Sharif Digital Repository

Objective: This study aimed to employ nonlinear dynamic approaches to assess trunk dynamic stability with speed, symmetry, and load during repetitive flexion-extension (FE) movements for individuals with and without nonspecific low back pain (NSLBP). Background: Repetitive trunk FE movement is a typical work-related LBP risk factor contingent on speed, symmetry, and load. Improper settings/adjustments of these control parameters could undermine the dynamic stability of the trunk, hence leading to low back injuries. The underlying stability mechanisms and associated control impairments during such dynamic movements remain elusive. Method: Thirty-eight male volunteers (19 healthy, 19 NSLBP)... 

This article addresses the stabilization of noiseless nonlinear dynamic systems over limited capacity communication channels. It is shown that the stability of nonlinear dynamic systems over memory-less communication channels implies an inequality condition between the Shannon channel capacity and the summation of the positive equilibrium Lyapunov exponents of the dynamic system or, equivalently, the logarithms of the magnitude of the unstable eigenvalues of system Jacobian. Furthermore, we propose an encoder, decoder, and a controller to prove that scalar nonlinear dynamic systems are stabilizable under the aforementioned inequality condition over the digital noiseless and the packet... 

This paper will consider the mathematical definition of chaos (in sense of Devaney) in order to select appropriate chaos tests. The tests chosen according to investigate the properties mentioned in the definition. In fact, these are prerequisites of chaoticity. Either it will be represented that "sensitivity dependence on initial conditions" is not equivalent to chaos, although some researchers considering it. Hence, it is implied that checking all of the properties mentioned in the definition are required to establish chaos. As our case study, some sample stocks were selected from Tehran Stock Exchange (TSE) and the chosen tests implemented on their returns time series. Incoming results... 

In this paper, we show that an amplitude phase frequency model (APFM) which is used as a nonlinear adaptive filter in signal processing can exhibit chaotic behavior. It is illustrated that both frequency and amplitude of the input components have effect on the filter characteristics which can lead the filter to behave chaotically for some values of these parameters. We have exploited different measures such as the Lyapunov exponents, bifurcation diagram, sensitivity to initial condition, and 0-1 test on time series to confirm our claim. Existence of the chaotic behavior in APFM does not conform to the prior conjectures about this filter. © 2008 Elsevier B.V. All rights reserved  

Topological defects are interesting phenomena which can be observed in ordered phases such as oriented active fluids or nematic liquid crystals. Topological defects are determined by the overall structure of the director field in an active fluid in nematic phase and by exerting force to the units of the active particles they can interact or cause motion in the environment. Studying them as particles with dynamical equations, instead of studying the director field of the nematic environment, would provide us the power to study the characteristics of their motion. The equations of motion for multi-defect systems have been previously studied and in this work we focus on the chaotic properties... 

Remote observation of the state trajectory of nonlinear dynamic systems over limited capacity communication channels is studied. It is shown that two extreme cases are possible: Either the system is fully observable or the error in estimation blows up. The key observation is that such behavior is determined by the relationship between the Shannon capacity and the Lyapunov exponents; the well-known characterizing parameters of a communication channel on one side, and a dynamic system from the other side. In particular, it is proved that for nonlinear systems with initial state x0, the minimum capacity of an additive white Gaussian noise channel required for full observation of the system in... 

In this paper, chaos in spatial attitude dynamics of a triaxial rigid satellite in an elliptic orbit is investigated analytically and numerically. The goal in the analytical part is to prove the existence of chaos and then to find a relation for the width of chaotic layers (i.e. the initial values needed to have a chaotic attitude motion) based on the parameters of the system. The numerical part is aimed at validating the analytical method using the Poincaré maps and the maximum value of the Lyapunov exponents. The rotational–translational Hamiltonian of the system is first derived. This Hamiltonian has six degrees of freedom. Choosing a proper set of coordinates and given the fact that the... 

In this paper, chaos in spatial attitude dynamics of a triaxial rigid satellite in an elliptic orbit is investigated analytically and numerically. The goal in the analytical part is to prove the existence of chaos and then to find a relation for the width of chaotic layers (i.e. the initial values needed to have a chaotic attitude motion) based on the parameters of the system. The numerical part is aimed at validating the analytical method using the Poincaré maps and the maximum value of the Lyapunov exponents. The rotational–translational Hamiltonian of the system is first derived. This Hamiltonian has six degrees of freedom. Choosing a proper set of coordinates and given the fact that the... 

Objective: This study aimed to employ nonlinear dynamic approaches to assess trunk dynamic stability with speed, symmetry, and load during repetitive flexion-extension (FE) movements for individuals with and without nonspecific low back pain (NSLBP). Background: Repetitive trunk FE movement is a typical work-related LBP risk factor contingent on speed, symmetry, and load. Improper settings/adjustments of these control parameters could undermine the dynamic stability of the trunk, hence leading to low back injuries. The underlying stability mechanisms and associated control impairments during such dynamic movements remain elusive. Method: Thirty-eight male volunteers (19 healthy, 19 NSLBP)... 

The chaotic dynamics of roto-translatory motion of a triaxial Kelvin-type gyrostat satellite under gravity gradient perturbations is considered. The Hamiltonian approach is used for modelling of the coupled spin-orbit equations of motion. The complex Hamiltonian of the system is reduced via the extended Deprit canonical transformation using the Serret- Andoyer variables. Therefore, this reduction leads to the derivation of the perturbation form of the Hamiltonian that can be used in the Ricci curvature criterion based on the Riemannian manifold geometry for the analysis of chaos phenomenon. The results obtained from Ricci method as well as the values from the Lyapunov exponent demonstrate... 

In this paper, we propose a new one-dimensional, two-segmental nonlinear map by combining tent, triangle and parabola curve functions. We call the proposed map, Mehrab map since its return maps shape is similar to an altar (which we call it "Mehrab"). Definition and properties of Mehrab map along with orbit diagrams, Lyapunov exponents, and its histograms are considered. To generate more uniform density function maps, two modified versions of the proposed Mehrab map are also defined. In the first modification of Mehrab map (FMM), vertical symmetry and transformation to the right are used. Sensitivity to initial condition and total chaotic range of FMM are medium. Probability density function... 

Stable and unstable limit cycles are important orbits in chaotic systems. So many works are done to find and to quench chaos by stabilizing them. In this paper a new family of limit cycle orbits around the Moon is introduced as a result of restricted three-body problem. The family is completely spatial and can be used as an out-of-plane velocity magnifier. Lyapunov exponent in the Floquet theory has also been checked and stability of the orbits has been measured  

Synchronization of two coupled Chen systems through one of their variables is experimentally studied in this paper. We explore the chaotic behavior of the rescaled Chen system by the bifurcation analysis and computing its Lyapunov exponents which these results are also verified by circuitry realization of the system. Also, using 0-1 test, the chaotic manner of the circuit signals is validated. Finally, we synchronize two Chen circuits using unidirectional continues coupling with only one state variable and show despite the presence of the noise and the fact that two implemented circuits are not completely identical; the circuits achieve complete synchronization. © ICROS  

Variational principle is used to derive the nonlinear response of the floating roof of cylindrical liquid storage tanks due to harmonic base excitations. The formulation accounts for nonlinearity due to large deflections of the floating roof. The derived nonlinear governing equation for the sloshing response of the floating roof has a cubic nonlinear stiffness term similar to the well known Duffing equation. It is shown that accounting for large deflections could substantially reduce the wave elevation for near resonance harmonic excitations. Evaluating the response of the nonlinear model for increasing amplitudes of near resonance harmonic excitations gives rise to the appearance of sub and... 

Background: Comparison of the kinematic variability and dynamic stability of the trunk between healthy and low back pain patient groups can contribute to gaining valuable information about the movement patterns and neuromotor strategies involved in various movement tasks. Methods: Fourteen chronic low back pain patients with mild symptoms and twelve healthy male volunteers performed repeated trunk flexion-extension movements in the sagittal plane at three different speeds: 20 cycles/min, self-selected, and 40 cycles/min. Mean standard deviations, coefficient of variation and variance ratio as variability measures; maximum finite-time Lyapunov exponents and maximum Floquet multipliers as...