Dynamics of a class of ODEs more general than almost periodic

A temporally global solution, if it exists, of a nonautonomous ordinary differential equation need not be periodic, almost periodic or almost automorphic when the forcing term is periodic, almost periodic or almost automorphic, respectively. An alternative class of functions extending periodic and almost periodic functions which has the property that a bounded temporally global solution solution of a nonautonomous ordinary differential equation belongs to this class when the forcing term does is introduced here. Specifically, the class of functions consists of uniformly continuous functions, defined on the real line and taking values in a Banach space, which have pre-compact ranges. Besides periodic and almost periodic functions, this class also includes many nonrecurrent functions. Assuming a hyperbolic structure for the unperturbed linear equation and certain properties for the linear and nonlinear parts, the existence of a special bounded entire solution, as well the existence of stable and unstable manifolds of this solution are established. Moreover, it is shown that this solution and these manifolds inherit the temporal behaviour of the vector field equation. In the stable case it is shown that this special solution is the pullback attractor of the system. A class of infinite dimensional examples involving a linear operator consisting of a time independent part which generates a C(0)-semigroup plus a small time dependent part is presented and applied to systems of coupled heat and beam equations. (C) 2010 Elsevier Ltd. All rights reserved.

Homoclinic bifurcations in reversible Hamiltonian systems

We study the existence of homoclic solutions for reversible Hamiltonian systems taking the family of differential equations u(iv) + au - u +f(u, b) = 0 as a model, where fis an analytic function and a, b real parameters. These equations are important in several physical situations such as solitons and in the existence of finite energy stationary states of partial differential equations, but no assumptions of any kind of discrete symmetry is made and the analysis here developed can be extended to others Hamiltonian systems and successfully employed in situations where standard methods fail. We reduce the problem of computing these orbits to that of finding the intersection of the unstable manifold with a suitable set and then apply it to concrete situations. We also plot the homoclinic values configuration in parameters space, giving a picture of the structural distribution and a geometrical view of homoclinic bifurcations. (c) 2005 Published by Elsevier B.V.

Statistical properties for a dissipative model of relativistic particles in a wave packet: A parameter space investigation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Continuity of Dynamical Structures for Nonautonomous Evolution Equations Under Singular Perturbations

In this paper we study the continuity of invariant sets for nonautonomous infinite-dimensional dynamical systems under singular perturbations. We extend the existing results on lower-semicontinuity of attractors of autonomous and nonautonomous dynamical systems. This is accomplished through a detailed analysis of the structure of the invariant sets and its behavior under perturbation. We prove that a bounded hyperbolic global solutions persists under singular perturbations and that their nonlinear unstable manifold behave continuously. To accomplish this, we need to establish results on roughness of exponential dichotomies under these singular perturbations. Our results imply that, if the limiting pullback attractor of a nonautonomous dynamical system is the closure of a countable union of unstable manifolds of global bounded hyperbolic solutions, then it behaves continuously (upper and lower) under singular perturbations.

An estimate on the fractal dimension of attractors of gradient-like dynamical systems

This paper is dedicated to estimate the fractal dimension of exponential global attractors of some generalized gradient-like semigroups in a general Banach space in terms of the maximum of the dimension of the local unstable manifolds of the isolated invariant sets, Lipschitz properties of the semigroup and the rate of exponential attraction. We also generalize this result for some special evolution processes, introducing a concept of Morse decomposition with pullback attractivity. Under suitable assumptions, if (A, A*) is an attractor-repeller pair for the attractor A of a semigroup {T(t) : t >= 0}, then the fractal dimension of A can be estimated in terms of the fractal dimension of the local unstable manifold of A*, the fractal dimension of A, the Lipschitz properties of the semigroup and the rate of the exponential attraction. The ingredients of the proof are the notion of generalized gradient-like semigroups and their regular attractors, Morse decomposition and a fine analysis of the structure of the attractors. As we said previously, we generalize this result for some evolution processes using the same basic ideas. (C) 2012 Elsevier Ltd. All rights reserved.

A geometric mechanism of diffusion: Rigorous verification in a priori unstable Hamiltonian systems

In this paper we consider a representative a priori unstable Hamiltonian system with 2+1/2 degrees of freedom, to which we apply the geometric mechanism for diffusion introduced in the paper Delshams et al., Mem.Amer.Math. Soc. 2006, and generalized in Delshams and Huguet, Nonlinearity 2009, and provide explicit, concrete and easily verifiable conditions for the existence of diffusing orbits. The simplification of the hypotheses allows us to perform explicitly the computations along the proof, which contribute to present in an easily understandable way the geometric mechanism of diffusion. In particular, we fully describe the construction of the scattering map and the combination of two types of dynamics on a normally hyperbolic invariant manifold.

Application of the center manifold theory to the study of slewing flexible Non-ideal structures with nonlinear curvature: a case study

In this paper is Analyzed the local dynamical behavior of a slewing flexible structure considering nonlinear curvature. The dynamics of the original (nonlinear) governing equations of motion are reduced to the center manifold in the neighborhood of an equilibrium solution with the purpose of locally study the stability of the system. In this critical point, a Hopf bifurcation occurs. In this region, one can find values for the control parameter (structural damping coefficient) where the system is unstable and values where the system stability is assured (periodic motion). This local analysis of the system reduced to the center manifold assures the stable / unstable behavior of the original system around a known solution.

Shoulder Muscular Activity During Isometric Three-Point Kneeling Exercise on Stable and Unstable Surfaces

The purpose of this study was to determine if performing isometric 3-point kneeling exercises on a Swiss ball influenced the isometric force output and EMG activities of the shoulder muscles when compared with performing the same exercises on a stable base of support. Twenty healthy adults performed the isometric 3-point kneeling exercises with the hand placed either on a stable surface or on a Swiss ball. Surface EMG was recorded from the posterior deltoid, pectoralis major, biceps brachii, triceps brachii, upper trapezius, and serratus anterior muscles using surface differential electrodes. All EMG data were reported as percentages of the average root mean square (RMS) values obtained in maximum voluntary contractions for each muscle studied. The highest load value was obtained during exercise on a stable surface. A significant increase was observed in the activation of glenohumeral muscles during exercises on a Swiss ball. However, there were no differences in EMG activities of the scapulothoracic muscles. These results suggest that exercises performed on unstable surfaces may provide muscular activity levels similar to those performed on stable surfaces, without the need to apply greater external loads to the musculoskeletal system. Therefore, exercises on unstable surfaces may be useful during the process of tissue regeneration.

Coactivation of the shoulder and arm muscles during closed kinetic chain exercises on an unstable surface

Introduction: The purpose of this study was to compare the electromyography index of muscle coactivation of the following muscle pairs: posterior deltoid and pectoralis major (PD/PM); triceps brachii and biceps brachii (TB/BB); and serratus anterior and upper trapezius (SA/UT) during three different closed kinetic chain exercises (wall-press, bench-press and push-up) on an unstable surface at the maximal load. Methods: A total of 20 healthy sedentary men participated in the study. Integral linear values were obtained from three sustained contractions of six seconds each for the three proposed exercises. Mean coactivation index values were compared using the mixed-effects linear model, with a five percent significance level. Results: Electromyography indexes of muscle coactivation showed significant differences for the PD/PM and TB/BB muscle pairs. No differences were found between exercises for the SA/UT muscle pair. Conclusion: Our results seem to differ from those of previous studies, which reported that the similarity in exercises performed is responsible for the comparable muscle activation levels.

Experimentally tracking unstable steady states by large periodic modulation

Experimental suppression of chaos has been achieved in an optically pumped far-infrared (NH3)-N-15 laser which displays Lorenz-like chaos. The method of control involves the application of a large amplitude slow (i.e., nonresonant) modulation of the pump power. This may be related to a delayed bifurcation to chaos observed when the pump power is ramped at a constant late.

Reliability of electromyographic amplitude values of the upper limb muscles during closed kinetic chain exercises with stable and unstable surfaces

The purpose of the present study was to evaluate the intra and interday reliability of surface electromyographic amplitude values of the scapular girdle muscles and upper limbs during 3 isometric closed kinetic chain exercises, involving upper limbs with the fixed distal segment extremity on stable base of support and on a Swiss ball (relatively unstable). Twenty healthy adults performed the exercises push-up, bench-press and wall-press with different effort levels (80% and 100% maximal load). Subjects performed three maximal voluntary contractions (MVC) in muscular testing position of each muscle to obtain a reference value for root mean square (RMS) normalization. Individuals were instructed to randomly perform three isometric contraction series, in which each exercise lasted 6 s with a 2-min resting-period between series and exercises. Intra and interday reliabilities were calculated through the intraclass correlation coefficient (ICC 2.1), standard error of the measurement (SEM). Results indicated an excellent intraday reliability of electromyographic amplitude values (ICC >= 0.75). The interday reliability of normalized RMS values ranged between good and excellent (ICC 0.52-0.98). Finally, it is suggested that the reliability of normalized electromyographic amplitude values of the analyzed muscles present better values during exercises on a stable surface. However, load levels used during the exercises do not seem to have any influence on variability levels, possibly because the loads were quite similar. (C) 2007 Elsevier Ltd. All rights reserved.

Lanczos algorithm on the grassmann manifold

5th. European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2008) 8th. World Congress on Computational Mechanics (WCCM8)

Influence of wearing an unstable shoe on thigh and leg muscle activity and venous response in upright standing

Purpose: To quantify the effect of unstable shoe wearing on muscle activity and haemodynamic response during standing. Methods: Thirty volunteers were divided into 2 groups: the experimental group wore an unstable shoe for 8 weeks, while the control group used a conventional shoe for the same period. Muscle activity of the medial gastrocnemius, tibialis anterior, rectus femoris and biceps femoris and venous circulation were assessed in quiet standing with the unstable shoe and barefoot. Results: In the first measurement there was an increase in medial gastrocnemius activity in all volunteers while wearing the unstable shoe. On the other hand, after wearing the unstable shoe for eight weeks these differences were not verified. Venous return increased in subjects wearing the unstable shoe before and after training. Conclusions: The unstable shoe produced changes in electromyographic characteristics which were advantageous for venous circulation even after training accommodation by the neuromuscular system.

Influence of an unstable shoe on compensatory postural adjustments: an experimental evaluation

This study attempted to evaluate the influence of using an unstable shoe in muscle re-cruitment strategies and center of pressure (CoP) displacement after the application of an external perturba-tion. Fourteen healthy female subjects participated in this study. The electromyographic activity of medial ga-strocnemius, tibialis anterior, rectus femoris, biceps femoris, rectus abdominis and erector spinae muscles and the kinetic values to calculate the CoP were collected and analyzed after the application of an external pertur-bation with the subject in standing position, with no shoes and using unstable footwear. The results showed increased in medial gastrocnemius activity during the first compensatory postural adjustments and late com-pensatory postural adjustments when using an unstable shoe. There were no differences in standard deviation and maximum peak of anteroposterior displacement of CoP between measurements. From the experimental findings, one can conclude that the use of an unstable shoe leads to an increase in gastrocnemius activity with no increase in CoP displacement following an unexpected external perturbation.