Functional shift-induced degenerate transcritical neimark–sacker bifurcation in a discrete hypercycle
In this paper, we investigate the impact of functional shifts in a time-discrete cross-catalytic system. We use the hypercycle model considering that one of the species shifts from a cooperator to a degrader. At the bifurcation caused by this functional shift, an invariant curve collapses to a point...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/407258 |
| Acceso en línea: | https://hdl.handle.net/2117/407258 https://dx.doi.org/10.1142/S0218127424500457 |
| Access Level: | acceso abierto |
| Palabra clave: | Discrete geometry Dynamics Differential equations, Nonlinear Discrete dynamical system Continuous dynamical system Neimark–Sacker bifurcation Transcritical bifurcation Nonlinear population dynamics Cooperation Functional shift Geometria discreta Dinàmica Equacions diferencials no lineals Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics |
| Sumario: | In this paper, we investigate the impact of functional shifts in a time-discrete cross-catalytic system. We use the hypercycle model considering that one of the species shifts from a cooperator to a degrader. At the bifurcation caused by this functional shift, an invariant curve collapses to a point P while, simultaneously, two fixed points collide with P in a transcritical bifurcation. Moreover, all points of a line containing P become fixed points at the bifurcation and only at the bifurcation in a degenerate scenario. We provide a complete analytical description of this degenerate bifurcation. As a result of our study, we prove the existence of the invariant curve arising from the transition to cooperation. |
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