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.
Highlights
Finding chaotic systems with novel dynamics is still exciting [1,2]
They added a constant control parameter to the Sprott E chaotic system [4] so that the stability of its equilibrium changed while its chaotic dynamics were preserved
This study reported a new 3-D chaotic system with only one stable equilibrium
Summary
A chaotic system with only one stable equilibrium was presented by Wang and Chen [3] They added a constant control parameter to the Sprott E chaotic system [4] so that the stability of its equilibrium changed while its chaotic dynamics were preserved. This discovery opened up a new direction in the field of chaos. The system dynamics and the effect of changing the control parameter are studied by bifurcation analysis, Lyapunov exponent analysis, representing the different basins of attraction, and the calculating connecting curves of the system
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
