Coexistence of attractors in a quasiperiodically forced Lozi map

We study the quasiperiodically forced Lozi system in the weak dissipative limit. Different types of coexisting attractors and their basins of attraction are investigated. For different parameters, different types of coexistence are analyzed from the perspective of basin of attraction. Multiple coexisting quasiperiodic attractors and strange nonchaotic attractors (SNAs) have been vividly illustrated by phase diagrams, the largest Lyapunov exponent and phase sensitivity exponents. SNAs are also identified by recursive diagram and distribution of finite-time Lyapunov exponent. We show that the basin of SNAs may not necessarily be the largest among those of all coexisting attractors. Coexisting SNAs are also easier to be created as the conservative limit is approached.