Dynamics of a Modified Sprott A System
Muhammad Nuur Rohman, Johan Matheus Tuwankotta, Eric Harjanto

Institut Teknologi Bandung

Abstract

We consider a modified Sprott A system, which is one of the 17 systems that exhibit chaotic behavior with no equilibrium, introduced by Jafari, Sprott, and Golpayegani (2013). For some parameter values, the modified system still preserves the original invariant sphere. We investigate the stability of the equilibria occured in the system using the stereographic map and
prove that all orbits except the unstable equilibrium point converge to the
stable equilibrium point. For some other parameter values, we found no
invariant spheres and equilibrium points. Here the state space is foliated by tori, unlike the original one.

Keywords: Sprott A system, invariant sphere, stereographic map, tori

Topic: Minisymposia Dynamical Systems