Generating chaotic attractors with multiple merged basins of attraction: a switching piecewise-linear control approach

This paper presents several new chaos generators, switching piecewise-linear controllers, which can generate some new chaotic attractors with two or three merged basins of attraction from a given three-dimensional linear autonomous system within a wide range of parameter values. Based on this success, chaotic attractors with n merged basins of attraction are further generated using a formalized controller design methodology. Basic dynamical behaviors of the controlled chaotic system are then investigated via both theoretical analysis and numerical simulation. To that end, the underlying chaos-generation mechanism is further explored by analyzing the parameterization of the controlled system and the dynamics of the system orbits.