En este artículo se hace un análisis de la bifurcación de Hopf del sistema tridimensional tipo Lorenz introducido por Xianyi Li y Qianjun Ou (2011), este análisis consiste en identificar una región de parámetros del sistema donde la bifurcación de Hopf es no degenerada y supercrítica, aspecto que no es abordado en el artículo de Xianyi Li y Qianjun Ou. Para lograr este objetivo se utiliza el Teorema de la Variedad Central y el Teorema de Hopf. Además, para ilustrar los resultados, se muestran gráficas de algunas trayectorias del sistema, las cuales fueron obtenidas mediantesimulación numérica.
This article investigates the dynamics of cancer through a coupled system of three nonlinear ordinary differential equations. The evolution of the cancer tumour is examined under the variation of the immune cell activation parameter, and the study determines the values of this parameter that cause changes in the dynamics of this evolution; these changes are a consequence of two transcritical bifurcations and a supercritical Hopf bifurcation that exist in the system. These results reveal the range of immune cell activation for which tumour escape or tumour latency, or oscillatory behavior due to the appearance of limit cycles, is achieved. In addition, an optimal value is distinguished for which a minimum number of active immune response cells is sufficient to bring the tumour to a latent state.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.