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Chaoticity and invariant measures for a cell population model. (English) Zbl 1308.92088

Summary: We present a structured model of a cell reproduction system given by a partial differential equations with a nonlocal division term. This equation generates semiflows acting on some subspaces of locally integrable functions. We show that these semiflows possess invariant mixing measures positive on open sets. From this it follows that the system is chaotic, i.e., it has dense trajectories and each trajectory is unstable. We also show the chaoticity of this system in the sense of Devaney.

MSC:

92D25 Population dynamics (general)
92C17 Cell movement (chemotaxis, etc.)
35Q92 PDEs in connection with biology, chemistry and other natural sciences
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