We study reversible, SO(2)-invariant vector fields in R depending on a real parameter = which possess for ==0 a primary family of homoclinic orbits T:H0 , : # S. Under a transversality condition with respect to = the existence of homoclinic n-pulse solutions is demonstrated for a sequence of parameter values = (n) k 0 for k . The existence of cascades of 2 3-pulse solutions follows by showing t...

By deriving an N-dimensional Poincare map, we explore the enhanced stability of Josephson series arrays using capacitive junctions. The analytic expression for the critical Floquet multiplier has a direct physical interpretation, affording new insight into the conditions that affect inphase stability. In particular, we generalize the well-known stability principle previously established for arr...

In this paper, we prove that every metric line in the Poincare ball model of hyperbolic geometry is exactly a classical line of itself. We also proved nonexistence of periodic lines in the Poincare ball model of hyperbolic geometry.

Abstrnct -This paper discusses an approach toward higher dimensional autonomous chaotic circuits. We especially consider a particular class of circuits which includes only one nonlinear element, a three segments piecewise-linear resistor, and one small inductor La serially connected with it. The contents are divided into two parts. Part 1 gives a simple fourdimensional example that realizes hyp...

For the representation of eigenstates on a Poincare section at the boundary of a billiard different variants have been proposed. We compare these Poincare Husimi functions, discuss their properties, and based on this select one particularly suited definition. For the mean behavior of these Poincare Husimi functions an asymptotic expression is derived, including a uniform approximation. We estab...

We derive a family of singular iterated maps--closely related to Poincare maps--that describe chaotic interactions between colliding solitary waves. The chaotic behavior of such solitary-wave collisions depends on the transfer of energy to a secondary mode of oscillation, often an internal mode of the pulse. This map allows us to go beyond previous analyses and to understand the interactions in...

This paper investigates two fundamental structures for biped robots and a control strategy to achieve stable biped running. The first biped structure contains straight legs with telescopic springs, and the second one contains knees with compliant elements in parallel with the motors. With both configurations we can use a standard linear discrete-time state-feedback control strategy to achieve a...

Poincare polinomials of hyperbolic Lie algebras, which are given by HA2 and HA3 in the Kac’s notation, are calculated explicitly. The results show that there is a significant form for hyperbolic Poincare polinomials. Their explicit forms tend to be seen as the ratio of a properly chosen finite Poincare polinomial and a polinomial of finite degree. To this end, by choosing the Poincare polinomia...

BACKGROUND Poincare plots are commonly used to study the nonlinear behavior of physiologic signals. The aim of this study is to evaluate the Poincare plot indices of human heart rate signals during meditation. METHODS For this purpose, heart rate time series of eight Chi meditators available in Physionet database were used. Poincare plots with lags of 1 and 6 were constructed, and the ratio o...