Strong Memory and Recognition in the RRTN Model

For studying nonlinear response of complex systems, we developed a Random Resistor cum Tunneling (t) bond Network (RRTN) model. Here the ohmic (o) bonds occupy random positions on an insulating host lattice and a t-bond is placed in the gap between two o-bonds separated by one nearest neighbour distance and no farther. These t-bonds have a threshold voltage above which it is ´active´ (charges flow through) and below which it remains insulating. This gives rise to a macroscopic threshold or breakdown voltage in the RRTN. The early dynamics is scale-free with two power-law regimes, as observed in many systems of Nature with statistically correlated randomness. Eventually, the dynamics becomes exponentially fast (i.e., acquires a timescale) as it approaches a steady state is very robust against arbitrarily chosen initial field distributions. This strong memory attribute of the steady state, in spite of its intrinsic disorder, should be very useful in the field of cognitive processes, learning, fault-tolerant coding etc.