Garner cancerous model, KCC theory, Jacobi stability, chaotic behavior, bifurcation, critical point

 

In cell proliferation, a cancer cell copies its DNA and divides into two cells. If this division is more rapid, then we can say that cancer is the fastest growing or it may be highly graded effective cancer. It is necessary to differentiate cancer stem cells from healthy stem cells. In the present paper, Garner’s cancer model (GCM) has been geometrically studied by using the KCC-Jacobi theory. In the KCC theory, the second-order dynamical system and the geodesic equation associated with the Finsler space are topologically equivalent. The Jacobi stability based on the KCC theory and the Lyapunov linear stability of the model are discussed in detail. The particular value of parameters has been chosen to compare the Jacobi and Lyapunov linear stability, and it has been found that the Jacobi stability on the basis of KCC theory is global than the linear stability. The critical values of the bifurcating parameters are found and their effects on the model have been investigated. This study will be helpful in measuring and preventing cancer cell growth. In this study, it has been observed that an unstable stage of cancer/tumor occurs only when there is a severe effect of any parameter present.

 

Author(s) Details

T.N. Mishra
School of Engineering and Technology, Sanjeev Agrawal Global Educational University, Bhopal, India.

 

Kalpana Deshmukh
School of Science, Sanjeev Agrawal Global Educational University, Bhopal, India.

 

Anjali Chouhan
School of Engineering and Technology, Sanjeev Agrawal Global Educational University, Bhopal, India.

 

Please see the book here :- https://doi.org/10.9734/bpi/mcsru/v7/5752