Birth-and-Death Type Systems with Parameter and Chaotic Dynamics of some Linear Kinetic Models

Abstract

J. Banasiak and M. Lachowicz proved in [Math. Models Methods Appl. Sci. 12 (2002), 755 – 775] that, under certain conditions on the coefficients, the dynamics generated by birth-and-death type systems with proliferation was chaotic. In this paper we extend this result to systems with parameter-dependent coefficients and present an application to a linear Boltzmann equation describing inelastic collisions.