Narrow Results

Nonlinear dynamical models are frequently used to approximate and predict observed physical, biological and economic systems. Such models will be subject to errors both in the model dynamics, and the observations of the underlying system. In order to improve models, it is necessary to understand the causes of error growth. A complication with chaotic models is that small errors may be amplified by the model dynamics. This paper proposes a technique for estimating levels of both dynamical and observational noise, based on the model drift. The method is demonstrated for a number of models, for cases with both stochastic and nonstochastic dynamical errors. The effect of smoothing or treating the observations is also considered. It is shown that use of variational smoothing techniques in the presence of dynamical model errors can lead to potentially deceptive patterns of error growth.

The analysis of delay dynamics (DD) is the basic big picture in networked control systems (NCS) research since the knowledge of its behavior may improve the design of more robust controllers, and consequently, the system performance. However, the extreme complexity of modern communications and networks, coupled with their traffic characteristics, makes the characterization of their performance through analytical models a difficult task. Relying on fractional calculus (FC), this paper studies the dynamics of IP delays and attempts to clarify the most important features of network traffic, providing the reader some connections between traffic in communication networks and FC. Likewise, a fractional order model of DD is presented based on a survey of current network traffic models. Some simulations are given to validate the proposed model.

The role of the geometry of prefractal interfaces in Laplacian transport is analyzed through its "harmonic geometrical spectrum." This spectrum summarizes the properties of the Dirichlet-to-Neumann operator associated with these geometries. Numerical analysis shows that very few eigenmodes contribute significantly to the macroscopic response of the system. The hierarchical spatial frequencies of these particular modes correspond to the characteristic length scales of the interface. From this result, a simplified analytical model of the response of self-similar interfaces is developed. This model reproduces the classical low and high frequency asymptotic limits and gives an approximate constant phase angle behavior for the intermediate frequency region. It also provides an analytical description for the crossovers between these regimes and for their dependency on the order of the prefractal interface. In this frame, it is shown that the properties of any generation prefractal can be deduced from the properties of the fractal generator, which are easy to reach numerically.