GIANT TRANSITORY EXCITATION - THERMOKINETIC MODEL

Giant transitory excitation, as is familiar in nerve impulse propagation, is derived from a simple thermo-kinetic model. The temperature, or the concentration of energy is included as an independent reference variable which is affected by the reaction heat. The rate of reaction is affected in turn by the temperature through Arrhenius' formula. The strong non-linearity involved in the Arrhenius' formula leads to a multiple steady state which is connected with the existence of a threshold for the excitation. The dynamic large excursion along an almost closed path in phase space is related to the existence of a nearby limit cycle, which is generated by an inverted bifurcation. Thus the interplay of the soft- and hard-mode instabilities is shown to form the background of the giant transitory excitation. © 1979.