Dynamical Systems

Abstract

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Quantum neural network

“…The key to analyzing the stability of the equilibrium points is a set of rules based on the form of the eigenvalues of the local Jacobian matrix (Tu, 1994). For present purposes, these rules require that for a stable attractor, the real part of each eigenvalue be negative, or else the equilibrium is unstable.…”

“…The analysis used to determine which equilibrium points are actually stable attractors is conducted using the local linearization of the Jacobian matrix A = OFi/Oyjly ~ of the equations of motion in conjunction with the Hartman-Grobman linearization theorem (Tu, 1994).…”

The Poincaré-Bendixson Theorem: from Poincaré to the XXIst century

“…Some applications in economy are described in [76]. For some applications in biology, see for example [45].…”

Dynamic Model

“…R is the vector of the initial stocks (Tu, 1994) which can be calculated according to note 3. Therefore, λ m = γ and each stock will grow at the same rate; due to the stationarity of the stocks, we expect λ m <1, that is, long-run stability (Enders, 1995;Tu, 1994). Finally, the associated eigenvector ν m can be interpreted as the stable mix between the stocks.…”