Non‐linear structured population dynamics with co‐variates

Co‐variates are incorporated into a general model of non‐linear structured population dynamics. The proof of the existence and uniqueness of the solutions results from those of a special set, the invariance envelope. It is also valid in presence of state constraints, and solutions need only to have a closed graph (instead of being weakly differentiable as requested in semi‐group theory). Moreover, this invariance envelope provides a simple way to build the solutions, either explicitly in the linear exogenous case, or algo‐rithmically in the non‐linear case, both with co‐variates. The case of age‐structured systems and a model of demographic transition are discussed for illustration.

Keywords:

• Lotka‐McKendrick
• Viability theory Communicated by S. Tuljapurkar

Notes

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