The work is devoted to the analysis of dynamics of traveling waves in a chain of self-oscillators with period-doubling route to chaos. As a model we use a ring of Chua’s circuits symmetrically coupled via a resistor. We consider how complicated are temporal regimes with parameters changing influences on spatial structures in the chain. We demonstrate that spatial periodicity exists until transi...

A number of schemes have been proposed for communication using chaos over the past years. Regardless of the exact modulation method used, the transmitted signal must go through a physical channel which undesirably introduces distortion to the signal and adds noise to it. The problem is particularly serious when coherent-based demodulation is used because the necessary process of chaos synchroni...

In previous works, the theoretical and experimental deterministic scalar kinematic structures, vector dynamic structures have been developed to compute exact solution for chaos of exponential pulsons oscillons that is governed by nonstationary three-dimensional Navier-Stokes equations. To explore properties kinetic energy, rectangular, diagonal, triangular summations a matrix energy general ter...

Chaotic neural networks have received a great deal of attention these last years. In this paper we establish a precise correspondence between the so-called chaotic iterations and a particular class of artificial neural networks: global recurrent multi-layer perceptrons. We show formally that it is possible to make these iterations behave chaotically, as defined by Devaney, and thus we obtain th...

We use a combinatorial idea of Peter Lax to construct, on any compact manifold, a self homeomorphism which is chaotic in the sense of Devaney. Moreover we show that such transformations are dense, with respect to the uniform topology, in the space of volume preserving homeomorphisms of the closed unit cube I n ; n 2: This work extends that of John Oxtoby, who in 1937 proved similar results for ...

In this chapter, we consider a class of discrete dynamical systems defined on the homogeneous space associated with a regular tiling of R , whose most familiar example is provided by the N−dimensional torus T . It is proved that any dynamical system in this class is chaotic in the sense of Devaney, and that it admits at least one positive Lyapunov exponent. Next, a chaossynchronization mechanis...

For 0 < λ < 1/e the Julia set of λez is an uncountable union of pairwise disjoint simple curves tending to infinity [Devaney and Krych 1984], the Hausdorff dimension of this set is two [McMullen 1987], but the set of curves without endpoints has Hausdorff dimension one [Karpińska 1999]. We show that these results have three-dimensional analogues when the exponential function is replaced by a qu...

Analyses and investigations on river flow behavior are major issues in design, operation and studies related to water engineering. Thus, recently the application of chaos theory and new techniques, such as chaos theory, has been considered in hydrology and water resources due to relevant innovations and ability. This paper compares the performance of chaos theory with Anfis model and discusses ...

– We report a novel mechanism for the occurrence of chaos at the macroscopic level induced by the frustration of interaction, namely frustration-induced chaos, in a nonmonotonic sequential associative memory model. We succeed in deriving exact macroscopic dynamical equations from the microscopic dynamics in the case of the thermodynamic limit and prove that two order parameters dominate this la...

We investigate geodesics in non-homogeneous vacuum pp-wave solutions and demonstrate their chaotic behavior by rigorous analytic and numerical methods. For the particular class of solutions considered, distinct “outcomes” (channels to infinity) are identified, and it is shown that the boundary between different outcomes has a fractal structure. This seems to be the first example of chaos in exa...