Chaos control of a nonlinear oscillator with shape memory alloy using an optimal linear control: Part I: Ideal energy source

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On non-linear dynamics and control designs applied to the ideal and non-ideal variants of the Fitzhugh-Nagumo (FN) mathematical model

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Synchronization of the unified chaotic system and application in secure communication

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Remarks on an Optimal Linear Control Design Applied to a Nonideal and an Ideal Structure Coupled to an Essentially Nonlinear Oscillator

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Chaos control of a nonlinear oscillator with shape memory alloy using an optimal linear control: Part II: Nonideal energy source

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Suppressing grazing chaos in impacting system by structural nonlinearity

In this note we investigate the influence of structural nonlinearity of a simple cantilever beam impacting system on its dynamic responses close to grazing incidence by a means of numerical simulation. To obtain a clear picture of this effect we considered two systems exhibiting impacting motion, where the primary stiffness is either linear (piecewise linear system) or nonlinear (piecewise nonlinear system). Two systems were studied by constructing bifurcation diagrams, basins of attractions, Lyapunov exponents and parameter plots. In our analysis we focused on the grazing transitions from no impact to impact motion. We observed that the dynamic responses of these two similar systems are qualitatively different around the grazing transitions. For the piecewise linear system, we identified on the parameter space a considerable region with chaotic behaviour, while for the piecewise nonlinear system we found just periodic attractors. We postulate that the structural nonlinearity of the cantilever impacting beam suppresses chaos near grazing. (C) 2007 Elsevier Ltd. All rights reserved.

On energy transfer between vibrating systems under linear and nonlinear interactions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On energy transfer between linear and nonlinear oscillators

In this paper energy transfer in a dissipative mechanical system is analysed. Such system is composed of a linear and a nonlinear oscillator with a nonlinearizable cubic stiffness. Depending on initial conditions, we find energy transfer either from linear to nonlinear oscillator (energy pumping) or from nonlinear to linear. Such results are valid for two different potentials. However, under resonance and absence of external excitation, if the mass of the nonlinear oscillator is adequately small then the linear oscillator always loses energy. Our approach uses rigorous Regular Perturbation Theory. Besides, we have included the case of two linear oscillators under linear or cubic interactions. Comparisons with the earlier case are made. (c) 2008 Elsevier Ltd. All rights reserved.

Short Comments on an Energy Pumping Levels in a MEMS Gyroscope Vibrating Problem, by Using of an Global and Local Optimal Linear Control Design

This paper deals with an energy pumping that occurs in a (MEMS) Gyroscope nonlinear dynamical system, modeled with a proof mass constrained to move in a plane with two resonant modes, which are nominally orthogonal. The two modes are ideally coupled only by the rotation of the gyro about the plane's normal vector. We also developed a linear optimal control design for reducing the oscillatory movement of the nonlinear systems to a stable point.

On non-linear dynamics and an optimal control synthesis of the action potential of membranes (ideal and non-ideal cases) of the Hodgkin-Huxley (HH) mathematical model

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On control and synchronization in chaotic and hyperchaotic systems via linear feedback control

This paper presents the control and synchronization of chaos by designing linear feedback controllers. The linear feedback control problem for nonlinear systems has been formulated under optimal control theory viewpoint. Asymptotic stability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function which can clearly be seen to be the solution of the Hamilton-Jacobi-Bellman equation thus guaranteeing both stability and optimality. The formulated theorem expresses explicitly the form of minimized functional and gives the sufficient conditions that allow using the linear feedback control for nonlinear system. The numerical simulations were provided in order to show the effectiveness of this method for the control of the chaotic Rossler system and synchronization of the hyperchaotic Rossler system. (C) 2007 Elsevier B.V. All rights reserved.

An Optimal Linear Control Design for Nonlinear Systems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Characterization of micro-bubble size distribution and flow configuration in DAF contact zone by a non-intrusive image analysis system and tracer tests

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Evaluation and Application of TS-FF-AAS System Using Ceramic Tube as Atomization Cell for Tin Determination in Canned Foods

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Age impact on the eferent system actitivies in cochlear mechanical properties in normal hearing individuals

O trato olivococlear medial realiza o controle eferente das células ciliadas externas, regulando as contrações lentas e atenuando as rápidas. Com a pesquisa da amplitude das emissões otoacústicas sem e com estimulação acústica contra, ipsi ou bilateralmente, é possível estimar as condições desse trato, uma vez que o efeito resultante de redução/supressão das emissões indica seu funcionamento. O envelhecimento implica em diminuição da atividade do sistema auditivo central, em função da degeneração das estruturas envolvidas nas habilidades auditivas. OBJETIVO: O objetivo foi investigar o efeito da idade na atividade do trato sobre a cóclea, com a análise da amplitude das emissões com estimulação acústica contralateral. MATERIAL E MÉTODO: A casuística foi composta por 75 indivíduos agrupados conforme a idade. A metodologia foi o modo convencional, com clique linear e o ruído branco. ESTUDO DE CASO: A análise considerou a resposta das orelhas e a comparação entre os grupos. RESULTADOS: Os resultados revelam diferenças estatisticamente significantes entre o response das emissões sem e com estimulação acústica contralateral, nos indivíduos (20 a 39 anos). O efeito redução/supressão das emissões diminui com a idade (quarta década). CONCLUSÃO: O envelhecimento prejudica a efetividade da atividade do trato.