Bifurcation structures of a two-dimensional piecewise linear discontinuous map: analysis of a cobweb model with regime-switching expectations

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27510%2F24%3A10254872" target="_blank" >RIV/61989100:27510/24:10254872 - isvavai.cz</a>

Result on the web

<a href="https://link.springer.com/article/10.1007/s11071-024-09545-4" target="_blank" >https://link.springer.com/article/10.1007/s11071-024-09545-4</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11071-024-09545-4" target="_blank" >10.1007/s11071-024-09545-4</a>

Result language

angličtina

Original language name

Bifurcation structures of a two-dimensional piecewise linear discontinuous map: analysis of a cobweb model with regime-switching expectations

Original language description

We consider the bifurcations occurring in a two-dimensional piecewise-linear discontinuous map that describes the dynamics of a cobweb model in which firms rely on a regime-switching expectation rule. In three different partitions of the phase plane, separated by two discontinuity lines, the map is defined by linear functions with the same Jacobian matrix, having two real eigenvalues, one of which is negative and one equal to 0. This leads to asymptotic dynamics that can belong to two or three critical lines. We show that when the basic fixed point is attracting, it may coexist with at most three attracting cycles. We have determined their existence regions, in the two-dimensional parameter plane, bounded by border collision bifurcation curves. At parameter values for which the basic fixed point is repelling, chaotic attractors may exist - either one that is symmetric with respect to the basic fixed point, or, if not symmetric, the symmetric one also exists. The homoclinic bifurcations of repelling cycles leading to the merging of chaotic attractors are commented by using the first return map on a suitable line. Moreover, four different kinds of homoclinic bifurcations of a saddle 2-cycle, leading to divergence of the generic trajectory, are determined.

Czech name

—

Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

50202 - Applied Economics, Econometrics

Project

<a href="/en/project/GA23-06282S" target="_blank" >GA23-06282S: Evolutionary economic dynamics with finite populations: Modeling and applications</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2024

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Nonlinear Dynamics

ISSN

0924-090X

e-ISSN

1573-269X

Volume of the periodical

112

Issue of the periodical within the volume

17

Country of publishing house

US - UNITED STATES

Number of pages

20

Pages from-to

15601-15620

UT code for WoS article

001209544100003

EID of the result in the Scopus database

2-s2.0-85191777611