Periodicity in a delayed version of the kaldor trade cycle model

We are concerned with the Kaldor's trade cycle model under the effect of a delay which represents a gestation lag between a decision of investment and its effect on the capital stock. Taking the adjustment coefficient in the goods market as a bifurcation parameter, we achieve global branches of periodic solutions. In our setting the delay is a constant inherent to the specific economy. Copyright © 2013 Watam Press.

Ciclos limites de sistemas lineares por partes

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Estudo de sistemas lineares por parte com três zonas e aplicação na análise de um circuito elétrico envolvendo um memristor

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A peculiar stable region around Pluto

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

Escape through a time-dependent hole in the doubling map

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Bifurcations Leading to Nonlinear Oscillations in a 3D Piecewise Linear Memristor Oscillator

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

Limit cycles of cubic polynomial differential systems with rational first integrals of degree 2

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Zero, minimum and maximum relative radial acceleration for planar formation flight dynamics near triangular libration points in the Earth-Moon system

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

A dissipative Fermi-Ulam model under two different kinds of dissipation

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

Equações diferenciais implícitas com descontinuidade

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Secondary nontwist phenomena in area-preserving maps

Phenomena as reconnection scenarios, periodic-orbit collisions, and primary shearless tori have been recognized as features of nontwist maps. Recently, these phenomena and secondary shearless tori were analytically predicted for generic maps in the neighborhood of the tripling bifurcation of an elliptic fixed point. In this paper, we apply a numerical procedure to find internal rotation number profiles that highlight the creation of periodic orbits within islands of stability by a saddle-center bifurcation that emerges out a secondary shearless torus. In addition to the analytical predictions, our numerical procedure applied to the twist and nontwist standard maps reveals that the atypical secondary shearless torus occurs not only near a tripling bifurcation of the fixed point but also near a quadrupling bifurcation. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4750040]

Multi-planet extrasolar systems - detection and dynamics

20 years after the discovery of the first planets outside our solar system, the current exoplanetary population includes more than 700 confirmed planets around main sequence stars. Approximately 50% belong to multiple-planet systems in very diverse dynamical configurations, from two-planet hierarchical systems to multiple resonances that could only have been attained as the consequence of a smooth large-scale orbital migration. The first part of this paper reviews the main detection techniques employed for the detection and orbital characterization of multiple-planet systems, from the (now) classical radial velocity (RV) method to the use of transit time variations (TTV) for the identification of additional planetary bodies orbiting the same star. In the second part we discuss the dynamical evolution of multi-planet systems due to their mutual gravitational interactions. We analyze possible modes of motion for hierarchical, secular or resonant configurations, and what stability criteria can be defined in each case. In some cases, the dynamics can be well approximated by simple analytical expressions for the Hamiltonian function, while other configurations can only be studied with semi-analytical or numerical tools. In particular, we show how mean-motion resonances can generate complex structures in the phase space where different libration islands and circulation domains are separated by chaotic layers. In all cases we use real exoplanetary systems as working examples.

Congenital Nystagmus eye movements analysis and oculomotor system models evaluation

The term Congenital Nystagmus (Early Onset Nystagmus or Infantile Nystagmus Syndrome) refers to a pathology characterised by an involuntary movement of the eyes, which often seriously reduces a subject’s vision. Congenital Nystagmus (CN) is a specific kind of nystagmus within the wider classification of infantile nystagmus, which can be best recognized and classified by means of a combination of clinical investigations and motility analysis; in some cases, eye movement recording and analysis are indispensable for diagnosis. However, interpretation of eye movement recordings still lacks of complete reliability; hence new analysis techniques and precise identification of concise parameters directly related to visual acuity are necessary to further support physicians’ decisions. To this aim, an index computed from eye movement recordings and related to the visual acuity of a subject is proposed in this thesis. This estimator is based on two parameters: the time spent by a subject effectively viewing a target (foveation time - Tf) and the standard deviation of eye position (SDp). Moreover, since previous studies have shown that visual acuity largely depends on SDp, a data collection pilot study was also conducted with the purpose of specifically identifying eventual slow rhythmic component in the eye position and to characterise in more detail the SDp. The results are presented in this thesis. In addition, some oculomotor system models are reviewed and a new approach to those models, i.e. the recovery of periodic orbits of the oculomotor system in patients with CN, is tested on real patients data. In conclusion, the results obtained within this research consent to completely and reliably characterise the slow rhythmic component sometimes present in eye position recordings of CN subjects and to better classify the different kinds of CN waveforms. Those findings can successfully support the clinicians in therapy planning and treatment outcome evaluation.

Experimental evidence of a hard transition to chaos

A generic, sudden transition to chaos has been experimentally verified using electronic circuits. The particular system studied involves the near resonance of two coupled oscillators at 2:1 frequency ratio when the damping of the first oscillator becomes negative. We identified in the experiment all types of orbits described by theory. We also found that a theoretical, ID limit map fits closely a map of the experimental attractor which, however, could be strongly disturbed by noise. In particular, we found noisy periodic orbits, in good agreement with noise theory.

Experimental implementation of a biometric laser synaptic sensor

We fabricate a biometric laser fiber synaptic sensor to transmit information from one neuron cell to the other by an optical way. The optical synapse is constructed on the base of an erbium-doped fiber laser, whose pumped diode current is driven by a pre-synaptic FitzHugh–Nagumo electronic neuron, and the laser output controls a post-synaptic FitzHugh–Nagumo electronic neuron. The implemented laser synapse displays very rich dynamics, including fixed points, periodic orbits with different frequency-locking ratios and chaos. These regimes can be beneficial for efficient biorobotics, where behavioral flexibility subserved by synaptic connectivity is a challenge.