{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:18:31Z","timestamp":1760149111921,"version":"build-2065373602"},"reference-count":57,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,7,11]],"date-time":"2023-07-11T00:00:00Z","timestamp":1689033600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Key Laboratory of Complex Dynamics System and Application Analysis of Department of Education of Yunnan Province"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper considers the dual hybrid effects of discrete-time stochastic genetic regulatory networks and discrete-space stochastic genetic regulatory networks in difference formats of exponential Euler difference and second-order central finite difference. The existence of a unique-weight pseudo-\u03b8-almost periodic sequence solution for discrete-time and discrete-space stochastic genetic regulatory networks on the basis of discrete constant variation formulation is discussed, as well as the theory of semi-flow and metric dynamical systems. Furthermore, a finite-time guaranteed cost controller is constructed to reach global exponential stability of these discrete networks via establishing a framework of drive, response, and error networks. The results indicate that spatial diffusions of non-negative dense coefficients have no influence on the global existence of the unique weighted pseudo-\u03b8-almost periodic sequence solution of the networks. The present study is a basic work in the consideration of discrete spatial diffusion in stochastic genetic regulatory networks and serves as a foundation for further study.<\/jats:p>","DOI":"10.3390\/axioms12070682","type":"journal-article","created":{"date-parts":[[2023,7,12]],"date-time":"2023-07-12T01:05:01Z","timestamp":1689123901000},"page":"682","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Weighted Pseudo-\u03b8-Almost Periodic Sequence and Finite-Time Guaranteed Cost Control for Discrete-Space and Discrete-Time Stochastic Genetic Regulatory Networks with Time Delays"],"prefix":"10.3390","volume":"12","author":[{"given":"Shumin","family":"Sun","sequence":"first","affiliation":[{"name":"City College, Kunming University of Science and Technology, Kunming 650051, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6777-1668","authenticated-orcid":false,"given":"Tianwei","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Yunnan University, Kunming 650091, China"}]},{"given":"Zhouhong","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Yuxi Normal University, Yuxi 653100, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Alon, U. 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