Nonlinear Quantum Neuro-Psycho-Dynamics with Topological Phase Transitions

Abstract

We have proposed a novel model of general quantum, stochastic and chaotic psychodynamics. The model is based on the previously developed Life-Space Foam (LSF) framework to motivational and c ognitive dynamics. The present model extends the LSF-approach by incorporating chaotic and topological non-equilibrium phase transitions. Such extended LSF-model is applied for rigorous description of multi-agent joint action. The present model is related to Haken-Kelso-Bunz model of self-organization in the human motor system (including: multi-stability, phase transitions and hysteresis effects, presenting a contrary view to the purely feedback driven neural systems), as well as the entropy-approach to adaptation in human goal-directed motor control.

Adaptive-Wave Alternative for the Black-Scholes Option Pricing Model

“…as well as periodic solutions (30). Inserting (14) back into (33) gives the double-kink solution for the Manakov system: σ(s, t) = ±(w/ √ 2) tanh(w s/ √ 2) e −iw 2 t , ψ(s, t) = ±(w/ √ 2) tanh(w s/ √ 2)e −iw 2 t .…”

“…Lo [49,50]; 2. My adaptive path integral approach to human cognition [29,30,31]; 3. Elliott wave (fractal) market theory [51,52,53]; and 4.…”

“…ϕ(s) = A cos(Bs) and φ(s) = A sin(Bs), (30) where A = √ w 2 + B 2 (with B an arbitrary parameter). For 0 < w < 1 there is also another, in general asymmetric, one-parameter family of solutions for each fixed w in which ϕ is symmetric and φ antisymmetric.…”

“…which, for w σ = w ψ = w, allow for kink-shaped localized soliton solutions (see the right part of Figure 14) given by [75] ϕ(s) = ±φ(s) = (w/ √ 2) tanh(w s/ √ 2), (36) as well as periodic solutions (30). Inserting (14) back into (33) gives the double-kink solution for the Manakov system: σ(s, t) = ±(w/ √ 2) tanh(w s/ √ 2) e −iw 2 t , ψ(s, t) = ±(w/ √ 2) tanh(w s/ √ 2)e −iw 2 t .…”

$\infty-$Dimensional Cerebellar Controller for Realistic Human Biodynamics

“…Theoretically, equations (1-4) define an ∞−dimensional neural network (see [IA07,IAY08,II08c]). Practically, in a computer simulation we can use 10 7 ≤ n ≤ 10 8 , roughly corresponding to the number of neurons in the cerebellum [II07a,II07b].…”