Bifurcation-based neural computation

Quadratic logistic map (QLM) is proposed as a generalized form of an artificial neuron (AN). Dynamics of the QLM not only exhibits computational abilities, but also has certain common features with the one of the modified Hodgkin-Huxley models of a neuron. The rest state of the QLM neuron is wandering within a chaotic attractor. Applied input is an additional bifurcation parameter of the system. Input of a certain range induces emergence of corresponding stable orbit. An arbitrary large number of attractors can be stored in a single QLM neuron. We explore the computational abilities of the QLM dynamics and argue that it may reflect certain aspects of dynamics of biological neurons