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:...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2019-01-01
|
| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2019/5484629 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| ISSN: | 1076-2787 1099-0526 |