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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

50202 - Applied Economics, Econometrics

Projekt

<a href="/cs/project/GA23-06282S" target="_blank" >GA23-06282S: Evoluční ekonomická dynamika s konečnou populací: Modelování a aplikace</a><br>

Návaznosti

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

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

Nonlinear Dynamics

ISSN

0924-090X

e-ISSN

1573-269X

Svazek periodika

112

Číslo periodika v rámci svazku

17

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

20

Strana od-do

15601-15620

Kód UT WoS článku

001209544100003

EID výsledku v databázi Scopus

2-s2.0-85191777611