Transitions and heteroclinic cycles in the general Gierer-Meinhardt equation and cardiovascular calcification model

The article is concerned with transitions and pattern selection analysis of the inhibitor-activator system proposed in connection with recent studies of cardiovascular calcification patterns. Explicit criteria are derived to enable us to distinguish between stable and metastable patterns. By deriving a reduced system of equations, the existence of certain complicated structures is discussed; in particular, heteroclinic cycles are identified and their properties are studied. It is also discussed that the change of boundary conditions can affect the transitions of the system. In this connection, we will also study asymptotic behavior of patterns after transitions and will compare the results with numerical simulations.