The average lifetime of a chaotic transient versus a system parameter is studied for the case wherein a chaotic attractor is converted into a chaotic transient upon collision with its basin boundary (a crisis). Typically the a~erage lifetime T depends upon the system parameter p via T —~p —p, ~ &, where p, denotes the value of p at the crisis and we caII y the critical exponent of the chaotic t...

This paper presents a true random-bit generation through a continuous-time chaotic oscillator, which provides automatically chaotic signals and is fully implemented on 0.18 CMOS standard technology. Chaotic dynamics of the oscillator are exhibited in terms of chaotic strange attractor in phase-space domain. In order to achieve true-random property, a simple designed of post-processing method is...

The complex valued neural networks are the extended version of conventional real valued neural networks Input and output signals weighting factors and neuron nonlinear functions are determined using complex number so that the information geometry of the network is constructed in complex space This feature is advantageously used especially for learning and expressing smooth dynamical attractors ...

Applying attractor reconstruction techniques and other chaotic measurements, it is shown that the long-term dynamics of a vertical, underactuated, two-degrees-of-freedom robot called Pendubot may exhibit complex dynamics including chaotic behavior. These techniques use only the measurement of some available variable of the system, and the resulting reconstruction allows us to identify unstable ...

Robust chaos occurs when a dynamical system has a neighborhood in parameter space such that there is one unique chaotic attractor, and no periodic attractors are present [Barreto et al., 1997; Banerjee et al., 19981. This behavior, expected to be relevant for any practical applications of chaos, was shown to exist in a general family of piecewise-smooth twodimensional maps, but conjectured to b...

Riddled basins denote a characteristic type of fractal domain of attraction that can arise when a chaotic motion is restricted to an invariant subspace of total phase space. An example is the synchronized motion of two identical chaotic oscillators. The paper examines the conditions for the appearance of such basins for a system of two symmetrically coupled logistic maps. We determine the regio...

Approximation of a continuous dynamics by discrete dynamics in the form of Poincare map is one of the fascinating mathematical tool which can describe the approximate behaviour of the dynamics of the dynamical system in lesser dimension than the embedding diemnsion. The present article considers a very rare biomedical signal like Electromyography (EMG) signal. It determines suitable time delay ...

Chaotic attractors are known to often exhibit not only complex dynamics but also a complex geometry in phase space. In this work, we provide a detailed characterization of chaotic electrochemical oscillations obtained experimentally as well as numerically from a corresponding mathematical model. Power spectral density and recurrence time distributions reveal a considerable increase of dynamic c...

In this paper we study the dynamics of a Burgers’ type equation (1.1). First, we use a new method called attractor bifurcation introduced by Ma and Wang in [4, 6] to study the bifurcation of Burgers’ type equation out of the trivial solution. For Dirichlet boundary condition, we get pitchfork attractor bifurcation as the parameter λ crosses the first eigenvalue. For periodic boundary condition,...

Applying attractor reconstruction techniques and other chaotic measurements, it is shown that the long-term dynamics of a vertical, underactuated, two-degrees-of-freedom robot called Pendubot may exhibit complex dynamics including chaotic behavior. These techniques use only the measurement of some available variable of the system, and the resulting reconstruction allows us to identify unstable ...