Modeling And Analysis Of Bilinear Systems

  • Panos M. Pardalos
  • Vitaliy Yatsenko
Part of the Springer Optimization and Its Applications book series (SOIA, volume 11)

The problem of reconstruction of nonlinear and bilinear dynamics has been studied in a number of physical simulations ranging from Whitney's theorem (Loskutov and Mikhailov, 1990; Nicolis and Prigogine, 1977; Nerenberg and Essex, 1986) to state-space representation (Chang, Hübler, and Packard, 1989; Takens, 1981; Grassberger and Procaccia, 1982). This problem is also related to the flow method developed by Cremers and Hübler (1987). The flow method is a procedure for reconstructing a set of coupled maps (CMs) or ordinary differential equations (ODEs) from a trajectory of the system in state space. This chapter presents methods for determining nonlinear dynamical systems and application to small target detection from sea clutter and modeling of nonlinear chaotic dynamics. We show that this methodology may easily be adapted to systems with hidden variables.

In Section 8.1we present a method for the reconstruction of bilinear equation reconstruction of nonlinear and bilinear equations...


Time Series Fractal Dimension Master Equation Hide Variable Planck Equation 
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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Panos M. Pardalos
    • 1
  • Vitaliy Yatsenko
    • 2
  1. 1.Department of Industrial and SystemsUniversity of FloridaGainesvilleU.S.A.
  2. 2.Institute of Space ResearchNASUKyivUkraine

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