Quasiattractors

A quasiattractor is a concept in the study of nonlinear dynamical systems, particularly in the context of chaos theory. It was introduced by Edward Ott and colleagues in the 1990s as a way to understand and characterize certain types of complex behavior in physical and mathematical systems.

A quasiattractor is a set of states or trajectories that exhibit properties similar to those of traditional attractors, such as being invariant and having a basin of attraction. However, unlike traditional attractors, quasiattractors are not necessarily stable or unique in the long run. In fact, quasiattractors can exhibit a high degree of variability and sensitivity to initial conditions, making them look similar to chaotic or turbulent behavior.

One of the key features of quasiattractors is their coexistence with other types of attractors or invariant sets in the same dynamical system. This can lead to complex and intriguing dynamics, such as the coexistence of multiple quasiattractors or the emergence of strange attractors. Quasiattractors have been observed in a wide range of systems, including fluid dynamics, population growth models, and electronic circuits.

From a mathematical perspective, quasiattractors are often associated with the presence of horseshoes or other types of invariant sets that exhibit saddle-like behavior. The study of quasiattractors has led to new insights into the behavior of complex systems and has sparked a range of new research directions in nonlinear dynamics and chaos theory. Research on quasiattractors continues to be an active area of study, with new results and applications emerging regularly.