Heteroclinic Contours in Neural Ensembles and the Winnerless Competition Principle

The ability of nonlinear dynamical systems to process incoming information is a key problem of many fundamental and applied sciences. Information processing by computation with attractors (steady states, limit cycles and strange attractors) has been a subject of many publications. In this paper we discuss a new direction in information dynamics based on neurophysiological experiments that can be applied for the explanation and prediction of many phenomena in living biological systems and for the design of new paradigms in neural computation. This new concept is the Winnerless Competition (WLC) principle. The main point of this principle is the transformation of the incoming identity or spatial inputs into identity-temporal output based on the intrinsic switching dynamics of the neural system. In the presence of stimuli the sequence of the switching, whose geometrical image in the phase space is a heteroclinic contour, uniquely depends on the incoming information. The key problem in the realization of the WLC principle is the robustness against noise and, simultaneously, the sensitivity of the switching to the incoming input. In this paper we prove two theorems about the stability of the sequential switching and give several examples of WLC networks that illustrate the coexistence of sensitivity and robustness. Paper in press for ’International Journal of Bifurcation and Chaos’ (2004), Vol. 14 (4).