{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T07:33:37Z","timestamp":1780472017488,"version":"3.54.1"},"reference-count":26,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,7,27]],"date-time":"2023-07-27T00:00:00Z","timestamp":1690416000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This manuscript explores the analysis of passivity and synchronization criteria for a complex fractional-order dynamical network model with derivative couplings and time-varying delays. The passivity problem of the proposed network model is deduced using various inequality methods and presented as a linear matrix inequality. To ensure complete synchronization for a fractional-order complex dynamical network with derivative couplings (CDNMDC), we derive suitable criteria using an adaptive feedback control method. Additionally, we investigate the synchronization criterion of these complex networks while accounting for parameter uncertainties. Finally, we provide an example to demonstrate the effectiveness of the proposed solutions.<\/jats:p>","DOI":"10.3390\/axioms12080730","type":"journal-article","created":{"date-parts":[[2023,7,28]],"date-time":"2023-07-28T02:10:45Z","timestamp":1690510245000},"page":"730","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Passivity Analysis and Complete Synchronization of Fractional Order for Both Delayed and Non-Delayed Complex Dynamical Networks with Couplings in the Derivative"],"prefix":"10.3390","volume":"12","author":[{"given":"S.","family":"Aadhithiyan","sequence":"first","affiliation":[{"name":"Center for Computational Modeling, Chennai Institute of Technology, Chennai 600069, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"R.","family":"Raja","sequence":"additional","affiliation":[{"name":"Ramanujan Centre for Higher Mathematics, Alagappa University, Karaikudi 630004, India"},{"name":"Department of Computer Science and Mathematics, Lebanese American University, Beirut P.O. Box 13-5053, Lebanon"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5262-1138","authenticated-orcid":false,"given":"Jehad","family":"Alzabut","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"},{"name":"Department of Industrial Engineering, OST\u0130M Technical University, Ankara 06374, Turkey"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"G.","family":"Rajchakit","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Maejo University, Chiang Mai 50290, Thailand"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0634-2370","authenticated-orcid":false,"given":"Ravi P.","family":"Agarwal","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Texas A & M University-Kingsville, Kingsville, TX 78363, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"110884","DOI":"10.1016\/j.automatica.2023.110884","article-title":"Synchronization of power systems under stochastic disturbances","volume":"151","author":"Wang","year":"2023","journal-title":"Automatica"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"113142","DOI":"10.1016\/j.chaos.2023.113142","article-title":"Traffic-driven explosive synchronization with adaptive local routing in complex networks","volume":"168","author":"Chen","year":"2023","journal-title":"Chaos Solitons Fractals"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"132928","DOI":"10.1016\/j.physd.2021.132928","article-title":"Dynamic coupling in small world outer synchronization of chaotic networks","volume":"423","year":"2021","journal-title":"Phys. D Nonlinear Phenom."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"101436","DOI":"10.1016\/j.jocs.2021.101436","article-title":"Adaptive complete synchronization of two complex networks with uncertain parameters, structures, and disturbances","volume":"54","author":"Wang","year":"2021","journal-title":"J. Comput. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"121753","DOI":"10.1016\/j.physa.2019.121753","article-title":"Successive lag synchronization on complex dynamical networks via delay-dependent impulsive control","volume":"531","author":"Qiu","year":"2019","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"206","DOI":"10.3182\/20130708-3-CN-2036.00079","article-title":"Global asymptotical synchronization of delayed complex dynamical networks with switching topology","volume":"46","author":"Lu","year":"2013","journal-title":"IFAC Proc. Vol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1182","DOI":"10.1016\/j.nonrwa.2012.09.009","article-title":"Function projective synchronization in complex dynamical networks with time delay via hybrid feedback control","volume":"14","author":"Du","year":"2013","journal-title":"Nonlinear Anal. Real World Appl."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Xiao-Xiao, Z., Jin-Liang, W., Yan-Li, H., and Shun-Yan, R. (2017, January 26\u201328). Passivity analysis of multi-weighted complex dynamical networks with fixed and switching topologies. Proceedings of the 2017 36th Chinese Control Conference (CCC), Dalian, China.","DOI":"10.23919\/ChiCC.2017.8028574"},{"key":"ref_9","unstructured":"Zhao, Y. (2011, January 22\u201324). Passivity analysis of complex dynamical networks with general topology. Proceedings of the Proceedings of the 30th Chinese Control Conference, Yantai, China."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1016\/j.isatra.2018.02.002","article-title":"Passivity analysis of memristor-based impulsive inertial neural networks with time-varying delays","volume":"74","author":"Wan","year":"2018","journal-title":"ISA Trans."},{"key":"ref_11","first-page":"125786","article-title":"Passivity-based synchronization for Markov switched neural networks with time delays and the inertial term","volume":"394","author":"Fang","year":"2021","journal-title":"Appl. Math. Comput."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.vlsi.2021.05.012","article-title":"Experimental verification of the multi-scroll chaotic attractors synchronization in PWL arbitrary-order systems using direct coupling and passivity-based control","volume":"81","author":"Serrano","year":"2021","journal-title":"Integration"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"366","DOI":"10.1007\/s11424-019-8121-4","article-title":"Global Asymptotic Synchronization of a Class of BAM Neural Networks with Time Delays via Integrating Inequality Techniques","volume":"33","author":"Lin","year":"2020","journal-title":"J. Syst. Sci. Complex."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"672","DOI":"10.1007\/s11424-020-8209-x","article-title":"General Decay Synchronization for Recurrent Neural Networks with Mixed Time Delays","volume":"33","author":"Muhammadhaji","year":"2020","journal-title":"J. Syst. Sci. Complex."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1016\/j.neucom.2018.05.058","article-title":"Finite-time passivity of delayed multi-weighted complex dynamical networks with different dimensional nodes","volume":"312","author":"Huang","year":"2018","journal-title":"Neurocomputing"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1221","DOI":"10.1016\/j.jfranklin.2019.12.003","article-title":"Analysis and pinning control for passivity and synchronization of multiple derivative coupled reaction diffusion neural networks","volume":"357","author":"Wang","year":"2020","journal-title":"J. Frankl. Inst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"845","DOI":"10.1016\/j.matcom.2022.10.029","article-title":"Passivity of fractional-order coupled neural networks with interval uncertainties","volume":"205","author":"Qiu","year":"2023","journal-title":"Math. Comput. Simul."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"558","DOI":"10.1016\/j.neucom.2021.12.070","article-title":"PD control for passivity of coupled reaction-diffusion neural networks with multiple state couplings or spatial diffusion couplings","volume":"489","author":"Liang","year":"2022","journal-title":"Neurocomputing"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1016\/j.neucom.2021.12.106","article-title":"Passivity analysis of fractional-order neural networks with interval parameter uncertainties via an interval matrix polytope approach","volume":"477","author":"Xiao","year":"2022","journal-title":"Neurocomputing"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.neucom.2016.06.076","article-title":"Passivity and pinning passivity of complex dynamical networks with spatial diffusion coupling","volume":"227","author":"Ren","year":"2017","journal-title":"Neurocomputing"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/j.neucom.2015.12.071","article-title":"Synchronization of complex dynamical networks with uncertain inner coupling and successive delays based on passivity theory","volume":"186","author":"Kaviarasan","year":"2016","journal-title":"Neurocomputing"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1016\/j.neucom.2021.05.050","article-title":"Passivity of fractional-order coupled neural networks with multiple state\/derivative couplings","volume":"455","author":"Liu","year":"2021","journal-title":"Neurocomputing"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1016\/j.matcom.2021.08.023","article-title":"Mixed passivity based stability analysis of fractional-order gene regulatory networks with variable delays","volume":"192","author":"Padmaja","year":"2022","journal-title":"Math. Comput. Simul."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/j.chaos.2015.11.027","article-title":"Passivity analysis of Markovian switching complex dynamic networks with multiple time-varying delays and stochastic perturbations","volume":"83","author":"Ye","year":"2016","journal-title":"Chaos Solitons Fractals"},{"key":"ref_25","unstructured":"Podlubny, I. (1999). Fractional Derivatives and Integrals, Elsevier. Chapter 2."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1635","DOI":"10.1002\/acs.3056","article-title":"Stability analysis and robust synchronization of fractional-order competitive neural networks with different time scales and impulsive perturbations","volume":"33","author":"Pratap","year":"2019","journal-title":"Int. J. Adapt. Control. Signal Process."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/8\/730\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:20:29Z","timestamp":1760127629000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/8\/730"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,27]]},"references-count":26,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2023,8]]}},"alternative-id":["axioms12080730"],"URL":"https:\/\/doi.org\/10.3390\/axioms12080730","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,7,27]]}}}