Complex-order forced van der Pol oscillator

In this paper we consider a complex-order forced van der Pol oscillator. The complex derivative Dα1jβ, with α, β ∈ ℝ+, is a generalization of the concept of an integer derivative, where α = 1, β = 0. The Fourier transforms of the periodic solutions of the complex-order forced van der Pol oscillator are computed for various values of parameters such as frequency ω and amplitude b of the external forcing, the damping μ, and parameters α and β. Moreover, we consider two cases: (i) b = 1, μ = {1.0, 5.0, 10.0}, and ω = {0.5, 2.46, 5.0, 20.0}; (ii) ω = 20.0, μ = {1.0, 5.0, 10.0}, and b = {1.0, 5.0, 10.0}. We verified that most of the signal energy is concentrated in the fundamental harmonic ω0. We also observed that the fundamental frequency of the oscillations ω0 varies with α and μ. For the range of tested values, the numerical fitting led to logarithmic approximations for system (7) in the two cases (i) and (ii). In conclusion, we verify that by varying the parameter values α and β of the complex-order derivative in expression (7), we accomplished a very effective way of perturbing the dynamical behavior of the forced van der Pol oscillator, which is no longer limited to parameters b and ω.

Complex order van der Pol oscillator

In this paper a complex-order van der Pol oscillator is considered. The complex derivative Dα±ȷβ , with α,β∈R + is a generalization of the concept of integer derivative, where α=1, β=0. By applying the concept of complex derivative, we obtain a high-dimensional parameter space. Amplitude and period values of the periodic solutions of the two versions of the complex-order van der Pol oscillator are studied for variation of these parameters. Fourier transforms of the periodic solutions of the two oscillators are also analyzed.

A coinfection model for HIV and HCV

We study a mathematical model for the human immunodeficiency virus (HIV) and hepatites C virus (HCV) coinfection. The model predicts four distinct equilibria: the disease free, the HIV endemic, the HCV endemic, and the full endemic equilibria. The local and global stability of the disease free equilibrium was calculated for the full model and the HIV and HCV submodels. We present numerical simulations of the full model where the distinct equilibria can be observed. We show simulations of the qualitative changes of the dynamical behavior of the full model for variation of relevant parameters. From the results of the model, we infer possible measures that could be implemented in order to reduce the number of infected individuals.

Effects of treatment, awareness and condom use in a coinfection model for HIV and HCV in MSM

We develop a new a coinfection model for hepatitis C virus (HCV) and the human immunodeficiency virus (HIV). We consider treatment for both diseases, screening, unawareness and awareness of HIV infection, and the use of condoms. We study the local stability of the disease-free equilibria for the full model and for the two submodels (HCV only and HIV only submodels). We sketch bifurcation diagrams for different parameters, such as the probabilities that a contact will result in a HIV or an HCV infection. We present numerical simulations of the full model where the HIV, HCV and double endemic equilibria can be observed. We also show numerically the qualitative changes of the dynamical behavior of the full model for variation of relevant parameters. We extrapolate the results from the model for actual measures that could be implemented in order to reduce the number of infected individuals.

Cascades of Hopf bifurcations from boundary delay

We consider a 1-dimensional reaction-diffusion equation with nonlinear boundary conditions of logistic type with delay. We deal with non-negative solutions and analyze the stability behavior of its unique positive equilibrium solution, which is given by the constant function u equivalent to 1. We show that if the delay is small, this equilibrium solution is asymptotically stable, similar as in the case without delay. We also show that, as the delay goes to infinity, this equilibrium becomes unstable and undergoes a cascade of Hopf bifurcations. The structure of this cascade will depend on the parameters appearing in the equation. This equation shows some dynamical behavior that differs from the case where the nonlinearity with delay is in the interior of the domain. (C) 2009 Elsevier Inc. All rights reserved.

A full family of multimodal maps on the circle

We exhibit a family of trigonometric polynomials inducing a family of 2m-multimodal maps on the circle which contains all relevant dynamical behavior.

Chaos theory and assessment of forest stakeholder attitudes towards Australian forest policy

The Regional Forest Agreement process has dominated Australian forest policy for the past decade. The RFA process set in place a mechanism by which benchmark conservation values were established for forest  ecosystems, whilst addressing the needs of the timber industry. The outcomes of a number of RFA's have been fraught with controversy. Key stakeholder groups have shown disagreement with processes and  outcomes of methods employed by government both in establishing conservation reserves and areas allocated to timber harvesting. This research uses non-linear techniques to examine the dynamical behavior in stakeholder responses and to identify patterns of behavior that may lead to prediction of stakeholder responses. The method developed in this research provides a bridge between social sciences and Chaos theory.¹

Comportamento dos processos intra-organizacionais de aprendizagem tecnológica frente a uma mudança de estrutura de propriedade: o caso da TermoMacaé - PETROBRÁS

This academic work describes the interfirm technological learning processes behavior at a thermo plant throughout the years 2001 till 2007. Its former ownership structure was composed by two foreigners companies. This structure was changed by the acquisition of the company control by a Brazilian state owned company on April 2006. The company is a Natural Gas Fired Power Plant placed at Macaé City, at Rio de Janeiro State, Brazil generating electric power right to National Integrated System (SIN). The goal of this research is verify how the technological knowledge had been acquired by the firm and how it had been spread out throughout the organization before and after the change of the ownership structure. The taxonomy applied to determining of ownership structure take in account three parameters: type, specific characteristic and the ownership structure itself. Technological Learning Interfirm Processes have been examined from a model of systemic approach that establishes four key characteristics: ¿variety, intensity, functioning and interaction¿. During 2001 until 2006, till the change of owner structure, the firm developed its own learning processes in its own operational routines. The main learning processes have been identified from empirical evidences. It has been adopted the cut line at year of 2006 for the comparison among the technological learning processes behavior, when the change of ownership structure took place. The data capture occurred within April and August 2007 covering since 2001. Verified the behavior of these learning processes before and after the ownership structure changed from private property to state owned property. The conclusion of this case study suggests that interfirm processes of technological learning identified by the research had their dynamical behavior promptly affected by a change from private to ownerstate ownership structure, exposing the company to a poor performance in its industry, due to the lack of 51% of the technological intrafirm learning processes and reduction of the acquisition of new technical knowledge and its conversion throughout the organization.

PERIODIC PERTURBATION of QUADRATIC SYSTEMS WITH TWO INFINITE HETEROCLINIC CYCLES

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Bifurcation Analysis of a Van der Pol-Duffing Circuit with Parallel Resistor

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Periodic perturbations of quadratic planar polynomial vector fields

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Propriedades físicas de bicamadas magnéticas

The magnetic order of bylayers composed by a ferromagnetic film (F) coupled with an antiferromagnetic film (AF) is studied. Piles of coupled monolayers describe the films and the interfilm coupling is described by an exchange interaction between the magnetic moments at the interface. The F has a cubic anisotropy while the AF has a uniaxial anisotropy. We analyze the effects of an external do magnetic field applied parallel to the interface. We consider the intralayer coupling is strong enough to keep parallel all moments of the monolayer an then they are described by one vector proportional to the magnetization of the layer. The interlayer coupling is represented by an exchange interaction between these vectors. The magnetic energy of the system is the sum of the exchange. Anisotropy and Zeeman energies and the equilibrium configuration is one that gives the absolute minimum of the total energy. The magnetization of the system is calculated and the influence of the external do field combined with the interfilm coupling and the unidirectional anisotropy is studied. Special attention is given to the region near of the transition fields. The torque equation is used to study dynamical behavior of these systems. We consider small oscillations around the equilibrium position and we negleet nonlinear terms to obtain the natural frequencies of the system. The dependence of the frequencies with the external do field and their behavior in the phase transition region is analized

Modeling the dielectric response of lanthanum modified lead zirconate titanate ferroelectric ceramics-an approach to the phase transitions in relaxor ferroelectrics

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

The influence of energy changes in breathers

This work studies the dynamical behavior of breathers in a single nonlinear lattice under the influence of energy changes. To create the breather we used the anti-continuous limit and studied its stability through the Floquet theory. Using the information entropy we calculated the effective number of oscillators with significant energy and determined if there is or not the formation of a spatially localized structure.

GLOBAL DYNAMICS IN THE POINCARE BALL of THE CHEN SYSTEM HAVING INVARIANT ALGEBRAIC SURFACES

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)