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| In this work, we introduce and analyze a model of sequential hermaphroditism in
the framework of continuously structured population models with sexual reproduction.
The mathematical tools used for this model are systems of two partial differential equations where each one describe immature and mature life stage of hermaphrodite population. We assume that birth function depends on female and male allocation functions, the competition between adults for reproduction will affect the mature mortality rate and that the recruitment of immature individuals didn't occur at a fixed size. Using the method of characteristics we convert the problem to an equivalent system of a non-linear integral equations involving the birth rate and then we transform it in a delay system. The steady states of the delay system are
analyzed and illustrated for several cases. In particular, neglecting the competition
for resources we have explicitly found a conditions of stability for the of the non-trivial equilibrium. |
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