Аннотация:
Обобщено понятие квадратичного бистохастического оператора и введено понятие произвольного бистохастического оператора. Доказано необходимое условие для бистохастичности оператора. Также получено, что для бистохастических операторов выполняется эргодическая теорема.
Yu. Kh. Eshkabilov, J. Z. Istamov, “Properties of stochastic operators of order v on a finite-dimensional simplex”, jour, 166:4 (2024), 651
Kh. Kh. Saburov, “Krause Mean Processes Generated by Cubic Stochastic Matrices with Weak Influences”, Lobachevskii J Math, 44:12 (2023), 5384
Д. Б. Эшмаматова, М. А. Таджиева, Р. Н. Ганиходжаев, “Критерии существования внутренних неподвижных точек дискретных динамических систем Лотки-Вольтерры c однородными турнирами”, Известия вузов. ПНД, 30:6 (2022), 702–716
洋 刘, “Ancient and Modern Literature on the Classical Formula of Linggui Zhugan Decoction”, TCM, 10:05 (2021), 699
Abdulghafor R., Almotairi S., Almohamedh H., Almutairi B., Bajahzar A., Almutairi S.S., “a Nonlinear Convergence Consensus: Extreme Doubly Stochastic Quadratic Operators For Multi-Agent Systems”, Symmetry-Basel, 12:4 (2020), 540
Abdulghafor R., Abdullah Sh.Sh., Turaev Sh., Zeki A., Al-Shaikhli I., “Linear and Nonlinear Stochastic Distribution For Consensus Problem in Multi-Agent Systems”, Neural Comput. Appl., 32:1, SI (2020), 261–277
Abdulghafor R., Abdullahb Sh.Sh., Turaev Sh., Hassan R., “the Nonlinear Limit Control of Edsqos on Finite Dimensional Simplex”, Automatika, 60:4 (2019), 404–412
Abdulghafor R., Turaev Sh., “Consensus of Fractional Nonlinear Dynamics Stochastic Operators For Multi Agent Systems”, Inf. Fusion, 44 (2018), 1–21
Abdulghafor R., Turaev Sh., Zeki A., Al-Shaikhli I., “Reach a Nonlinear Consensus For Mas Via Doubly Stochastic Quadratic Operators”, Int. J. Control, 91:6 (2018), 1431–1459
Abdulghafor R., Abdullah Sh.Sh., Turaev Sh., Othman M., “An Overview of the Consensus Problem in the Control of Multi-Agent Systems”, Automatika, 59:2 (2018), 143–157
Abdulghafor R., Turaev Sh., Zeki A., Abubaker A., “Nonlinear Convergence Algorithm: Structural Properties With Doubly Stochastic Quadratic Operators For Multi-Agent Systems”, J. Artif. Intell. Soft Comput. Res., 8:1 (2018), 49–61
Abdulghafor R., Shahidi F., Zeki A., Turaev Sh., “Dynamics of Doubly Stochastic Quadratic Operators on a Finite-Dimensional Simplex”, Open Math., 14 (2016), 509–519
Rawad Abdulghafor, Sherzod Turaev, Adamu Abubakar, Akram Zeki, 2015 4th International Conference on Advanced Computer Science Applications and Technologies (ACSAT), 2015, 192
Shahidi F., “Necessary and Sufficient Conditions for Doubly Stochasticity of Infinite-Dimensional Quadratic Operators”, Linear Alg. Appl., 438:1 (2013), 96–110