Phase Bifurcation Analysis of Nonlinear Dynamical Systems

Abstract

In this paper, we introduce a tool for analysis of nonlinear dynamical systems, which we call as phase bifurcation diagrams. This type of diagrams is based on information about the intervals between the peak values of a system state variables, while conventional bifurcation diagrams utilize amplitude values. On the example of the RCL-shunted Josephson junction circuit, we demonstrate the distinctive features, which can only be seen in phase diagrams. The combined application of classical and phase bifurcation diagrams allows us to proceed to the adequate construction of multi-parametric dynamical maps by solving the clustering problem. The optimal clustering was obtained with the density-based machine learning method-DBSCAN. The results of the work are algorithms and software in the LabVIEW environment for the construction of one- and two-dimensional bifurcation diagrams, which can be also applied in the design of neuromorphic systems based on emerging nonlinear devices.