A Novel Viewpoint on Parameter Estimation in a Chaotic Neuron Model

Is there any geometrical information in the nervous system?

“…Since chaotic systems are sensitive to initial conditions (Hilborn, 2000), lots of signals with minimum similarity in time domain could have a same source; such behavior might be better understood by analyzing those signals in the phase space and from geometrical viewpoint (Jafari et al, 2013d), as although chaotic signals have pseudorandom behavior in time, they are ordered in phase space (i.e., if one plots the signals as a trajectory in a coordinate of system variables, he will encounter an ordered and specific topology which is called strange attractor) (Hilborn, 2000). …”

“…In fact in many applications of chaotic signals and systems, using temporal properties without being careful about this sensitivity to initial conditions, could lead to important misinterpretations (Jafari et al, 2012, 2013a,c,d). Hence, it seems that more than temporal patterns, it is of paramount importance to investigate topological patterns in such impulse trains.…”