Degenerated Bogdanov-Takens bifurcations in an immuno-tumor model

Degenerated Bogdanov-Takens bifurcations in an immuno-tumor model

Blog Article

A mathematical immuno-tumor model proposed by A.Kavaliauskas [Nonlinear Anal.Model.Control 8, 55 (2003)] and consisting of a Cauchy problem for a system of two first-order ordinary differential equations is studied.For some particular parameters values, this model has saddle-node, Hopf and Bogdanov-Takens (BT) singularities.

In the case of the BT singularities, we herein derive the normal forms of the governing equations by using ideas and airsoft pfp a method from S.-N.Chow, C.Li, and D.Wang [Normal forms and bifurcation of planar vector fields (1994)] and Yu.

A.Kuznetsov [Elements of applied bifurcation theory (1994)], based on an appropriate splitting of associated Hilbert spaces.It is found that a limit case of parameters associated with medicine administration corresponds to degenerate BT bifurcations and, so, to a large variety of responses to the medical treatments for admissible parameters near the mg09aca18te limit ones.