Nonlinear Phenomena in Complex Systems, 2000, Vol.3, No.3, pp.231--241

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2000, Volume 3, Number 3, pp.231--241

Characterization of the Topological Structure and Stability for a Vector Map Derived from a Delay Differential Equation.
Victor F. Dailyudenko

Statistical characteristics of the attractor for investigated complex system have been defined by dispersion analysis of obtained topological curves in a form of asymptotic estimations of convergence to exact stabilization. The delay functional and matrix operator and corresponding Jacobian-matrix for successive calculation of segments of nonlinear time series have been obtained, the vector field divergence is modeled by the obtained analytical model. As the structure of phase trajectories is shown to be fractal, some components of the multifractal dimensions spectrum have been defined applying modified "sand-box" method. time series, asymptotic estimations, fractal.
Key words: attractor, asymptotic estimations, fractal.

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