We define Persistent Mutual Information (PMI) as the Mutual (Shannon) Information between the past history of a system and its evolution significantly later in the future. This quantifies how much past observations enable long-term prediction, which we propose as the primary signature of...

The percentage of organized motion of the chaotic zone (which shall from now on be referred to as percentage of order) for the logistic, the sine-square and the 4-exponent map, is calculated. The calculations are reached via a sampling method that incorporates the Lyapunov exponent. Although...

We propose a novel methodology for forecasting chaotic systems which is based on the nearest-neighbor predictor and improves upon it by incorporating local Lyapunov exponents to correct for its inevitable bias. Using simulated data, we show that gains in prediction accuracy can be substantial....

We highlight the potentiality of a special Information Theory (IT) approach in order to unravel the intricacies of nonlinear dynamics, the methodology being illustrated with reference to the logistic map. A rather surprising dynamic feature→plane-topography map becomes available.

In this Chapter, we provide the definitions, notions and examples relevant for the analysis of the dynamical systems of interest to us in the remainder of this book. We start with with a description of dynamical systems and we provide a taxonomy. Then, we define continuous-time dynamical systems...

In this chapter, the Logistic Map is taken as the example demonstrating the generic stability properties of fixed points and limit cycles, in dependence of the strength of nonlinearity. To identify attracting periodic orbits, we use the Schwarz derivative. The chapter ends with an application of...

This paper deals with a two-dimensional discrete time competition model. The corresponding twodimensional iterative map is represented in terms of its bifurcation diagram in the parameter plane. A number of bifurcation sequences for attractors and their basins are studied.

Population games describe strategic interactions among large numbers of small, anonymous agents. Behavior in these games is typically modeled dynamically, with agents occasionally receiving opportunities to switch strategies, basing their choices on simple myopic rules called revision protocols....

We study the effect of endogenous time preference in a simple neo-classical model of growth. The variation of time preference causes the economy to have multiple steady states, some of which are similar to poverty traps. The stability properties of these steady states are analyzed. The results...