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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.

MSC:
34A33Lattice differential equations
34D05Asymptotic stability of ODE
34G10Linear ODE in abstract spaces
47A16Cyclic vectors, hypercyclic and chaotic operators
47D03(Semi)groups of linear operators
34D20Stability of ODE
34C28Complex behavior, chaotic systems (ODE)