Superpositions between non linear intermittency maps, application in biological neurons networks

Abstract

In a series of works of ours we have shown that we can represent the critical and tricritical points of the Statistical Physics of critical phenomena as a Dynamical phenomenon expressed by time series produced by the type I intermittency that exhibits a weak chaos. Recently we have also shown that if we couple these two chaotic dynamics, namely critical and tricritical, we can produce a time sequence which is a temporal Spike Train (ST) of biological-type . In the present work we generalize this issue producing superpositions of critical-tricritical intermittencies with different parameter values. Now arise the question whether the coupling occurs between time series that have resulted from the superposition, will preserved or destroyed the ST biological type , as the number of intermittencies in the superposition will increase? In the other side in present work we find that the spikes produced by the chaotic dynamics of the intermittencies, under the action of superpositions and coupling remain biological-type too. Thus we can say that the dynamics of the fluctuations of the values of the time series produced by the coupling of the superpositions of the intermittencies is the same as the dynamics of the fluctuations of the membrane potential of the biological neuron. Given also that we can manipulate the numerical experiment of superposition and coupling as we wish, we will be able, in future, to approach the cause of neurological problems and decline in thinking ability due to loss of spikes in the brain.