Luis Fernando Mello

Bifurcation analysis of the Watt governor system

This paper pursues the study carried out by the authors in Stability and Hopf bifurcation in the Watt governor system [14], focusing on the codimension one Hopf bifurcations in the centrifugal Watt governor differential system, as presented in Pontryagins book Ordinary Differential Equations, [13]. Here are studied the codimension two and three Hopf bifurcations and the pertinent Lyapunov stability coefficients and bifurcation diagrams, illustrating the number, types and positions of bifurcating small amplitude periodic orbits, are determined. As a consequence it is found a region in the space of parameters where an attracting periodic orbit coexists with an attracting equilibrium.

DEGENERATE HOPF BIFURCATIONS IN CHUA'S SYSTEM

In this paper we study the local codimension one, two and three Hopf bifurcations which occur in the classical Chuas differential equations with cubic nonlinearity. A detailed analytical description of the regions in the parameter space for which multiple small periodic solutions bifurcate from the equilibria of the system is obtained. As a consequence, a complete answer for the challenge proposed in [Moiola & Chua, 1999] is provided.

More Than Three Limit Cycles in Discontinuous Piecewise Linear Differential Systems with Two Zones in the Plane

In this paper, we study the existence of limit cycles for piecewise linear differential systems with two zones in the plane. More precisely, we prove the existence of piecewise linear differential systems with two zones in the plane with four, five, six and seven limit cycles. From our results we conjecture the existence of piecewise linear differential systems with two zones in the plane having exactly n limit cycles for all n ∈ ℕ.

Inductorless Chua's Circuit: Experimental Time Series Analysis

We have implemented an operational amplifier inductorless realization of the Chuas circuit. We have registered time series from its dynamical variables with the resistor R as the control parameter and varying from 1300 Ω to 2000 Ω. Experimental time series at fixed R were used to reconstruct attractors by the delay vector technique. The flow attractors and their Poincare maps considering parameters such as the Lyapunov spectrum, its subproduct the Kaplan-Yorke dimension, and the information dimension are also analyzed here. The results for a typical double scroll attractor indicate a chaotic behavior characterized by a positive Lyapunov exponent and with a Kaplan-Yorke dimension of 2.14. The occurrence of chaos was also investigated through numerical simulations of the Chuas circuit set of differential equations.

Hopf Bifurcations in a Watt Governor with a Spring

Abstract This paper pursues the study carried out in [10], focusing on the codimension one Hopf bifurcations in the hexagonal Watt governor system. Here are studied Hopf bifurcations of codimensions two, three and four and the pertinent Lyapunov stability coefficients and bifurcation diagrams. This allows to determine the number, types and positions of bifurcating small amplitude periodic orbits. As a consequence it is found an open region in the parameter space where two attracting periodic orbits coexist with an attracting equilibrium point.

New spatial central configurations in the 5-body problem

In this paper we show the existence of new families of convex and concave spatial central configurations for the 5-body problem. The bodies studied here are arranged as follows: three bodies are at the vertices of an equilateral triangle T , and the other two bodies are on the line passing through the barycenter of T that is perpendicular to the plane that contains T .

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

We study the local codimension one, two, and three bifurcations which occur in a recently proposed Van der Pol-Duffing circuit (ADVP) with parallel resistor, which is an extension of the classical Chuas circuit with cubic nonlinearity. The ADVP system presents a very rich dynamical behavior, ranging from stable equilibrium points to periodic and even chaotic oscillations. Aiming to contribute to the understand of the complex dynamics of this new system we present an analytical study of its local bifurcations and give the corresponding bifurcation diagrams. A complete description of the regions in the parameter space for which multiple small periodic solutions arise through the Hopf bifurcations at the equilibria is given. Then, by studying the continuation of such periodic orbits, we numerically find a sequence of period doubling and symmetric homoclinic bifurcations which leads to the creation of strange attractors, for a given set of the parameter values.

Orthogonal Asymptotic Lines on Surfaces Immersed in R 4

In this paper we study some properties of surfaces immersed in R 4 whose asymptotic lines are orthogonal. We also analyze necessary and sufficient conditions for the hypersphericity of surfaces in R 4 .

Configurações centrais planares do tipo pipa

In this paper we study the kite planar central configurations for the 4-body problem. We show the existence of such configurations for the 4-body problem in two cases: kite concave and kite convex.

Configurações centrais planares encaixantes

In this paper we show the existence of a family of planar central configurations for the 6-body problem with the following properties: the six bodies are on the vertices of two equilateral triangles with common barycenters and the smaller triangle is rotated of p/3 with respect to the larger one.