A memristive chaotic map with only one bifurcation parameter

Discrete memristor can be introduced for chaos producing conveniently even combined with easy amplitude control. Such a case is designed in this work, in which all the rest parameters are independent amplitude controllers except the only one for bifurcation. The memristor-related parameters only rescale the sequence partially or totally without revising the Lyapunov exponents. More controllers bring greater convenience for chaos application, meanwhile, less bifurcation parameters pose less risks for chaos-based engineering. The STM32-based circuit is constructed to verify the characteristics of amplitude control. Furthermore, a secure optical communication system is built based on the memristive map showing its high performance in engineering applications.