Solitary solutions to a metastasis model represented by two systems of coupled Riccati equations

Abstract

Solitary solutions to a two-tumor metastasis model represented by a system of multiplicatively coupled Riccati equations are considered in this paper. The interaction between tumors is modelled by a one-sided diffusive coupling when one coupled Riccati system influences the other, but not the opposite. Necessary and sufficient conditions for the existence of solitary solutions to the composite system of Riccati equations are derived in the explicit form. Computational experiments are used to demonstrate the transitions from one steady-state to another via non-monotonous trajectories.

Keywords

• 35C08
• 34A25
• 92C50