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Keywords = chenciner

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19 pages, 1951 KiB  
Article
Another Case of Degenerated Discrete Chenciner Dynamic System and Economics
by Sorin Lugojan, Loredana Ciurdariu and Eugenia Grecu
Mathematics 2022, 10(20), 3782; https://doi.org/10.3390/math10203782 - 13 Oct 2022
Viewed by 1364
Abstract
The non-degenerate Chenciner bifurcation of a discrete dynamical system is studied using a transformation of parameters which must be regular at the origin of the parameters (the condition CH.1 of the well-known treatise of Kuznetsov). The article studies a complementary case, where the [...] Read more.
The non-degenerate Chenciner bifurcation of a discrete dynamical system is studied using a transformation of parameters which must be regular at the origin of the parameters (the condition CH.1 of the well-known treatise of Kuznetsov). The article studies a complementary case, where the transformation is no longer regular at the origin, representing a degeneration. Four different bifurcation diagrams appear in that degenerated case, compared to only two in the non-degenerated one. Degeneracy may cause volatility in economics systems modeled by discrete Chenciner dynamical systems. Full article
(This article belongs to the Special Issue Dynamical System and Stochastic Analysis)
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17 pages, 2521 KiB  
Article
Chenciner Bifurcation Presenting a Further Degree of Degeneration
by Sorin Lugojan, Loredana Ciurdariu and Eugenia Grecu
Mathematics 2022, 10(9), 1603; https://doi.org/10.3390/math10091603 - 8 May 2022
Cited by 2 | Viewed by 2184
Abstract
Chenciner bifurcation appears for some two-dimensional systems with discrete time having two independent variables. Investigated here is a special case of degeneration where the implicit function theorem cannot be used around the origin, so a new approach is necessary. In this scenario, there [...] Read more.
Chenciner bifurcation appears for some two-dimensional systems with discrete time having two independent variables. Investigated here is a special case of degeneration where the implicit function theorem cannot be used around the origin, so a new approach is necessary. In this scenario, there are many more bifurcation diagrams than in the two non-degenerated cases. Several numerical simulations are presented. Full article
(This article belongs to the Special Issue Dynamical System and Stochastic Analysis)
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14 pages, 3129 KiB  
Article
New Elements of Analysis of a Degenerate Chenciner Bifurcation
by Sorin Lugojan, Loredana Ciurdariu and Eugenia Grecu
Symmetry 2022, 14(1), 77; https://doi.org/10.3390/sym14010077 - 5 Jan 2022
Cited by 2 | Viewed by 2027
Abstract
A new transformation of parameters for generic discrete-time dynamical systems with two independent parameters is defined, for when the degeneracy occurs. Here the classical transformation of parameters (α1,α2)(β1,β2) is [...] Read more.
A new transformation of parameters for generic discrete-time dynamical systems with two independent parameters is defined, for when the degeneracy occurs. Here the classical transformation of parameters (α1,α2)(β1,β2) is not longer regular at (0,0); therefore, implicit function theorem (IFT) cannot be applied around the origin, and a new transformation is necessary. The approach in this article to a case of Chenciner bifurcation is theoretical, but it can provide an answer for a number of applications of dynamical systems. We studied the bifurcation scenario and found out that, by this transformation, four different bifurcation diagrams are obtained, and the non-degenerate Chenciner bifurcation can be described by two bifurcation diagrams. Full article
(This article belongs to the Topic Dynamical Systems: Theory and Applications)
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