Abstract
Threshold and shaping actions of a dynamical system are analyzed in the phase plane. Attention is focussed on two kinds of curves (A-type and R-type curves) of the trajectory. The A-type curve causes the stabilization of the process, such as the shaping action; while the R-type curve causes the growth of the difference between two states of the system, such as the threshold action. As curves corresponding to the A-type (or R-type) curves, an A-inflector (or R-inflector) is defined. Their properties are investigated. The A-type (R-type) curve is located in the neighborhood of the A-inflector (R-inflector). The BVP model of an excitable membrane is taken as an example. This model is analyzed by the use of the A-inflector and the R-inflector. An algebraical equation for the threshold value and a necessary condition for the occurrence of threshold action are discussed.
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