scholarly journals Signal processing of nonlinear dynamic systems

2021 ◽  
Vol 2094 (2) ◽  
pp. 022057
Author(s):  
S V Sarkisov ◽  
S Z El-Salim ◽  
A V Bondarev ◽  
A N Korpusov ◽  
P A Putilin
Keyword(s):  
Wavelet Decomposition ◽  
Nonlinear Dynamical Systems ◽  
Hermite Polynomials ◽  
Nonlinear Dynamical ◽  
Self Similar ◽  
Quality Of Approximation ◽  
Approximation Coefficients ◽  
Similar Basis ◽  
Decomposition Of Functions

Abstract The paper considers Hermite polynomials that act as a self-similar basis for the decomposition of functions in phase space. It is shown that the equations of behavior of nonlinear dynamical systems are simplified. It is also noted that the wavelet decomposition over Hermite polynomials reduces the number of approximation coefficients and improves the quality of approximation.

ELECTRONIC STATES OF QUASIPERIODIC SYSTEMS: FIBONACCI AND PENROSE LATTICES

1987 ◽  
Vol 01 (01) ◽  
pp. 31-49 ◽  
Author(s):  
MAHITO KOHMOTO
Keyword(s):  
Electronic Properties ◽  
Disordered Systems ◽  
Nonlinear Dynamical Systems ◽  
One Dimension ◽  
Renormalization Group Theory ◽  
Nonlinear Dynamical ◽  
Self Similar ◽  
Quasiperiodic Systems ◽  
Fibonacci Lattice ◽  
Pentagonal Symmetry

Since the experiment of Shechtman et al. which suggests the crystal with the pentagonal symmetry (quasicrystal), there has been a lot of interest in the quasiperiodic systems. These can be regarded as being intermediate between ordered and disordered systems, and novel physical properties are expected. In fact, the quasicrystal in one-dimension is known to have exotic electronic properties: Cantor set energy spectrum, existence of self-similar and fractal wavefunctions and so on. These properties have intrinsically related to the renormalization-group theory and the nonlinear dynamical systems which could lead to chaos. The electronic properties of the Fibonacci lattice (1-D quasicrystal) and the Penrose lattice (2-D quasicrystal) are discussed.

Linear and Nonlinear Dynamic Behaviour

2018 ◽  
Author(s):  
Ray Huffaker ◽  
Marco Bittelli ◽  
Rodolfo Rosa
Keyword(s):  
Dynamic Behavior ◽  
Dynamic Systems ◽  
Dynamic Behaviour ◽  
Nonlinear Dynamical Systems ◽  
Logistic Map ◽  
Nonlinear Dynamical ◽  
Deterministic Dynamic ◽  
Random Behavior ◽  
Single Solution ◽  
Equivalent Systems

In this chapter, we describe how highly erratic dynamic behavior can arise from a nonlinear logistic map, and how this apparently random behavior is governed by a surprising order. With this lesson in mind, we should not be overly surprised that highly erratic and random appearing observed data might also be generated by parsimonious deterministic dynamic systems. At a minimum, we contend that researchers should apply NLTS to test for this possibility. We also introduced tools to analyze dynamic behavior that form the foundation for NLTS. In particular, we have stressed the quite unexpected capability to achieve some form of predictability even with only one trajectory at hand. In subsequent chapters, we treat known nonlinear dynamical systems as unknown, and investigate how NLTS methods rely on a single solution (or multiple solutions) generated by them to reconstruct equivalent systems. This is a conventional approach in the literature for seeing how NLTS methods work since we know what needs to be reconstructed.

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