scholarly journals Current-Mode Network Structures Dedicated for Simulation of Dynamical Systems with Plane Continuum of Equilibrium

2018 ◽  
Vol 27 (09) ◽  
pp. 1830004 ◽  
Author(s):  
Jiri Petrzela ◽  
Tomas Gotthans ◽  
Milan Guzan
Keyword(s):  
Dynamical Systems ◽  
Current Mode ◽  
Equilibrium Structure ◽  
Third Order ◽  
Active Devices ◽  
Real Behavior ◽  
Dependent Model ◽  
The Rich ◽  
Frequency Dependent Model ◽  
Plane Continuum

This review paper describes different lumped circuitry realizations of the chaotic dynamical systems having equilibrium degeneration into a plane object with topological dimension of the equilibrium structure equals one. This property has limited amount (but still increasing, especially recently) of third-order autonomous deterministic dynamical systems. Mathematical models are generalized into classes to design analog networks as universal as possible, capable of modeling the rich scale of associated dynamics including the so-called chaos. Reference state trajectories for the chaotic attractors are generated via numerical analysis. Since used active devices can be precisely approximated by using third-level frequency dependent model, it is believed that computer simulations are close enough to capture real behavior. These simulations are included to demonstrate the existence of chaotic motion.

scholarly journals Current-Mode Third-Order Quadrature Oscillator Using CDTAs

2009 ◽  
Vol 2009 ◽  
pp. 1-5 ◽  
Author(s):  
Jiun-Wei Horng
Keyword(s):  
Theoretical Analysis ◽  
Phase Difference ◽  
Oscillation Frequency ◽  
Current Mode ◽  
Third Order ◽  
Quadrature Oscillator ◽  
Oscillation Condition ◽  
Transconductance Amplifiers ◽  
Simulation Results ◽  
A Current

This paper describes a current-mode third-order quadrature oscillator based on current differencing transconductance amplifiers (CDTAs). Outputs of two current-mode sinusoids with90°phase difference are available in the quadrature oscillator circuit. The oscillation condition and oscillation frequency are orthogonal controllable. The proposed circuit employs only grounded capacitors and is ideal for integration. Simulation results are included to confirm the theoretical analysis.

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 A Frequency-Dependent Model for the Shape of the Fourier Amplitude Spectrum of Acceleration at High Frequencies

2020 ◽  
Vol 110 (6) ◽  
pp. 2743-2754 ◽  
Author(s):  
Annabel Haendel ◽  
John G. Anderson ◽  
Marco Pilz ◽  
Fabrice Cotton
Keyword(s):  
Frequency Dependence ◽  
Amplitude Spectrum ◽  
Frequency Interval ◽  
Borehole Data ◽  
High Frequencies ◽  
Dependent Model ◽  
Fourier Amplitude Spectrum ◽  
Log Linear ◽  
Frequency Dependent Model ◽  
Quality Factor Q

ABSTRACT The high-frequency decay term of the acceleration spectrum κ is a commonly used parameter in engineering seismology. In recent years, the assumption of a linearly decaying spectrum in log–linear space has been recognized to not always be valid as the value of κ depends on the analyzed frequency band. We present an alternative model for the spectral falloff in which the frequency dependence is explicitly taken into account. This is motivated by observations that the quality factor Q has a power-law dependence on frequency at high frequencies. The new model describes the spectral decay with the help of two variables, opposite to the single parameter κ. The approach is applied to borehole data of the EUROSEISTEST site in Greece. The misfit between modeled and observed spectra is reduced with the new approach compared with the classical kappa model. The new estimates compare well with κ estimates if the same frequency interval is considered but additionally allows for the capture of the frequency dependence of the spectral shape.

scholarly journals Nilpotent integrability, reduction of dynamical systems and a third-order Calogero–Moser system

2019 ◽  
Vol 198 (5) ◽  
pp. 1513-1540
Author(s):  
A. Ibort ◽  
G. Marmo ◽  
M. A. Rodríguez ◽  
P. Tempesta
Keyword(s):  
Dynamical Systems ◽  
Third Order ◽  
Moser System

Periodic Behavior of a Nonlinear Third Order Vibrating System

2002 ◽  
Author(s):  
Gholamreza Nakhaie Jazar ◽  
Mohammad H. Alimi ◽  
Mohammad Mahinfalah ◽  
Ali Khazaei
Keyword(s):  
Differential Equation ◽  
Dynamical Systems ◽  
Ad Hoc ◽  
Order Differential Equation ◽  
Second Order ◽  
Order System ◽  
Third Order ◽  
Modeling Process ◽  
Third Order Differential Equation ◽  
Second Order Systems

In modeling of dynamical systems, differential equations, either ordinary or partial, are a common outcome of the modeling process. The basic problem becomes the existence of solution of these deferential equations. In the early days of the solution of deferential equations at the beginning of the eighteenth century the methods for determining the existence of nontrivial solution were so limited and developed very much on an ad hoc basis. Most of the efforts on dynamical system are related to the second order systems, derived by applying Newton equation of motion to dynamical systems. But, behavior of some dynamical systems is governed by equations falling down in the general nonlinear third order differential equation x″′+f(t,x,x′,x″)=0, sometimes as a result of combination of a first and a second order system. It is shown in this paper that these equations could have nontrivial solutions, if x, x′, x″, and f(t,x,x′,x″) are bounded. Furthermore, it is shown that the third order differential equation has a τ-periodic solution if f(t,x,x′,x″) is an even function with respect to x′. For this purpose, the concept of Green’s function and the Schauder’s fixed-point theorem has been used.

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