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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 {\it A. Bobrowski} and {\it M. Kimmel} [J. Biol. Syst. 7, No. 1, 33--43 (1999), \url{doi:10.1142/S0218339099000048}]. Moreover, for a range of parameters, they give an explicit description of subspaces which cannot generate chaotic orbits.

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)
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