Discrete-time stimulation of the oscillatory and excitable forms of a FitzHugh-Nagumo model applied to the pulsatile release of luteinizing hormone releasing hormone

A model for the pulsatile release of luteinizing hormone releasing hormone (LHRH) can be reduced to a FitzHugh-Nagumo model subject to regular and quasiregular (i.e., with slight random variation in the interstimulus interval), discrete-time stimulation. The relationship of output pulse frequency (OPF) to stimulus frequency is compared between the excitable and oscillatory forms of the model and discussed in the context of results from other pulse-driven model systems. Some examples of the changes in OPF caused by quasiregular and purely Poissonian stimuli are given for the excitable case. The unstimulated system frequently interacts with the stimulation in such a complex manner that the OPF bears little resemblance to the frequency of stimulation or of the unstimulated system. Furthermore, the inability of the oscillatory form of the model to allow complete suppression of output pulses for moderate stimulation frequencies suggests that the LHRH system can be more appropriately described by the excitable form of the model. (c) 1995 American Institute of Physics.     

Partial order complementation graphs

Two partial ordersP andQ on a setX arecomplementary (written asPQ) if they share no ordered pairs (except for loops) but the transitive closure of the union is all possible ordered pairs. For each positive integern we form a graph Pos _n consisting of all nonempty partial orders on {1, ,n} with edges denoting complementation. We investigate here properties of the graphs Pos _n . In particular, we show: