Complex dynamics of knowledgeable monopoly models with gradient mechanisms

Simulation of Pedestrian Dynamics with Macroscopic and Microscopic Mathematical Models

Here, we collect two parts of a research project on the pedestrian flow modeling. Rapid growth in the volume of public transport and the need for its reasonable, efficient planning have made the description and modeling of transport and pedestrian behaviors as important research topics in the past twenty years. First, we present a macroscopic model for the pedestrian flow based on continuum mec...

Complex dynamics on a Monopoly Market with Discrete Choices and Network Externality

In this paper, we explore the effects of the introduction of localised externalities through interaction structures upon local and global properties of the simplest market model: the discrete choice model with a single homogeneous product and a single seller (monopoly). Following Kirman, the resulting market is viewed as a complex interactive system. We use an ACE (Agent based Computational Eco...

Learning In Neural Models With Complex Dynamics

Interest in the ANN field has recently focused on dynamical neural networks for performing temporal operations, as more realistic models of biological information processing, and to extend ANN learning techniques. While this represents a step towards realism, it is important to note that individual neurons are complex dynamical systems, interacting through nonlinear, nonmonotonic connections. T...

Parameter Estimation in Models with Complex Dynamics

Mathematical models of real life phenomena are highly nonlinear involving multiple parameters and often exhibiting complex dynamics. Experimental data sets are typically small and noisy, rendering estimation of parameters from such data unreliable and difficult. This paper presents a study of the Bayesian posterior distribution for unknown parameters of two chaotic discrete dynamical systems co...

Gradient dynamics models for liquid films with soluble surfactant