Generalized Energy Functions for a Class of Third-Order Nonlinear Dynamical Systems

2020 ◽  
pp. 1-1
Author(s):  
Luis Fernando Costa Alberto ◽  
Daniel Siqueira ◽  
Newton Geraldo Bretas ◽  
Hsiao-Dong Chiang
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Third Order ◽  
Energy Functions ◽  
Nonlinear Dynamical

scholarly journals NOISE IMMUNITY RESEARCH FOR NONLINEAR DYNAMICAL SYSTEMS IDENTIFICATION BASED ON VOLTERRA MODEL IN FREQUENCY DOMAIN

2014 ◽  
pp. 34-41
Author(s):  
Vitaliy Pavlenko ◽  
Sergei Pavlenko ◽  
Viktor Speranskyy
Keyword(s):  
Dynamical Systems ◽  
Frequency Domain ◽  
Noise Immunity ◽  
Nonlinear Dynamical Systems ◽  
Interpolation Method ◽  
Test System ◽  
Volterra Model ◽  
Third Order ◽  
Nonlinear Dynamical ◽  
Systems Identification

The accuracy and noise immunity of the interpolation method of nonlinear dynamical systems identification based on the Volterra model in the frequency domain is studied in this paper. The polyharmonic signals are used for the testing the method. The algorithmic and software toolkit in Matlab is developed for the identification procedure. This toolkit is used to construct the informational models of test system and communication channel. The model is built as a first-, second- and third-order amplitude–frequency and phase–frequency characteristics. The comparison of obtained characteristics with previous works is given. Wavelet denoising is studied and applied to reduce measurement noise.

ON THE ONSET OF QUASI-PERIODIC SOLUTIONS IN THIRD-ORDER NONLINEAR DYNAMICAL SYSTEMS

2005 ◽  
Vol 15 (10) ◽  
pp. 3165-3180 ◽  
Author(s):  
R. GENESIO ◽  
C. GHILARDI
Keyword(s):  
Dynamical Systems ◽  
Periodic Solutions ◽  
Harmonic Balance ◽  
Nonlinear Dynamical Systems ◽  
General Relation ◽  
Three Dimensional ◽  
Third Order ◽  
Van Der Pol ◽  
Nonlinear Dynamical ◽  
Classical Systems

The paper considers the existence of quasi-periodic solutions in three-dimensional systems. Since these solutions commonly arise as a consequence of a Neimark–Sacker bifurcation of a limit cycle, a fairly general relation connected to this phenomenon is pointed out as the main result of the paper. Then, the application of harmonic balance techniques makes possible to exploit such a relation. In particular, a simplified condition denoting the quasi-periodicity onset can be derived, in making evident the main elements for this transition in terms of structure and parameters, and hence some remarks on the features of the interested systems. Several examples show the application of the above condition to detect "tori" in the state space in a qualitative (not simply numerical) way. They consider classical systems — Rössler, where such behavior seems to be unknown, Chua, forced Van der Pol — and new quadratic systems.

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