Chaos in Duopoly Games via Furstenberg Family Couple
Assume that H1 and H2 are two given closed subintervals of ℝ and that f2:H1⟶H2 and f1:H2⟶H1 are continuous maps. Let ϒh1,h2=f1h2,f2h1 be a Cournot map over the space H1×H2. In this paper, we study G1,G2-chaos (resp. strong G1,G2-chaos) of such a Cournot map. We will show that the following are true:...
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Wiley
2019-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2019/5484629 |
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| author | Yu Zhao Risong Li |
| author_facet | Yu Zhao Risong Li |
| author_sort | Yu Zhao |
| collection | DOAJ |
| description | Assume that H1 and H2 are two given closed subintervals of ℝ and that f2:H1⟶H2 and f1:H2⟶H1 are continuous maps. Let ϒh1,h2=f1h2,f2h1 be a Cournot map over the space H1×H2. In this paper, we study G1,G2-chaos (resp. strong G1,G2-chaos) of such a Cournot map. We will show that the following are true: (1) ϒ is G1,G2-chaotic (resp. strong G1,G2-chaotic) if and only if ϒ2Λ1 is G1,G2-chaotic (resp. strong G1,G2-chaotic) if and only if Γ2Λ2 is G1,G2-chaotic (resp. strong G1,G2-chaotic). (2) ϒ is G1,G2-chaotic (resp. strong G1,G2-chaotic) if and only if ϒ2Λ1∪Λ2 is G1,G2-chaotic (resp. strong G1,G2-chaotic). (3) f1∘f2 is G1,G2-chaotic (resp. strong G1,G2-chaotic) if and only if so is f2∘f1. MR(2000) Subject Classification: Primary 37D45, 54H20, and 37B40 and Secondary 26A18 and 28D20. |
| format | Article |
| id | doaj-art-4eda964b01504a7a8946daa65bdd93d9 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
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| series | Complexity |
| spelling | doaj-art-4eda964b01504a7a8946daa65bdd93d92025-02-03T01:06:40ZengWileyComplexity1076-27871099-05262019-01-01201910.1155/2019/54846295484629Chaos in Duopoly Games via Furstenberg Family CoupleYu Zhao0Risong Li1School of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang 524025, ChinaSchool of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang 524025, ChinaAssume that H1 and H2 are two given closed subintervals of ℝ and that f2:H1⟶H2 and f1:H2⟶H1 are continuous maps. Let ϒh1,h2=f1h2,f2h1 be a Cournot map over the space H1×H2. In this paper, we study G1,G2-chaos (resp. strong G1,G2-chaos) of such a Cournot map. We will show that the following are true: (1) ϒ is G1,G2-chaotic (resp. strong G1,G2-chaotic) if and only if ϒ2Λ1 is G1,G2-chaotic (resp. strong G1,G2-chaotic) if and only if Γ2Λ2 is G1,G2-chaotic (resp. strong G1,G2-chaotic). (2) ϒ is G1,G2-chaotic (resp. strong G1,G2-chaotic) if and only if ϒ2Λ1∪Λ2 is G1,G2-chaotic (resp. strong G1,G2-chaotic). (3) f1∘f2 is G1,G2-chaotic (resp. strong G1,G2-chaotic) if and only if so is f2∘f1. MR(2000) Subject Classification: Primary 37D45, 54H20, and 37B40 and Secondary 26A18 and 28D20.http://dx.doi.org/10.1155/2019/5484629 |
| spellingShingle | Yu Zhao Risong Li Chaos in Duopoly Games via Furstenberg Family Couple Complexity |
| title | Chaos in Duopoly Games via Furstenberg Family Couple |
| title_full | Chaos in Duopoly Games via Furstenberg Family Couple |
| title_fullStr | Chaos in Duopoly Games via Furstenberg Family Couple |
| title_full_unstemmed | Chaos in Duopoly Games via Furstenberg Family Couple |
| title_short | Chaos in Duopoly Games via Furstenberg Family Couple |
| title_sort | chaos in duopoly games via furstenberg family couple |
| url | http://dx.doi.org/10.1155/2019/5484629 |
| work_keys_str_mv | AT yuzhao chaosinduopolygamesviafurstenbergfamilycouple AT risongli chaosinduopolygamesviafurstenbergfamilycouple |