Breaking and Sustaining Bifurcations in <mml:mstyle>S</mml:mstyle>N-Invariant Equidistant Economy

• Type: Article in International Scientific Journal
• Date: 2020

Authors

Aizawa, H (Author) Other; Ikeda, K (Author) Other; Osawa, M (Author) Other; Gaspar, JM (Author) FEP

Journal

Title: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Vol. 30 No. 10

ISSN: 0218-1274

Publisher: World Scientific

Indexing

ISI Web of Knowledge - 5 Citations

Scopus - 5 Citations

Other information

Authenticus ID: P-00T-9GP

DOI: 10.1142/s0218127420502405

Abstract (EN): This paper elucidates the bifurcation mechanism of an equidistant economy in spatial economics. To this end, we derive the rules of secondary and further bifurcations as a major theoretical contribution of this paper. Then we combine them with pre-existing results of direct bifurcation of the symmetric group <mml:mstyle>S</mml:mstyle>N [Elmhirst, 2004]. Particular attention is devoted to the existence of invariant solutions which retain their spatial distributions when the value of the bifurcation parameter changes. Invariant patterns of an equidistant economy under the replicator dynamics are obtained. The mechanism of bifurcations from these patterns is elucidated. The stability of bifurcating branches is analyzed to demonstrate that most of them are unstable immediately after bifurcation. Numerical analysis of spatial economic models confirms that almost all bifurcating branches are unstable. Direct bifurcating curves connect the curves of invariant solutions, thereby creating a mesh-like network, which appears as threads of warp and weft. The theoretical bifurcation mechanism and numerical examples of networks advanced herein might be of great assistance in the study of spatial economics.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 17