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Complex Motions and Chaos in Nonlinear Systems

Part of the Nonlinear Systems and Complexity Book Series (volume 15)

Editors: Afraimovich, Valentin; Machado, José António Tenreiro; Zhang, Jiazhong

DOI: 10.1007/978-3-319-28764-5

ISBN: 978-3-319-28762-1

Publisher: Springer International Publishing - Springer Journals

Apr 23, 2016

1 - 10 of 10 Chapters

LitStream

Chapter 1Detection of Quasi-Periodic Processes in Experimental Measurements: Reduction to an “Ideal Experiment”

Nigmatullin, R. R.

Pages: 1 –37

[In this chapter, a general concept for the consideration of anyreproducible data, measured in many experiments, in one unified scheme is proposed. In addition, it has been demonstrated that successive and reproducible measurements have a memory, and this important fact makes it possible to group...
LitStream

Chapter 2Some Singularities in Fluid Dynamics and Their Bifurcation Analysis

Zhang, Jiazhong; Liu, Yan

Pages: 39 –73

[There exists a very large variety of singular or nonlinear phenomena in fluid dynamics and fluid–structure interactions that are affected by continuum mechanics; for example, the motion of fluid dynamics is often accompanied by the formation of transitional zones, where parameters (e.g.,...
LitStream

Chapter 3Finite-Element Analysis of Nonlinear Fluid–Membrane Interactions Using a Modified Characteristic-Based Split (CBS) Scheme

Sun, Xu; Zhang, Jiazhong

Pages: 75 –105

[A finite-element scheme based on a modified characteristic-based split (CBS) method is proposed for fluid–membrane interactions (FMIs) at low Reynolds numbers, and in particular the effects of structural density on the dynamic response of a flexible membrane wing are investigated. In this...
LitStream

Chapter 4Lock-In Behaviors of an Airfoil with Local Excitation in Low-Reynolds-Number Flow

Kang, Wei; Dai, Xiangyan

Pages: 107 –135

[A numerical computation for flow past an airfoil with local oscillation is presented at low Reynolds numbers to study the effect of local oscillation on the aerodynamic performance of the airfoil. The model for local oscillation is simplified as a periodic motion with prescribed equilibrium....
LitStream

Chapter 5Nanosecond Pulsed Plasma Flow Control: Progress and Problems

Wu, Yun; Jia, Min; Liang, Hua; Song, Huimin; Li, Yinghong

Pages: 137 –171

[Plasma flow control is a novel method of active flow control using plasma aerodynamic actuation based on plasma motion in the electromagnetic field, or temperature and air pressure rise during gas discharge. Nanosecond pulsed plasma flow control is a hot topic in this field due to its higher...
LitStream

Chapter 6Hidden dimensions in an Hamiltonian system on networks

de Nigris, Sarah; Leoncini, Xavier

Pages: 173 –202

[In this chapter we show how the topology of a particular network model influences the thermodynamic behavior of a dynamical system defined on it, namely, the Hamiltonian XY rotor model. More specifically, following an introduction, we first consider the regular networks described in De Nigris...
LitStream

Chapter 7Input-Output Mechanism of the Discrete Chaos Extension

Akhmet, Marat; Fen, Mehmet Onur

Pages: 203 –233

[In this chapter the extension of chaos in difference equations is discussed. The theoretical results are based on chaos in the sense of Devaney and a period-doubling cascade. The existence of homoclinic and heteroclinic orbits is rigorously proved, and a theoretical control technique for the...
LitStream

Chapter 8Steady state solution for a Rayleigh’s piston in a temperature gradient

Villain-Guillot, Simon

Pages: 235 –245

[As a toy model for the thermodiffusion of polymers, we look at the Rayleigh piston problem in which a solute macroparticle is represented by a piston wall in a 1D canal. This piston wall is assumed to be adiabatic (without internal degrees of freedom) and fluctuates owing to collisions with the...
LitStream

Chapter 9Analytical Period-m Motions in a Parametric, Quadratic Nonlinear Oscillator

Luo, Albert C. J.; Yu, Bo

Pages: 247 –258

[Analytical solutions of period-m motions in a parametric quadratic nonlinear oscillator are obtained through the finite Fourier series, and the corresponding stability and bifurcation analysis for periodic motions are discussed. The bifurcation trees of periodic motions to chaos in a parametric...
LitStream

Chapter 10Periodic Motions to Chaos in Duffing Oscillator via Discretization Technique

Guo, Yu; Luo, Albert C. J.

Pages: 259 –276

[In this chapter, the periodic motions of a Duffing oscillator are predicted using discrete implicit maps and mapping structures. Bifurcation trees of periodic motions to chaos are presented. The stability and bifurcation of periodic motions are determined through eigenvalue analysis. Finally,...

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