Critical bifurcation surfaces of 3D discrete dynamics
This paper deals with the analytical representation of bifurcations of each 3D discrete dynamics depending on the set of bifurcation parameters. The procedure of bifurcation analysis proposed in this paper represents the 3D elaboration and specification of the general algorithm of the n-dimensional...
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| Format: | Article |
| Language: | English |
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Wiley
2000-01-01
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| Series: | Discrete Dynamics in Nature and Society |
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| Online Access: | http://dx.doi.org/10.1155/S1026022600000315 |
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| _version_ | 1832545622842933248 |
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| author | Michael Sonis |
| author_facet | Michael Sonis |
| author_sort | Michael Sonis |
| collection | DOAJ |
| description | This paper deals with the analytical representation of bifurcations of each 3D discrete dynamics depending on the set of bifurcation parameters. The procedure of bifurcation analysis proposed in this paper represents the 3D elaboration and specification of the general algorithm of the n-dimensional linear bifurcation analysis proposed by the author earlier. It is proven that 3D domain of asymptotic stability (attraction) of the fixed point for a given 3D discrete dynamics is bounded by three critical bifurcation surfaces: the divergence, flip and flutter surfaces. The analytical construction of these surfaces is achieved with the help of classical Routh–Hurvitz conditions of asymptotic stability. As an application the adjustment process proposed by T. Puu for the Cournot oligopoly model is considered in detail. |
| format | Article |
| id | doaj-art-0944f7b0ab6f43e3a90f326091351377 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2000-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-0944f7b0ab6f43e3a90f3260913513772025-02-03T07:25:13ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2000-01-014433334310.1155/S1026022600000315Critical bifurcation surfaces of 3D discrete dynamicsMichael Sonis0Department of Geography, Bar-Ilan University, Ramat-Gan 52900, IsraelThis paper deals with the analytical representation of bifurcations of each 3D discrete dynamics depending on the set of bifurcation parameters. The procedure of bifurcation analysis proposed in this paper represents the 3D elaboration and specification of the general algorithm of the n-dimensional linear bifurcation analysis proposed by the author earlier. It is proven that 3D domain of asymptotic stability (attraction) of the fixed point for a given 3D discrete dynamics is bounded by three critical bifurcation surfaces: the divergence, flip and flutter surfaces. The analytical construction of these surfaces is achieved with the help of classical Routh–Hurvitz conditions of asymptotic stability. As an application the adjustment process proposed by T. Puu for the Cournot oligopoly model is considered in detail.http://dx.doi.org/10.1155/S1026022600000315Bifurcation surfacesRouth-Hurvitz conditionsCournot oligopoly. |
| spellingShingle | Michael Sonis Critical bifurcation surfaces of 3D discrete dynamics Discrete Dynamics in Nature and Society Bifurcation surfaces Routh-Hurvitz conditions Cournot oligopoly. |
| title | Critical bifurcation surfaces of 3D discrete dynamics |
| title_full | Critical bifurcation surfaces of 3D discrete dynamics |
| title_fullStr | Critical bifurcation surfaces of 3D discrete dynamics |
| title_full_unstemmed | Critical bifurcation surfaces of 3D discrete dynamics |
| title_short | Critical bifurcation surfaces of 3D discrete dynamics |
| title_sort | critical bifurcation surfaces of 3d discrete dynamics |
| topic | Bifurcation surfaces Routh-Hurvitz conditions Cournot oligopoly. |
| url | http://dx.doi.org/10.1155/S1026022600000315 |
| work_keys_str_mv | AT michaelsonis criticalbifurcationsurfacesof3ddiscretedynamics |