Hopf Bifurcation in a Cobweb Model with Discrete Time Delays
We develop a cobweb model with discrete time delays that characterise the length of production cycle. We assume a market comprised of homogeneous producers that operate as adapters by taking the (expected) profit-maximising quantity as a target to adjust production and consumers with a marginal will...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2014/137090 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832563826815401984 |
|---|---|
| author | Luca Gori Luca Guerrini Mauro Sodini |
| author_facet | Luca Gori Luca Guerrini Mauro Sodini |
| author_sort | Luca Gori |
| collection | DOAJ |
| description | We develop a cobweb model with discrete time delays that characterise the length of production cycle. We assume a market comprised of homogeneous producers that operate as adapters by taking the (expected) profit-maximising quantity as a target to adjust production and consumers with a marginal willingness to pay captured by an isoelastic demand. The dynamics of the economy is characterised by a one-dimensional delay differential equation. In this context, we show that (1) if the elasticity of market demand is sufficiently high, the steady-state equilibrium is locally asymptotically stable and (2) if the elasticity of market demand is sufficiently low, quasiperiodic oscillations emerge when the time lag (that represents the length of production cycle) is high enough. |
| format | Article |
| id | doaj-art-18c268328bc84db1ba8dd8a33e1deb77 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-18c268328bc84db1ba8dd8a33e1deb772025-02-03T01:12:20ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2014-01-01201410.1155/2014/137090137090Hopf Bifurcation in a Cobweb Model with Discrete Time DelaysLuca Gori0Luca Guerrini1Mauro Sodini2Department of Law, University of Genoa, Via Balbi 30/19, 16126 Genoa, ItalyDepartment of Management, Polytechnic University of Marche, Piazza Martelli 8, 60121 Ancona, ItalyDepartment of Economics and Management, University of Pisa, Via Cosimo Ridol 10, 56124 Pisa, ItalyWe develop a cobweb model with discrete time delays that characterise the length of production cycle. We assume a market comprised of homogeneous producers that operate as adapters by taking the (expected) profit-maximising quantity as a target to adjust production and consumers with a marginal willingness to pay captured by an isoelastic demand. The dynamics of the economy is characterised by a one-dimensional delay differential equation. In this context, we show that (1) if the elasticity of market demand is sufficiently high, the steady-state equilibrium is locally asymptotically stable and (2) if the elasticity of market demand is sufficiently low, quasiperiodic oscillations emerge when the time lag (that represents the length of production cycle) is high enough.http://dx.doi.org/10.1155/2014/137090 |
| spellingShingle | Luca Gori Luca Guerrini Mauro Sodini Hopf Bifurcation in a Cobweb Model with Discrete Time Delays Discrete Dynamics in Nature and Society |
| title | Hopf Bifurcation in a Cobweb Model with Discrete Time Delays |
| title_full | Hopf Bifurcation in a Cobweb Model with Discrete Time Delays |
| title_fullStr | Hopf Bifurcation in a Cobweb Model with Discrete Time Delays |
| title_full_unstemmed | Hopf Bifurcation in a Cobweb Model with Discrete Time Delays |
| title_short | Hopf Bifurcation in a Cobweb Model with Discrete Time Delays |
| title_sort | hopf bifurcation in a cobweb model with discrete time delays |
| url | http://dx.doi.org/10.1155/2014/137090 |
| work_keys_str_mv | AT lucagori hopfbifurcationinacobwebmodelwithdiscretetimedelays AT lucaguerrini hopfbifurcationinacobwebmodelwithdiscretetimedelays AT maurosodini hopfbifurcationinacobwebmodelwithdiscretetimedelays |