No abstract

The paper investigates the linear stability of mammalian physiology time-delayed flow for three distinct cases (normal cell cycle, a neoplasmic cell cycle, and multiple cell arrest states), for the Dirac, uniform, and exponential distributions. For the Dirac distribution case, it is shown that the model exhibits a Hopf bifurcation for certain values of the parameters involved in the system. As well, for these values, the structural stability of the SODE is studied, using the five KCC-invariants of the second-order canonical extension of the SODE, and all the cases prove to be Jacobi unstable.

No abstract

This paper is dedicated to the study of geometric dynamics (an Euler-Lagrange prolongation of a flow on a Riemannian manifold) from the point of view of KCC theory, Jacobi stability and Lyapounov stability. Section 1 recalls the geometncal roots of Jacobi stability and announces the subject of the paper. Section 2 introduces the variational ODEs (Jacobi fields ODEs), the KCC differential mvanants for a second order ODE system, and defines the Jacobi stability. SectIOn 3 studies the KCC differential mvanants asSOCiated to geometnc dynamiCs. SectIOn 4 descnbes vanous ImeanzatlOns of geometnc dynamiCs. SectIOn 5 studies the Jacobi stability for lineanzed geometnc dynamiCs around a statIOnary pomt of the field. SectIOn 6 shows that the lmeanzed geometnc dynamiCs around a cntlcal pomt of the energy can be Jacobi stable or unstable. SectIOn 7 proves the Lyapounov mstabllity of Jacobi fields ODEs along geometnc dynamiCs traJectones.

Abstract. The paper studies the existence of rest-points and the static bifurcation diagrams of a given nonlinear differential system modeling the cancer cell population evolution from biology. To this aim, the nullclines, the equilibrium points, the transient set, the static bifurcation equation and the associated versal deformation are investigated. The results are further discussed in view of potential applications to cancer therapy.