Hidden Attractors in Discrete Dynamical Systems

Abstract

Research using chaos theory allows for a better understanding of many phenomena modeled by means of dynamical systems. The appearance of chaos in a given process can lead to very negative effects, e.g., in the construction of bridges or in systems based on chemical reactors. This problem is important, especially when in a given dynamic process there are so-called hidden attractors. In the scientific literature, we can find many works that deal with this issue from both the theoretical and practical points of view. The vast majority of these works concern multidimensional continuous systems. Our work shows these attractors in discrete systems. They can occur in Newton’s recursion and in numerical integration.

Quality Evaluation for Reconstructing Chaotic Attractors

“…Chaotic systems are special cases of dynamical systems characterized by the existence of strange attractor-type trajectories [21]. This path is not the only defining feature of the system, but it is chaotic.…”