State point forcing permits validation of fixed point locations during chaotic epileptic bursting in the rat brain

In attempting to manipulate epileptiform bursting in the rat brain, one approach is to apply nonlinear chaos control techniques to alter this spontaneous electrical activity. A key element to implementing this technique is identification of unstable periodic orbits (UPOs), especially period-1 orbits and the location of fixed points within state space around which the bursting can be manipulated. However, experimental factors such as physiological noise and system nonstationarity have the potential to make the accuracy of fixed point location prone to inaccuracy. We developed a technique known as state point forcing in which we statistically compare the temporal evolution of a system state brought close to the postulated fixed point relative to other locations chosen within state space. This technique verified that our calculations of UPO location during spontaneous bursting in rat hippocampus were functionally accurate.