{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:33:30Z","timestamp":1760243610828,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2013,9,10]],"date-time":"2013-09-10T00:00:00Z","timestamp":1378771200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, we investigate the combination synchronization of three nonlinear complex hyperchaotic systems: the complex hyperchaotic Lorenz system, the complex hyperchaotic Chen system and the complex hyperchaotic L\u00a8u system. Based on the Lyapunov stability theory, corresponding controllers to achieve combination synchronization among three identical or different nonlinear complex hyperchaotic systems are derived, respectively. Numerical simulations are presented to demonstrate the validity and feasibility of the theoretical analysis.<\/jats:p>","DOI":"10.3390\/e15093746","type":"journal-article","created":{"date-parts":[[2013,9,11]],"date-time":"2013-09-11T03:51:10Z","timestamp":1378871470000},"page":"3746-3761","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Combination Synchronization of Three Identical or Different Nonlinear Complex Hyperchaotic Systems"],"prefix":"10.3390","volume":"15","author":[{"given":"Xiaobing","family":"Zhou","sequence":"first","affiliation":[{"name":"School of Information Science and Engineering, Yunnan University, Kunming 650091, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Murong","family":"Jiang","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Yunnan University, Kunming 650091, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yaqun","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Yunnan University, Kunming 650091, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2013,9,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/0167-2789(82)90057-4","article-title":"The complex Lorenz equations","volume":"4","author":"Fowler","year":"1982","journal-title":"Phys. D"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1951","DOI":"10.1016\/j.mcm.2011.11.053","article-title":"Dynamics and synchronization of new hyperchaotic complex Lorenz system","volume":"55","author":"Mahmoud","year":"2012","journal-title":"Math. Comput. Model."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"915","DOI":"10.1016\/j.chaos.2003.12.039","article-title":"Chaos control of chaotic limit cycles of real and complex van der Pol oscillators","volume":"21","author":"Mahmoud","year":"2004","journal-title":"Chaos Solitons Fractals"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"4295","DOI":"10.1142\/S0218127407019962","article-title":"Active control and global synchronization of the complex Chen and L\u00fc systems","volume":"17","author":"Mahmoud","year":"2007","journal-title":"Int. J. Bifur. Chaos"},{"key":"ref_5","first-page":"90","article-title":"hyperchaotic complex Chen system and its dynamics","volume":"12","author":"Mahmoud","year":"2007","journal-title":"Int. J. Appl. Math. Stat."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1477","DOI":"10.1142\/S0129183108013151","article-title":"Analysis of hyperchaotic complex Lorenz systems","volume":"19","author":"Mahmoud","year":"2008","journal-title":"Int. J. Mod. Phys. C"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"725","DOI":"10.1007\/s11071-009-9513-0","article-title":"On the hyperchaotic complex L\u00fc system","volume":"58","author":"Mahmoud","year":"2009","journal-title":"Nonlinear Dyn."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"e055104","DOI":"10.1088\/1751-8113\/41\/5\/055104","article-title":"Chaotic and hyperchaotic attractors of a complex nonlinear system","volume":"41","author":"Mahmoud","year":"2008","journal-title":"J. Phys. A Math. 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Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"875","DOI":"10.1007\/s11071-010-9770-y","article-title":"Complete synchronization of chaotic complex nonlinear systems with uncertain parameters","volume":"62","author":"Mahmoud","year":"2010","journal-title":"Nonlinear Dyn."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1007\/s11071-009-9637-2","article-title":"Phase and antiphase synchronization of two identical hyperchaotic complex nonlinear systems","volume":"61","author":"Mahmoud","year":"2010","journal-title":"Nonlinear Dyn."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"e055002","DOI":"10.1088\/0031-8949\/87\/05\/055002","article-title":"On projective synchronization of hyperchaotic complex nonlinear systems based on passive theory for secure communications","volume":"87","author":"Mahmoud","year":"2013","journal-title":"Phys. Scr."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"e035005","DOI":"10.1088\/0031-8949\/85\/03\/035005","article-title":"Adaptive modified function projective synchronization of general uncertain chaotic complex systems","volume":"85","author":"Liu","year":"2012","journal-title":"Phys. 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