Concept

# Integrodifference equation

Summary
In mathematics, an integrodifference equation is a recurrence relation on a function space, of the following form: : n_{t+1}(x) = \int_{\Omega} k(x, y), f(n_t(y)), dy, where {n_t}, is a sequence in the function space and \Omega, is the domain of those functions. In most applications, for any y\in\Omega,, k(x,y), is a probability density function on \Omega,. Note that in the definition above, n_t can be vector valued, in which case each element of {n_t} has a scalar valued integrodifference equation associated with it. Integrodifference equations are widely used in mathematical biology, especially theoretical ecology, to model the dispersal and growth of populations. In this case, n_t(x) is the population size or density at location x at time t, f(n_t(x)) describes the local population growth at location x
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