Controlling hidden dynamics and multi-stability of a class of two-dimensional maps via linear augmentation

Abstract

This paper reports the complex dynamics of a class of two-dimensional maps containing hidden attractors via linear augmentation. Firstly, the method of linear augmentation for continuous dynamical systems is generalised to discrete dynamical systems. Then three cases of a class of two-dimensional maps that exhibit hidden dynamics, the maps with no fixed point and the maps with one stable fixed point, are studied. Our numerical simulations show the effectiveness of the linear augmentation method. As the coupling strength of the controller increases or decreases, hidden attractor can be annihilated or altered to be self-excited, and multi-stability of the map can be controlled to bistable or monostable.