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A neuron's coding strategy is defined by the relationship between its inputs and its spiking output. Much of the computation performed by single neurons can be captured by a linear-nonlinear (LN) probabilistic model: a linear filter extracts the relevant feature in the stimulus that drives spiking, and a nonlinear decision function determines the probability of a spike for a particular value of the filtered stimulus. Statistical techniques can be used to identify LN models in real and simulated neurons. For many systems, the LN model varies in response to changes in stimulus statistics, a property known as adaptive coding. An open question is how the details of the LN model arise from the underlying nonlinear dynamics governing spike generation. In particular, how can adaptive coding arise from a dynamical system with fixed parameters? Using tools from the theory of stochastic dynamical systems, we examine how to derive the LN model from voltage-based dynamical models of the nonlinear integrate-and-fire type. Armed with some analytic results, we gain much insight into how to tune the dynamics to yield specific computational properties. In particular, we can see what must be true for a simple neuron to show contrast invariant coding--coding that is invariant with respect to the typical range of input fluctuations. This leads to experimentally-testable predictions about dynamical properties of real neurons.