Parameter adaptive global synchronization of Lorenz chaotic systems

Abstract

A parameter adaptive rule that globally synchronizes oscillatory Lorenz chaotic systems with initially different parameter values is reported. The response system is defined according to a master-slave type of coupling that guarantees synchronization when parameters are identical. The parameters of the response system are then adapted to reach convergence to the drive parameters. The rule is very robust and works efficiently with different coupling schemes. Although, in general, it needs to have access to the three state variables of the drive system, if some information about the parameters is available it can be readapted to work less demandingly. For instance, we report here global synchronization that requires access to variable x only, when one parameter from the drive system is known.