Synchronization and asynchronization in a lattice of Coupled Lorenz-type Maps

In this paper, we study synchronization and asynchronization in a Coupled Lorenz-type Map Lattice (CLML). Lorenz-type map forms a chaotic system with an appropriate discontinuous function. We prove that in a CLML with suitable coupling strength, there is a subset of full measure in the phase space such that chaotic synchronization occurs for any orbit starting from this subset and there is a dense subset of measure zero in the phase space such that synchronization will never occur. We also provide numerical observations to explain our results.