TABLE OF CONTENTS Nonlinear dynamics makes use of a number of archetype models. Within the area of dissipative nonlinear systems the logistic map, the sine-circle map, the tent map, Duffing s equation, and the R ssler system discussed in Chapter 1 are among the most well-known models. Other important models are the H non map, that we shall consider in the present chapter, the Lorenz system, the impact oscillator, the Chua circuit and, particularly in the Russian literature, various models of autonomous and non-autonomous generators with inertial nonlinearity [1]. For Hamiltonian systems and in the area of quantum chaos, other models, such as the twist map and the stadium model, play the role of archetypes. Some of these models derive directly from practical problems in science and technology, while other models have been constructed as the simplest possible set of equations required to demonstrate a particular dynamic phenomenon and isolate it from the parasitic influence of a more complicated structure. The logistic model, for instance, is the basic model for the description of the classic period-doubling route to chaos, and the sine-circle map is a starting point for discussions of phase locking (or synchronization) of interacting oscillators.
In recent years, coupled logistic maps and coupled R ssler systems have been used to study riddled basins of attraction, on-off intermittency, and different forms of chaotic synchronization [2]. Significant advances have also been made in the study of wave propagation and spatio-temporal chaos in lattices of chaotic oscillators and of...
