In this paper we consider some nonlinear discrete-time dynamic models proposed in the literature to represent marketing competition, and we use these models to critically discuss the statement, often made in economic literature, that identical agents behave identically and quasi-identical ones behave in a similar way. We show, through examples and some general mathematical statements, that the ...

This paper designs four simple adaptive feedback controllers for chaos synchronization with linear– nonlinear decomposition method. Synchronization of two identical chaotic systems is realized by designed controller; Synchronization of two different chaotic systems is also realized, and the proposed method is simple and robust. Numerical simulations are given to show the effectiveness of this m...

It has been recently pointed out than the Kalman filter is a powerful tool for the synchronization of chaos, which remains a major difficulty in the development of efficient chaos based digital communication systems, capable of operating over nonstationnary channels. The input signal power fluctuations, which often causes large errors in synchronizing chaotic waveforms, is discussed in this pap...

Fractal basin boundaries provide an important means of characterizing chaotic systems. We apply these ideas to general relativity, where other properties such as Lyapunov exponents are difficult to define in an observer independent manner. Here we discuss the difficulties in describing chaotic systems in general relativity and investigate the motion of particles in twoand three-black-hole space...

In this paper we show that a generalized form of Parrondo’s paradoxical game can be applied to discrete systems, working out the logistic map as a concrete example, to generate stable orbits. Written in Parrondos’ terms, this reads: chaos1 + chaos2 + ...+ chaosN = order, where chaosi, i = 1, 2, ..., N , are denoted the chaotic behaviors generated by N values of the parameter control, and by ord...

The level statistics of pseudointegrable fractal drums is studied numerically using periodic orbit theory. We find that the spectral rigidity ∆3(L), which is a measure for the correlations between the eigenvalues, decreases to quite small values (as compared to systems with only small boundary roughness), thereby approaching the behavior of chaotic systems. The periodic orbit results are in goo...

One of the most important techniques of feature extraction, i.e., the minor component analysis (MCA), has been widely employed in the field of data analysis. In order to meet the demands of real time computing and curtail the computational complexity, one instrument is often applied, namely, the MCA neural networks, whose learning algorithm, under some conditions, however, can produce complex d...

A biologically plausible, stochastic, neural network model that exhibits spontaneous transitions between a low-activity (normal) state and a high-activity (epileptic) state is studied by computer simulation. Brief excursions of the network to the high-activity state lead to spontaneous population bursting similar to the behavior observed in hippocampal slices bathed in a high-potassium medium. ...

It is one of the most puzzling problems in astrophysics to understand the anomalous resistivity in collisionless magnetic reconnection that is believed extensively to be responsible for the energy release in various eruptive phenomena. The magnetic null point in the reconnect current sheet, acting as a scattering center, can lead to chaotic motions of particles in the current sheet, which is on...

Nonlinear time series analysis has been widely used to search for signatures of low-dimensional chaos in light curves emanating from astrophysical bodies. A particularly popular example is the microquasar GRS 1915+105, whose irregular but systematic X-ray variability has been well studied using data acquired by the Rossi X-ray Timing Explorer (RXTE). With a view to building simpler models of X-...