Recurrent neurodynamic model of neuron with variable activation characteristic

The article deals with a recurrent neurodynamic model of the neuron with a broad class of activation functions, including sigmoidal, stepwise, bounded linear and other ones. We consider the activation characteristic of the neuron, which is the dependence of the output signal on the input one. We demonstrate analytically that regardless of the choice of a particular activation function from the class of functions under consideration, the activation characteristic will have a characteristic property. When the value of the so-called modulating parameter is varied, the type of this characteristic will change from a function close to the selected activation function to a curve containing hysteresis loops. In other words, through the modulating parameter, the neuron model can be tuned to operate in monostable mode or one of the admissible multi-stability modes. We demonstrate how to determine the bifurcation points of the regime change, the corresponding boundaries of the multi-stability regions, and the conditions for finding solutions in them. The results of numerical experiments confirm the validity of the conclusions.