No abstract

An in-depth analysis is made of the global 2-parameter bifurcation structures of the double scroll circuit in terms of their homoclinic, heteroclinic, and periodic orbits. Many fine details are uncovered via a 3-dimensional "unfolding" of the 2-parameter bifurcation structures. Major findings are: (i) The parameter sets which give rise to the homoclinic and heteroclinic orbits (homoclinic and heteroclinic bifurcation sets) studied in this paper are found to be all connected to each other via only one family of periodic orbits. (ii) Moreover, the structure of the windows of this family essentially determines the global structure of the periodic windows of the double scroll circuit. These bifurcation analyses are accomplished by deriving first the relevant bifurcation equations in exact analytic form and then solving these nonlinear equations by iterations. No numerical integration formula for differential equations are used.

No abstract

We provide several pieces of evidence for possible chaotic dynamics in the irregular behavior of normal speech signals of the Japanese vowel /a/. First, principal component analysis demonstrates that a simple geometric structure underlying the complex speech signal is well reconstructed in a three-dimensional delay-coordinate space. Observations of the reconstructed speech trajectory at multiple cross sections also display speech dynamics with stretching, folding and compressing. Second, Lyapunov spectrum analysis indicates sensitive dependence on initial conditions with a positive Lyapunov exponent for the speech signals of several different speakers. Third, nonlinear modeling analysis with an artificial neural network shows that the nonlinear dynamics of the vowel sound is well reproduced by a deterministic dynamical model.

SUMMARYWe present a simple piecewise-linear circuit which exhibits a chaotic attractor similar to that observed from the wellknown Lorenz equation. Whereas the non-linearities in the Lorenz equation consists of two product ferms between two state variables, the non-linearities in our circuit consists of two 'uncoupled' 2-terminal continuous non-linear resistors, each characterized by a 2-segment u-i characteristic.Both experiments and computer simulations of this circuit confirm a Lorenz-like strange attractor. The nature of the trajectories associated with this attractor is analysed and explained with the help of the circuit's piecewise-lineargeometry.