Stability analysis of Strange Attractors using Attractor Networks

Anonymous

Keywords: Nonlinear Differential Equations, Strange Attractors, Attractor Network

Abstract: Understanding the behavior of nonlinear differential equations is an extremely difficult problem. This problem is compounded by the frequent chaotic behavior demonstrated by high-dimensional dynamical systems. A subset of these systems, namely strange attractors, are of particular interest due to their sensitive dependence on initial conditions. Analytical reports on the stability of these attractors rely heavily on the ability to solve the underlying equations. In this work, an attractor network is used for the identification of different regions and the parameters resulting in that particular region, in well-defined strange attractors. The network takes in the initial configuration of the system, stores the pattern of neuronal firing as a state vector, and predicts the behavior of the attractor.

Publication Status: This work is unpublished.