserted-by":"publisher","first-page":"8","DOI":"10.1016\/j.ipl.2006.10.005","volume":"102","author":"M Jiang","year":"2007","unstructured":"Jiang M, Luo YP, Yang SY (2007) Stochastic convergence analysis and parameter selection of the standard particle swarm optimization algorithm. Inf Process Lett 102(1):8\u201316","journal-title":"Inf Process Lett"},{"issue":"3","key":"5502_CR16","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1109\/TEVC.2005.857077","volume":"10","author":"V Kadirkamanathan","year":"2006","unstructured":"Kadirkamanathan V, Selvarajah K, Fleming PJ (2006) Stability analysis of the particle dynamics in particle swarm optimizer. IEEE Trans Evol Comput 10(3):245\u2013255","journal-title":"IEEE Trans Evol Comput"},{"key":"5502_CR17","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1016\/j.ins.2015.12.017","volume":"337","author":"F Farivar","year":"2016","unstructured":"Farivar F, Shoorehdeli MA (2016) Stability analysis of particle dynamics in gravitational search optimization algorithm. Inf Sci 337:25\u201343","journal-title":"Inf Sci"},{"key":"5502_CR18","doi-asserted-by":"publisher","first-page":"2865","DOI":"10.1007\/s00366-020-00979-z","volume":"37","author":"MF Shirjini","year":"2021","unstructured":"Shirjini MF, Nikanjam A, Shoorehdeli MA (2021) Stability analysis of the particle dynamics in bat algorithm: standard and modified versions. Eng Comput 37:2865\u20132876","journal-title":"Eng Comput"},{"issue":"1","key":"5502_CR19","doi-asserted-by":"publisher","first-page":"1","DOI":"10.3233\/AIC-2009-0440","volume":"22","author":"S Dasgupta","year":"2009","unstructured":"Dasgupta S, Das S, Biswas A, Abraham A (2009) On stability and convergence of the population-dynamics in differential evolution. AI Commun 22(1):1\u201320","journal-title":"AI Commun"},{"issue":"4","key":"5502_CR20","doi-asserted-by":"publisher","first-page":"2385","DOI":"10.1007\/s13369-019-03991-8","volume":"45","author":"A Gopal","year":"2020","unstructured":"Gopal A, Sultani MM, Bansal JC (2020) On stability analysis of particle swarm optimization algorithm. Arab J Sci Eng 45(4):2385\u20132394","journal-title":"Arab J Sci Eng"},{"key":"5502_CR21","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1016\/j.swevo.2018.01.003","volume":"41","author":"JC Bansal","year":"2018","unstructured":"Bansal JC, Gopal A, Nagar AK (2018) Stability analysis of artificial bee colony optimization algorithm. Swarm Evol Comput 41:9\u201319","journal-title":"Swarm Evol Comput"},{"key":"5502_CR22","doi-asserted-by":"crossref","unstructured":"Gopal A, Bansal JC (2016) Stability analysis of differential evolution. In: 2016 International Workshop on Computational Intelligence (IWCI), IEEE, pp 221\u2013223","DOI":"10.1109\/IWCI.2016.7860370"},{"key":"5502_CR23","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1016\/j.asoc.2014.07.016","volume":"24","author":"S Jiang","year":"2014","unstructured":"Jiang S, Wang Y, Ji Z (2014) Convergence analysis and performance of an improved gravitational search algorithm. Appl Soft Comput 24:363\u2013384","journal-title":"Appl Soft Comput"},{"issue":"8","key":"5502_CR24","doi-asserted-by":"publisher","first-page":"1411","DOI":"10.1016\/j.ins.2010.11.036","volume":"181","author":"P Chakraborty","year":"2011","unstructured":"Chakraborty P, Das S, Roy GG, Abraham A (2011) On the convergence of the multi-objective particle swarm optimizers. Inf Sci 181(8):1411\u20131425","journal-title":"Inf Sci"},{"issue":"5","key":"5502_CR25","doi-asserted-by":"publisher","first-page":"474","DOI":"10.1140\/epjp\/s13360-021-01489-7","volume":"136","author":"F Souna","year":"2021","unstructured":"Souna F, Djilali S, Lakmeche A (2021) Spatiotemporal behavior in a predator-prey model with herd behavior and cross-diffusion and fear effect. Eur Phys J Plus 136(5):474","journal-title":"Eur Phys J Plus"},{"issue":"5","key":"5502_CR26","doi-asserted-by":"publisher","first-page":"2233","DOI":"10.1002\/mma.6036","volume":"43","author":"S Djilali","year":"2020","unstructured":"Djilali S (2020) Pattern formation of a diffusive predator-prey model with herd behavior and nonlocal prey competition. Math Methods Appl Sci 43(5):2233\u20132250","journal-title":"Math Methods Appl Sci"},{"issue":"11","key":"5502_CR27","doi-asserted-by":"publisher","first-page":"9128","DOI":"10.1002\/mma.7340","volume":"44","author":"S Djilali","year":"2021","unstructured":"Djilali S, Bentout S (2021) Pattern formations of a delayed diffusive predator-prey model with predator harvesting and prey social behavior. Math Methods Appl Sci 44(11):9128\u20139142","journal-title":"Math Methods Appl Sci"},{"issue":"01","key":"5502_CR28","doi-asserted-by":"publisher","first-page":"2050084","DOI":"10.1142\/S1793524520500849","volume":"14","author":"LN Guin","year":"2021","unstructured":"Guin LN, Pal S, Chakravarty S, Djilali S (2021) Pattern dynamics of a reaction-diffusion predator-prey system with both refuge and harvesting. Int J Biomath 14(01):2050084","journal-title":"Int J Biomath"},{"issue":"2","key":"5502_CR29","doi-asserted-by":"publisher","first-page":"718","DOI":"10.1002\/mma.7807","volume":"45","author":"A Mezouaghi","year":"2022","unstructured":"Mezouaghi A, Djilali S, Bentout S, Biroud K (2022) Bifurcation analysis of a diffusive predator-prey model with prey social behavior and predator harvesting. Math Methods Appl Sci 45(2):718\u2013731","journal-title":"Math Methods Appl Sci"},{"key":"5502_CR30","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1016\/j.swevo.2019.03.013","volume":"48","author":"A Yadav","year":"2019","unstructured":"Yadav A (2019) Aefa: Artificial electric field algorithm for global optimization. Swarm Evol Comput 48:93\u2013108","journal-title":"Swarm Evol Comput"},{"issue":"9","key":"5502_CR31","doi-asserted-by":"publisher","first-page":"10805","DOI":"10.1007\/s10489-021-02865-7","volume":"52","author":"A Sajwan","year":"2022","unstructured":"Sajwan A, Yadav A (2022) A study of exploratory and stability analysis of artificial electric field algorithm. Appl Intell 52(9):10805\u201310828","journal-title":"Appl Intell"},{"issue":"2","key":"5502_CR32","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1016\/0021-9991(74)90011-4","volume":"14","author":"RF Warming","year":"1974","unstructured":"Warming RF, Hyett BJ (1974) The modified equation approach to the stability and accuracy analysis of finite-difference methods. J Comput Phys 14(2):159\u2013179","journal-title":"J Comput Phys"},{"issue":"1\u20133","key":"5502_CR33","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1016\/0168-9274(93)90037-R","volume":"11","author":"K Burrage","year":"1993","unstructured":"Burrage K (1993) Parallel methods for initial value problems. Appl Numer Math 11(1\u20133):5\u201325","journal-title":"Appl Numer Math"},{"key":"5502_CR34","unstructured":"Richtmyer RD, Morton KW (1994) Difference methods for initial-value problems. Malabar"},{"key":"5502_CR35","volume-title":"Numerical partial differential equations: finite difference methods","author":"JW Thomas","year":"2013","unstructured":"Thomas JW (2013) Numerical partial differential equations: finite difference methods. Springer Science & Business Media, Berlin"},{"key":"5502_CR36","doi-asserted-by":"crossref","unstructured":"Vidyasagar M(2002) Nonlinear systems analysis. SIAM","DOI":"10.1137\/1.9780898719185"},{"key":"5502_CR37","doi-asserted-by":"crossref","unstructured":"Gazi V (2012) Stochastic stability analysis of the particle dynamics in the PSO algorithm. In: 2012 IEEE International Symposium on Intelligent Control, IEEE, pp 708\u2013713.","DOI":"10.1109\/ISIC.2012.6398264"},{"issue":"1","key":"5502_CR38","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1109\/72.822511","volume":"11","author":"S Sridhar","year":"2000","unstructured":"Sridhar S, Khalil Hassan K (2000) Output feedback control of nonlinear systems using RBF neural networks. IEEE Trans Neural Netw 11(1):69\u201379","journal-title":"IEEE Trans Neural Netw"},{"key":"5502_CR39","unstructured":"Rugh WJ (1996) Linear system theory. Prentice-Hall, Inc"},{"key":"5502_CR40","volume-title":"Design of feedback control systems","author":"RT Stefani","year":"2002","unstructured":"Stefani RT, Bahram S, Savant Clement J, Hostetter Gene H (2002) Design of feedback control systems. Oxford University Press, Oxford"},{"key":"5502_CR41","doi-asserted-by":"crossref","unstructured":"Byrnes CI, Lin W (1993) Discrete-time lossless systems, feedback equivalence and passivity. In: Proceedings of 32nd IEEE Conference on Decision and Control, IEEE, pp 1775\u20131781","DOI":"10.1109\/CDC.1993.325495"},{"key":"5502_CR42","unstructured":"Bergh Frans Van D (2007) An analysis of particle swarm optimizers. PhD thesis, University of Pretoria"},{"key":"5502_CR43","unstructured":"Mohamed AW, Hadi Anas A, Mohamed Ali K, Agrawal P, Kumar A, Suganthan PN, Problem definitions and evaluation criteria for the CEC, (2021) Special session and competition on single objective bound constrained numerical optimization. Tech Rep, p 2020"},{"issue":"9","key":"5502_CR44","doi-asserted-by":"publisher","first-page":"2194","DOI":"10.1080\/00207179.2018.1430900","volume":"92","author":"Y Jiaju","year":"2019","unstructured":"Jiaju Y, Shuanghe Y, Li J, Yan Y (2019) Fixed-time stability theorem of stochastic nonlinear systems. Int J Control 92(9):2194\u20132200","journal-title":"Int J Control"},{"issue":"1","key":"5502_CR45","doi-asserted-by":"publisher","first-page":"126","DOI":"10.1049\/cth2.12040","volume":"15","author":"Y Jiaju","year":"2021","unstructured":"Jiaju Y, Shuanghe Y, Yan Y (2021) Fixed-time stability of stochastic nonlinear systems and its application into stochastic multi-agent systems. IET Control Theory Appl 15(1):126\u2013135","journal-title":"IET Control Theory Appl"}],"container-title":["The Journal of Supercomputing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-023-05502-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11227-023-05502-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-023-05502-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,8]],"date-time":"2024-01-08T11:27:50Z","timestamp":1704713270000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11227-023-05502-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,4]]},"references-count":45,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,1]]}},"alternative-id":["5502"],"URL":"https:\/\/doi.org\/10.1007\/s11227-023-05502-x","relation":{},"ISSN":["0920-8542","1573-0484"],"issn-type":[{"value":"0920-8542","type":"print"},{"value":"1573-0484","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,7,4]]},"assertion":[{"value":"13 June 2023","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 July 2023","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"All the authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"This article does not contain any studies with human participants or animals performed by any of the authors.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}}]}}