Heteroclinic Contours in Neural Ensembles and the Winnerless Competition Principle

摘要

The ability of nonlinear dynamical systems to process incoming information isa key problem of many fundamental and applied sciences. Information processingby computation with attractors (steady states, limit cycles and strangeattractors) has been a subject of many publications. In this paper we discuss anew direction in information dynamics based on neurophysiological experimentsthat can be applied for the explanation and prediction of many phenomena inliving biological systems and for the design of new paradigms in neuralcomputation. This new concept is the Winnerless Competition (WLC) principle.The main point of this principle is the transformation of the incoming identityor spatial inputs into identity-temporal output based on the intrinsicswitching dynamics of the neural system. In the presence of stimuli thesequence of the switching, whose geometrical image in the phase space is aheteroclinic contour, uniquely depends on the incoming information. The keyproblem in the realization of the WLC principle is the robustness against noiseand, simultaneously, the sensitivity of the switching to the incoming input. Inthis paper we prove two theorems about the stability of the sequentialswitching and give several examples of WLC networks that illustrate thecoexistence of sensitivity and robustness.