On catastrophes in cancer dynamics through the trans-heteroclinic bifurcation [ Back ]

Date:
11.12.17   
Times:
16:00 to 17:00
Place:
UAB - Dept. Matemàtiques (C1/-128)
Speaker:
Josep Sardanyés
University:
Centre de Recerca Matemàtica

Abstract:

We introduce a phenotypic cancer model using the quasispecies replicator equation and MonteCarlo simulations. The differential equations model reveals a new global bifurcation responsible for a catastrophic extinction of tumor cells. This bifurcation, named trans-heteroclinic bifurcation, involves the exchange of stability between two distant fixed points with opposite stability that are connected heteroclinically. When this system is not at the bifurcation value, monostability occurs, and the population can either achieve the cancer or the healthy state, depending on the values of the control parameters, and independently of the initial conditions. Stochastic simulations reveal smoothing of the catastrophic shift and a novel type of noise-induced bistability.

This is a joint work with Regina Martínez (UAB), Carles Simó (UB), and Ricard Solé (UPF, IBE).