With the growth in world population, the density of crowds in public places has been increasing steadily, leading to a higher incidence of crowd disasters at high densities. Recent research suggests that emergent chaotic behavior at high densities-known collectively as crowd turbulence-is to blame. Thus, a deeper understanding of crowd turbulence is needed to facilitate efforts to prevent and p...

The problem of modeling chaotic nonlinear dynamical systems using hidden Markov models is considered. A hidden Markov model for a class of chaotic systems is developed from noise-free observations of the output of that system. A combination of vector quantization and the Baum-Welch algorithm is used for training. The importance of this combined iterative approach is demonstrated. The model is t...

in this work, different types of chaotic 1-manifolds which lie on the chaotic spheres or on a torus are introduced. some types of retractions of the chaotic spheres affect on the 1-chaotic systems, and other types of retractions occur to the geometric manifold but make the 1-chaotic manifold invariant. the existed retractions are discussed through new proved theorems. also we construct diffe...

A new methodology to characterize nonlinear systems is described. It is based on the measurement over the time series of two quantities: the "Dynamical order" and the "Self-correlation". The averaged "Scalar" and "Perpendicular" producís are introduced to measure these quantities. While this approach can be applied to general nonlinear systems, the aim of this work is to focus on the characteri...

<sec>In the last two years, discrete memristor has been proposed, and it is in early stages of research. Now, particularly important to use various simulation softwares expand applications model. Based on difference operator, this paper, a model with quadratic nonlinearity constructed. The addition, subtraction, multiplication division mathematical are clarified, charge <i>q</i&g...

In control engineering, it is well known that many physical process exhibit a chaotic component. In point of fact, it is also assumed that conventional modeling procedures disregard it, as stochastic noise, beside nonlinear universal approximators (like neural networks, fuzzy rule-based or genetic programming-based models,) can capture the chaotic nature of the process. In this paper we will sh...

Chaos is a special feature of complex parametric nonlinear dynamical systems. It has the random-like behavior usually seen in stochastic systems although it is associated with deterministic dynamics. Chaos is at the edge of stability and therefore could easily lead systems to an unstable, performance-degraded, or even catastrophic situation. In such cases, chaos is considered as undesired and s...

The ability to detect the chaotic signal from a finite time series observation of hydrologic systems is addressed in this paper. The presence of random and seasonal components in hydrological time series, like rainfall or runoff, makes the detection process challenging. Tests with simulated data demonstrate the presence of thresholds, in terms of noise to chaotic-signal and seasonality to chaot...