Dynamics of birth-and-death processes with proliferation – stability and chaos. (English) Zbl 1219.34014

The authors provide a detailed description of the long time dynamics of the semigroup associated with constant coefficient infinite birth-and-death systems with proliferation. They identify a range of parameters for which the semigroup is both stable and topologically chaotic. The results extend earlier stability results by A. Bobrowski and M. Kimmel [J. Biol. Syst. 7, No. 1, 33–43 (1999), doi:10.1142/S0218339099000048]. Moreover, for a range of parameters, they give an explicit description of subspaces which cannot generate chaotic orbits.


34A33 Ordinary lattice differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
34G10 Linear differential equations in abstract spaces
47A16 Cyclic vectors, hypercyclic and chaotic operators
47D03 Groups and semigroups of linear operators
34D20 Stability of solutions to ordinary differential equations
34C28 Complex behavior and chaotic systems of ordinary differential equations
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