scholarly journals Conservative Chaos Generators with CCII+ Based on Mathematical Model of Nonlinear Oscillator

2011 ◽  
pp. 345-354
Author(s):  
J Petr_ela ◽  
J Slezák
Keyword(s):  
Mathematical Model ◽  
Nonlinear Oscillator

Vertically-Aligned Springless Energy Harvester

2011 ◽  
Author(s):  
Mohamed Bendame ◽  
Karim Elrayes ◽  
Mohamed Mahmoud ◽  
Eihab M. Abdel-Rahman ◽  
Ehab El-Saadany ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Nonlinear Oscillator ◽  
Energy Harvester ◽  
Vibration Energy ◽  
Test Results ◽  
Impact Oscillator ◽  
Vibration Energy Harvester ◽  
Vertically Aligned

This paper analyzes a new configuration of a recently proposed “springless” vibration energy harvester. In this study, the harvester is positioned so that its oscillations are aligned vertically acting against gravity. The MPG response is investigated experimentally. Test results show that the VEH behaves as a softening nonlinear oscillator even for small excitations. A mathematical model of the underlying impact oscillator is also derived and its parameters are estimated.

Chaotic Oscillator Based on Fractional Order Memcapacitor

2019 ◽  
Vol 28 (14) ◽  
pp. 1950239 ◽  
Author(s):  
Akif Akgul
Keyword(s):  
Mathematical Model ◽  
Lyapunov Exponents ◽  
Fractional Order ◽  
Nonlinear Oscillator ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Chaotic Oscillator ◽  
State Equations ◽  
Chaotic Oscillators ◽  
Eigen Values

Many literatures have discussed fractional order memristor and memcapacitor-based chaotic oscillators but the entire oscillator model is considered to be of fractional order. My interest is to propose a nonlinear oscillator with considering only the memcapacitor element of fractional order. Hence, I propose a fractional order memcapacitor (FMC)-based novel chaotic oscillator. The complete mathematical model for the proposed oscillator is derived and presented in this paper. The dimensionless state equations are then analyzed by using the equilibrium points and their stability, Eigen values, Kaplan–Yorke dimensions and Lyapunov exponents. To understand the complete dynamical behavior, bifurcation graphs are obtained and presented. Finally, the proposed fractional memcapacitor oscillator is implemented by using the shelf components.

Solutions of a Dynamics Nonlinear In-Plane Vibration of Suspended Cable Investigated by the Mixed Averaging Method

2013 ◽  
Vol 275-277 ◽  
pp. 869-882
Author(s):  
Zhi Qian Wang ◽  
Lian Hua Wang ◽  
Qi Jian Liu ◽  
Yao Bing Zhao
Keyword(s):  
Mathematical Model ◽  
Linear Response ◽  
Nonlinear Oscillator ◽  
Averaging Method ◽  
Harmonic Excitation ◽  
Iteration Procedure ◽  
Quadratic Term ◽  
Suspended Cable ◽  
The Stability ◽  
Continuation Technique

In this paper, the continuation technique is used to investigate the non-linear response of a suspended cable under harmonic excitation. A modified iteration procedure is applied to the nonlinear oscillator containing a quadratic term. From the formulated mathematical model of the suspended cable, the solution for the cable is obtained by means of the mixed averaging method. Also we can give the frequency simple with the modified iteration procedure. Moreover, the results obtained by this method and the numerical integration are compared. Also the offset is studied. Finally, the effects of the amplitude of the harmonic excitation on the suspended cable and the stability of the system are investigated.

scholarly journals Local and global stability of a piecewise linear oscillator

1992 ◽  
Vol 338 (1651) ◽  
pp. 533-546 ◽  
Keyword(s):  
Mathematical Model ◽  
Numerical Analysis ◽  
Nonlinear Oscillator ◽  
Dynamic Behaviour ◽  
Piecewise Linear ◽  
Global Bifurcation ◽  
Simple Mathematical Model ◽  
Periodic Excitation ◽  
Restoring Force ◽  
Modern Methods

Machines and mechanisms with moving parts, subjected to periodic excitation, often show unexpected dynamic behaviour, and impacts due to their connection clearances may occur. The most simple mathematical model is a one degree-of-freedom nonlinear oscillator governed by a piecewise linear symmetric function to describe the restoring force. The system’s response, which can be quite rich and complicated, is described in detail. Modern methods for a combined analytical and numerical analysis are used to study local and global bifurcation conditions, coexisting solutions and their associated domains of attraction.

Mathematical model of hit phenomena and its application to movie advertisement

2008 ◽  
Author(s):  
Ishii Akira ◽  
Yoshida Narihiko ◽  
Hayashi Takafumi ◽  
Umemura Sanae ◽  
Nakagawa Takeshi
Keyword(s):  
Mathematical Model
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