Modified function projective synchronization of hyperchaotic systems through Open-Plus-Closed-Loop coupling

Recently introduced modified function projective synchronization (MFPS) in which chaotic systems synchronize up to a scaling function matrix has important applications in secure communications. We design coupling function for unidirectional coupling in identical and mismatched hyperchaotic oscillators to realize MFPS through Open-Plus-Closed-Loop (OPCL) coupling method. The arbitrary scaling function matrix elements are properly chosen such that we can produce function projective synchronization, synchronization, anti-synchronization and amplitude death on desired states of the response system simultaneously. Numerical simulations on identical hyperchaotic Rossler and mismatched hyperchaotic Lu system are presented to verify the effectiveness of the proposed scheme. A secure communication scheme based on MFPS is also presented.