Abstract
This paper reports a simple three-dimensional autonomous system with a single stable node equilibrium. The system has a constant controller which adjusts the dynamic of the system. It is revealed that the system exhibits both chaotic and non-chaotic dynamics. Moreover, chaotic or periodic attractors coexist with a single stable equilibrium for some control parameter based on initial conditions. The system dynamics are studied by analyzing bifurcation diagrams, Lyapunov exponents, and basins of attractions. Beyond a fixed-point analysis, a new analysis known as connecting curves is provided. These curves are one-dimensional sets of the points that are more informative than fixed points. These curves are the skeleton of the system, which shows the direction of flow evolution.
Funder
Chennai Institute of Technology
Slovak Research and Development Agency
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Cited by
6 articles.
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