Abstract
A mathematical method based on the G-projection of differential inclusions is used to construct dynamical models of population biology. We suppose that the system under study, not being limited by resources, may be described by a control system
\] where u is a control describing the choice of resources. Then considering the constraints that the system must satisfy we define a viability set K. Since there may not exist a control u(·) such that the corresponding solution satisfies x(t) ε K, we have to change the dynamics of the control system to get a viable solution. Using the G-projection we introduce so-called “projected” control system
that has a viable solution. The projected system has usually simpler dynamics than traditional models used in population biology.
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Křivan, V.: G-projection of differential inclusions. Preprint
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Křivan, V. Construction of population growth equations in the presence of viability constraints. J. Math. Biol. 29, 379–387 (1991). https://doi.org/10.1007/BF00167158
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DOI: https://doi.org/10.1007/BF00167158